section 1.4 problem solving in chemistry

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1.1 Problems and Problem Solving

1.2 types and kinds of problems, 1.3 novice versus expert problem solvers/problem solving heuristics, 1.4 chemistry problems, 1.4.1 problems in stoichiometry, 1.4.2 problems in organic chemistry, 1.5 the present volume, 1.5.1 general issues in problem solving in chemistry education, 1.5.2 problem solving in organic chemistry and biochemistry, 1.5.3 chemistry problem solving under specific contexts, 1.5.4 new technologies in problem solving in chemistry, 1.5.5 new perspectives for problem solving in chemistry education, chapter 1: introduction − the many types and kinds of chemistry problems.

• Published: 17 May 2021
• Special Collection: 2021 ebook collection Series: Advances in Chemistry Education Research
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G. Tsaparlis, in Problems and Problem Solving in Chemistry Education: Analysing Data, Looking for Patterns and Making Deductions, ed. G. Tsaparlis, The Royal Society of Chemistry, 2021, ch. 1, pp. 1-14.

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Problem solving is a ubiquitous skill in the practice of chemistry, contributing to synthesis, spectroscopy, theory, analysis, and the characterization of compounds, and remains a major goal in chemistry education. A fundamental distinction should be drawn, on the one hand, between real problems and algorithmic exercises, and the differences in approach to problem solving exhibited between experts and novices on the other. This chapter outlines the many types and kinds of chemistry problems, placing particular emphasis on studies in quantitative stoichiometry problems and on qualitative organic chemistry problems (reaction mechanisms, synthesis, and spectroscopic identification of structure). The chapter concludes with a brief look at the contents of this book, which we hope will act as an appetizer for more systematic study.

According to the ancient Greeks, “The beginning of education is the study of names”, meaning the “examination of terminology”. 1 The word “problem” (in Greek: «πρόβλημα » /“ problēma” ) derives from the Greek verb “ proballein ” (“pro + ballein”), meaning “to throw forward” ( cf. ballistic and ballistics ), and also “to suggest”, “to argue” etc. Hence, the initial meaning of a “ problēma ” was “something that stands out”, from which various other meanings followed, for instance that of “a question” or of “a state of embarrassment”, which are very close to the current meaning of a problem . Among the works of Aristotle is that of “ Problēmata ”, which is a collection of “why” questions/problems and answers on “medical”, “mathematical”, “astronomical”, and other issues, e.g. , “Why do the changes of seasons and the winds intensify or pause and decide and cause the diseases?” 1  

Problem solving is a complex set of activities, processes, and behaviors for which various models have been used at various times. Specifically, “problem solving is a process by which the learner discovers a combination of previously learned rules that they can apply to achieve a solution to a new situation (that is, the problem)”. 2   Zoller identifies problem solving, along with critical thinking and decision making, as high-order cognitive skills, assuming these capabilities to be the most important learning outcomes of good teaching. 3   Accordingly, problem solving is an integral component in students’ education in science and Eylon and Linn have considered problem solving as one of the major research perspectives in science education. 4  

Bodner made a fundamental distinction between problems and exercises, which should be emphasized from the outset (see also the Foreword to this book). 5–7   For example, many problems in science can be simply solved by the application of well-defined procedures ( algorithms ), thus turning the problems into routine/algorithmic exercises. On the other hand, a real/novel/authentic problem is likely to require, for its solution, the contribution of a number of mental resources. 8  

According to Sternberg, intelligence can best be understood through the study of nonentrenched ( i.e. , novel) tasks that require students to use concepts or form strategies that differ from those they are accustomed to. 9   Further, it was suggested that the limited success of the cognitive-correlates and cognitive-components approaches to measuring intelligence are due in part to the use of tasks that are more entrenched (familiar) than would be optimal for the study of intelligence.

The division of cognitive or thinking skills into Higher-Order (HOCS/HOTS) and Lower-Order (LOCS/LOTS) 3,10   is very relevant. Students are found to perform considerably better on questions requiring LOTS than on those requiring HOTS. Interestingly, performance on questions requiring HOTS often does not correlate with that on questions requiring LOTS. 10   In a school context, a task can be an exercise or a real problem depending on the subject's expertise and on what had been taught. A task may then be an exercise for one student, but a problem for another student. 11   I return to the issue of HOT/LOTS in Chapters 17 and 18.

Johnstone has provided a systematic classification of problem types, which is reproduced in Table 1.1 . 8   Types 1 and 2 are the “normal” problems usually encountered in academic situations. Type 1 is of the algorithmic exercise nature. Type 2 can become algorithmic with experience or teaching. Types 3 and 4 are more complex, with type 4 requiring very different reasoning from that used in types 1 and 2. Types 5–8 have open outcomes and/or goals, and can be very demanding. Type 8 is the nearest to real-life, everyday problems.

Classification of problems. Reproduced from ref. 8 with permission from the Royal Society of Chemistry.

Problem solving in chemistry, as in any other domain, is a huge field, so one cannot really be an expert in all aspects of it. Complementary to Johnstone's classification scheme, one can also identify the following forms: quantitative problems that involve mathematical formulas and computations, and qualitative ones; problems with missing or extraordinary data, with a unique solution/answer, or open problems with more than one solution; problems that cannot be solved exactly but need mathematical approximations; problems that need a laboratory experiment or a computer or a data bank; theoretical/thought problems or real-life ones; problems that can be answered through a literature search, or need the collaboration of specific experts, etc.

According to Bodner and Herron, “Problem solving is what chemists do, regardless of whether they work in the area of synthesis, spectroscopy, theory, analysis, or the characterization of compounds”. 12   Hancock et al. comment that: “The objective of much of chemistry teaching is to equip learners with knowledge they then apply to solve problems”, 13   and Cooper and Stowe ascertain that “historically, problem solving has been a major goal of chemistry education”. 14   The latter authors argue further that problem solving is not a monolithic activity, so the following activities “could all be (and have been) described as problem solving:

solving numerical problems using a provided equation

proposing organic syntheses of target compounds

constructing mechanisms of reactions

identifying patterns in data and making deductions from them

modeling chemical phenomena by computation

identifying an unknown compound from its spectroscopic properties

However, these activities require different patterns of thought, background knowledge, skills, and different types of evidence of student mastery” 14   (p. 6063).

Central among problem solving models have been those dealing with the differences in problem solving between experts and novices. Experts ( e.g., school and university teachers) are as a rule fluent in solving problems in their own field, but often fail to communicate to their students the required principles, strategies, and techniques for problem solving. It is then no surprise that the differences between experts and novices have been a central theme in problem solving education research. Mathematics came first, in 1945, with the publication of George Polya's classic book “ How to solve it: A new aspect of mathematical method ”: 15  

“The teacher should put himself in the student's place, he should see the student's case, he should try to understand what is going on in the student's mind, and ask a question or indicate a step that could have occurred to the student himself ”.

Polya provided advice on teaching problem solving and proposed a four-stage model that included a detailed list of problem solving heuristics. The four stages are: understand the problem, devise a plan, carry out the plan, and look back . In 1979, Bourne, Dominowski, and Loftus modeled a three-stage process, consisting of preparation, production , and evaluation . 16   Then came the physicists. According to Larkin and Reif, novices look for an algorithm, while experts tend to think conceptually and use general strategies . Other basic differences are: (a) the comprehensive and more complete scheme employed by experts, in contrast to the sketchy one used by novices; and (b) the extra qualitative analysis step usually applied by experts, before embarking on detailed and quantitative means of solution. 17,18   Reif (1981, 1983) suggested further that in order for one to be able to solve problems one must have available: (a) a strategy for problem solving; (b) the right knowledge base, and (c) a good organization of the knowledge base. 18,19  

Chemistry problem solving followed suit providing its own heuristics. Pilot and co-workers proposed useful procedures that include the steps that characterize expert solvers. 20–22   They developed an ordered system of heuristics, which is applicable to quantitative problem solving in many fields of science and technology. In particular, they devised a “ Program of Actions and Methods ”, which consists of four phases, as follows: Phase 1, analysis of the problem; Phase 2, transformation of the problem; Phase 3, execution of routine operations; Phase 4, checking the answer and interpretation of the results. Genya proposed the use of “sequences” of problems of gradually increasing complexity , with qualitative problems being used at the beginning. 23  

Randles and Overton compared novice students with expert chemists in the approaches they used when solving open-ended problems. 24     Open-ended problems are defined as problems where not all the required data are given, where there is no one single possible strategy and where there is no single correct answer to the problem. It was found that: undergraduates adopted a greater number of novice-like approaches and produced poorer quality solutions; academics exhibited expert-like approaches and produced higher quality solutions; the approaches taken by industrial chemists were described as transitional.

Finally, one can justify the differences between novices and experts by employing the concept of working memory (see Chapter 5). Experienced learners can group ideas together to see much information as one ‘ chunk ’, while novice learners see all the separate pieces of information, causing an overload of working memory, which then cannot handle all the separate pieces at once. 25,26  

Chemistry is unique in the diversity of its problems, some of which, such as problems in physical and analytical chemistry, are similar to problems in physics, while others, such problems in stoichiometry, in organic chemistry (especially in reaction mechanisms and synthesis), and in the spectroscopic identification of compounds and of molecular structure, are idiosyncratic to chemistry. We will have more to say about stoichiometry and organic chemistry below, but before that there is a need to refer to three figures whom we consider the originators of the field of chemistry education research: the Americans J. Dudley Herron and Dorothy L. Gabel and the Scot Alex H. Johnstone, for it is not a coincidence that all three dealt with chemistry problem solving.

For Herron, successful problem solvers have a good command of basic facts and principles; construct appropriate representations; have general reasoning strategies that permit logical connections among elements of the problem; and apply a number of verification strategies to ensure that the representation of the problem is consistent with the facts given, the solution is logically sound, the computations are error-free, and the problem solved is the problem presented. 27–29   Gabel has also carried out fundamental work on problem solving in chemistry. 30   For instance, she determined students’ skills and concepts that are prerequisites for solving problems on moles, through the use of analog tasks, and identified specific conceptual and mathematical difficulties. 31   She also studied how problem categorization enhances problem solving achievement. 32   Finally, Johnstone studied the connection of problem solving ability in chemistry (but also in physics and biology) with working memory and information processing. We will deal extensively with his relevant work in this book (see Chapter 5). In the rest of this section, reference will be made to some further foundational research work on problem solving in chemistry.

Working with German 16-year-old students in 1988, Sumfleth found that the knowledge of chemical terms is a necessary but not sufficient prerequisite for successful problem solving in structure-properties relationships and in stoichiometry. 33   In the U.S. it was realized quite early (in 1984) that students often use algorithmic methods without understanding the relevant underlying concepts. 32   Indeed, Nakhleh and Mitchell confirmed later (1993) that little connection existed between algorithmic problem solving skills and conceptual understanding. 34   These authors provided ways to evaluate students along a continuum of low-high algorithmic and conceptual problem solving skills, and admitted that the lecture method teaches students to solve algorithms rather than teaching chemistry concepts. Gabel and Bunce also emphasized that students who have not sufficiently grasped the chemistry behind a problem tend to use a memorized formula, manipulate the formula and plug in numbers until they fit. 30   Niaz compared student performance on conceptual and computational problems of chemical equilibrium and reported that students who perform better on problems requiring conceptual understanding also perform significantly better on problems requiring manipulation of data, that is, computational problems; he further suggested that solving computational problems before conceptual problems would be more conducive to learning, so it is plausible to suggest that students’ ability to solve computational/algorithmic problems is an essential prerequisite for a “progressive transition” leading to a resolution of novel problems that require conceptual understanding. 35–37  

Stoichiometry problems are unique to chemistry and at the same time constitute a stumbling block for many students in introductory chemistry courses, with students often relying on algorithms. A review of some fundamental studies follows.

Hans-Jürgen Schmid carried out large scale studies in 1994 and 1997 in Germany and found that when working on easy-to-calculate problems students tended to invent/create a “non-mathematical” strategy of their own, but changed their strategy when moving from an easy-to-calculate problem to a more difficult one. 38,39   Swedish students were also found to behave in a similar manner. 40   A recent (2016) study with junior pre-service chemistry teachers in the Philippines reported that the most prominent strategy was the (algorithmic) mole method, while very few used the proportionality method and none the logical method. 41  

Lorenzo developed, implemented, and evaluated a useful problem solving heuristic in the case of quantitative problems on stoichiometry and solutions. 42   The heuristic works as a metacognitive tool by helping students to understand the steps involved in problem solving, and further to tackle problems in a systematic way. The approach guides students by means of logical reasoning to make a qualitative representation of the solution to a problem before undertaking calculations, thus using a ‘backwards strategy’.

The problem format can serve to make a problem easier or more difficult. A large scale study with 16-year-old students in the UK examined three stoichiometry problems in a number of ways. 43   In Test A the questions were presented as they had previously appeared on National School Examinations, while in Test B each of the questions on Test A was presented in a structured sequence of four parts. An example of one of the questions from both Test A and Test B is given below.

• Test A. Silver chloride (AgCl) is formed in the following reaction: AgNO 3 + HCl → AgCl + HNO 3 Calculate the maximum yield of solid silver chloride that can be obtained from reacting 25 cm 3 of 2.0 M hydrochloric acid with excess silver nitrate. (AgCl = 143.5)

Test B. Silver chloride (AgCl) is formed in the following reaction:

(a) How many moles of silver chloride can be made from 1 mole of hydrochloric acid?

(b) How many moles are there in 25 cm 3 of 2.0 M hydrochloric acid?

(c) How many moles of silver chloride can be made from the number of moles of acid in (b)?

(d) What is the mass of the number of moles of silver chloride in (c)? (AgCl = 143.5)

Student scores on Test B were significantly higher than those on Test A, both overall and on each of the individual questions, showing that structuring serves to make the questions easier.

Drummond and Selvaratnam examined students’ competence in intellectual strategies needed for solving chemistry problems. 44   They gave students problems in two forms, the ‘standard’ one and one with ‘hint’ questions that suggested the strategies which should be used to solve the problems. Although performance in all test items was poor, it improved for the ‘hint’ questions.

Finally, Gulacar and colleagues studied the differences in general cognitive abilities and domain specific skills of higher- and lower-achieving students in stoichiometry problems and in addition they proposed a novel code system for revealing sources of students’ difficulties with stoichiometry. 45,46   The latter topic is tackled in Chapter 4 by Gulacar, Cox, and Fynewever.

Stoichiometry problems have also a place in organic chemistry, but non-mathematical problem solving in organic chemistry is quite a different story. 47   Studying the mechanisms of organic reactions is a challenging activity. The spectroscopic identification of the structure of organic molecules also requires high expertise and a lot of experience. On the other hand, an organic synthesis problem can be complex and difficult for the students, because the number of pathways by which students could synthesise target substance “X” from starting substance “A” may be numerous. The problem is then very demanding in terms of information processing. In addition, students find it difficult to accept that one starting compound treated with only one set of reagents could lead to more than one correct product. A number of studies have dealt with organic synthesis. 48–50   The following comments from two students echo the difficulties faced by many students (pp. 209–210): 50  

“… having to do a synthesis problem is one of the more difficult things. Having to put everything together and sort of use your creativity, and knowing that I know everything solid to come up with a synthesis problem is difficult… it's just you can remember… you can use H 2 and nickel to add hydrogen to a bond but then there's like four other ways so if you're just looking for like what you react with, you can remember just that one but if you need five options just in case it's one of the other options that's given on the test… So, you have to know like multiple ways… and some things are used to maybe reduce… for example, something is used to reduce like a carboxylic acid and something else, the same thing, is used to reduce an aldehyde but then something else is used to like oxidize”.

Qualitative organic chemistry problems are dealt with in Chapters 6 and 7.

The present volume is the result of contributions from many experts in the field of chemistry education, with a clear focus on what can be identified as problem solving research. We are particularly fortunate that George Bodner , an authority in chemistry problem solving, has written the foreword to this book. (George has also published a review of research on problem solving in chemistry. 8   )

The book consists of eighteen chapters that cover many aspects of problem solving in chemistry and are organized under the following themes: (I) General issues in problem solving in chemistry education; (II) Problem solving in organic chemistry and biochemistry; (III) Chemistry problem solving in specific contexts; (IV) New technologies in problem solving in chemistry, and (V) New perspectives for problem solving in chemistry education. In the rest of this introductory chapter, I present a brief preview of the following contents.

The book starts with a discussion of qualitative reasoning in problem solving in chemistry. This type of reasoning helps us build inferences based on the analysis of qualitative values ( e.g. , high, low, weak, and strong) of the properties and behaviors of the components of a system, and the application of structure–property relationships. In Chapter 2, Talanquer summarizes core findings from research in chemistry education on the challenges that students face when engaging in this type of reasoning, and the strategies that support their learning in this area.

For Graulich, Langner, Vo , and Yuriev (Chapter 3), chemical problem solving relies on conceptual knowledge and the deployment of metacognitive problem solving processes, but novice problem solvers often grapple with both challenges simultaneously. Multiple scaffolding approaches have been developed to support student problem solving, often designed to address specific aspects or content area. The authors present a continuum of scaffolding so that a blending of prompts can be used to achieve specific goals. Providing students with opportunities to reflect on the problem solving work of others – peers or experts – can also be of benefit in deepening students’ conceptual reasoning skills.

A central theme in Gulacar, Cox and Fynewever 's chapter (Chapter 4) is the multitude of ways in which students can be unsuccessful when trying to solve problems. Each step of a multi-step problem can be labeled as a subproblem and represents content that students need to understand and use to be successful with the problem. The authors have developed a set of codes to categorize each student's attempted solution for every subproblem as either successful or not, and if unsuccessful, identifying why, thus providing a better understanding of common barriers to success, illustrated in the context of stoichiometry.

In Chapter 5, Tsaparlis re-examines the “working memory overload hypothesis” and associated with it the Johnstone–El Banna predictive model of problem solving. This famous predictive model is based on the effect of information processing, especially of working-memory capacity on problem solving. Other factors include mental capacity or M -capacity, degree of field dependence/independence, and developmental level/scientific reasoning. The Johnstone–El Banna model is re-examined and situations are explored where the model is valid, but also its limitations. A further examination of the role of the above cognitive factors in problem solving in chemistry is also made.

Proposing reaction mechanisms using the electron-pushing formalism, which is central to the practice and teaching of organic chemistry, is the subject of Chapter 6 by Bahttacharyya . The author argues that MR (Mechanistic Reasoning) using the EPF (Electron-Pushing Formalism) incorporates several other forms of reasoning, and is also considered as a useful transferrable skill for the biomedical sciences and allied fields.

Flynn considers synthesis problems as among the most challenging questions for students in organic chemistry courses. In Chapter 7, she describes the strategies used by students who have been successful in solving synthetic problems. Associated classroom and problem set activities are also described.

We all know that the determination of chemical identity is a fundamental chemistry practice that now depends almost exclusively on the characterization of molecular structure through spectroscopic analysis. This analysis is a day-to-day task for practicing organic chemists, and instruction in modern organic chemistry aims to cultivate such expertise. Accordingly, in Chapter 8, Connor and Shultz review studies that have investigated reasoning and problem solving approaches used to evaluate NMR and IR spectroscopic data for organic structural determination, and they provide a foundation for understanding how this problem solving expertise develops and how instruction may facilitate such learning. The aim is to present the current state of research, empirical insights into teaching and learning this practice, and trends in instructional innovations.

The idea that variation exists within a system and the varied population schema described by Talanquer are the theoretical tools for the study by Rodriguez, Hux, Philips, and Towns , which is reported in Chapter 9. The subject of the study is chemical kinetics in biochemistry, and especially of the action and mechanisms of inhibition agents in enzyme catalysis, where a sophisticated understanding requires students to learn to reason using probability-based reasoning.

In Chapter 10, Phelps, Hawkins and Hunter consider the purpose of the academic chemistry laboratory, with emphasis on the practice of problem solving skills beyond those of an algorithmic mathematical nature. The purpose represents a departure from the procedural skills training often associated with the reason we engage in laboratory work (learning to titrate for example). While technical skills are of course important, if part of what we are doing in undergraduate chemistry courses is to prepare students to go on to undertake research, somewhere in the curriculum there should be opportunities to practice solving problems that are both open-ended and laboratory-based. The history of academic chemistry laboratory practice is reviewed and its current state considered.

Chapter 11 by Broman focuses on chemistry problems and problem solving by employing context-based learning approaches, where open-ended problems focusing on higher-order thinking are explored. Chemistry teachers suggested contexts that they thought their students would find interesting and relevant, e.g. , chocolate, doping, and dietary supplements. The chapter analyses students’ interviews after they worked with the problems and discusses how to enhance student interest and perceived relevance in chemistry, and how students’ learning can be improved.

Team Based Learning (TBL) is the theme of Chapter 12 by Capel, Hancock, Howe, Jones, Phillips , and Plana . TBL is a structured small group collaborative form of learning, where learners are required to prepare for sessions in advance, then discuss and debate potential solutions to problems with their peers. It has been found to be highly effective at facilitating active learning. The authors describe their experience with embedding TBL into their chemistry curricula at all levels, including a transnational degree program with a Chinese university.

The ability of students to learn and value aspects of the chemistry curriculum that delve into the molecular basis of chemical events relies on the use of models/molecular representations, and enhanced awareness of how these models connect to chemical observations. Molecular representations in chemistry is the topic of Chapter 13 by Polifka, Baluyut and Holme , which focuses on technology solutions that enhance student understanding and learning of these conceptual aspects of chemistry.

In Chapter 14, Limniou, Papadopoulos, Gavril, Touni , and Chatziapostolidou present an IR spectra simulation. The software includes a wide range of chemical compounds supported by real IR spectra, allowing students to learn how to interpret an IR spectrum, via a step by step process. The chapter includes a report on a pilot trial with a small-scale face-to-face learning environment. The software is available on the Internet for everyone to download and use.

In Chapter 15, Sigalas explores chemistry problems with computational quantum chemistry tools in the undergraduate chemistry curriculum, the use of computational chemistry for the study of chemical phenomena, and the prediction and interpretation of experimental data from thermodynamics and isomerism to reaction mechanisms and spectroscopy. The pros and cons of a series of software tools for building molecular models, preparation of input data for standard software, and visualization of computational results are discussed.

In Chapter 16, Stamovlasis and Vaiopoulou address methodological and epistemological issues concerning research in chemistry problem solving. Following a short review of the relevant literature with emphasis on methodology and the statistical modeling used, the weak points of the traditional approaches are discussed and a novel epistemological framework based on complex dynamical system theory is described. Notably, research using catastrophe theory provides empirical evidence for these phenomena by modeling and explaining mental overload effects and students’ failures. Examples of the application of this theory to chemistry problem solving is reviewed.

Chapter 17 provides extended summaries of the chapters, including a commentary on the chapters. The chapter also provides a brief coverage of various important issues and topics related to chemistry problem solving that are not covered by other chapters in the book.

Finally, in Chapter 18, a Postscript address two specific problem solving issues: (a) the potential synergy between higher and lower-order thinking skills (HOTS and LOTS,) and (b) When problem solving might descend to chaos dynamics. The synergy between HOTS and LOTS is demonstrated by looking at the contribution of chemistry and biochemistry to overcoming the current coronavirus (COVID-19) pandemic. One the other hand, chaos theory provides an analogy with the time span of the predictive power of problem solving models.

«Ἀρχὴ παιδεύσεως ἡ τῶν ὀνομάτων ἐπίσκεψις» (Archē paedeuseōs hē tōn onomatōn episkepsis). By Antisthenes (ancient Greek philosopher), translated by W. A. Oldfather (1925).

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Chapter Questions

Explain this statement in your own words and give an example. The properties of the substances around us depend on the atoms and molecules that compose them.

Explain the main goal of chemistry.

Describe the scientific approach to knowledge. How does it differ from other approaches?

Explain the differences between a hypothesis, a law, and a theory.

What observations did Antoine Lavoisier make? What law did he formulate?

What theory did John Dalton formulate?

What is wrong with the expression “That is just a theory,” if by theory the speaker is referring to a scientific theory?

What are two different ways to classify matter?

How do solids, liquids, and gases differ?

What is the difference between a crystalline solid and an amorphous solid?

Explain the difference between a pure substance and a mixture.

Explain the difference between an element and a compound.

Explain the difference between a homogeneous and a heterogeneous mixture

What kind of mixtures can be separated by filtration?

Explain how distillation is used to separate mixtures.

What is the difference between a physical property and a chemical property?

What is the difference between a physical change and a chemical change? List some examples of each.

Explain the significance of the law of conservation of energy.

What kind of energy is chemical energy? In what way is an elevated weight similar to a tank of gasoline?

What are the standard SI base units of length, mass, time, and temperature?

What are the three common temperature scales? Does the size of a degree differ among them?

What are prefix multipliers? List some examples.

What is a derived unit? List an example.

Explain the difference between density and mass.

Explain the difference between intensive and extensive properties.

What is the meaning of the number of digits reported in a measured quantity?

When multiplying or dividing measured quantities, what determines the number of significant figures in the result?

When adding or subtracting measured quantities, what determines the number of significant figures in the result?

What are the rules for rounding off the results of calculations?

Explain the difference between precision and accuracy.

Explain the difference between random error and systematic error.

What is dimensional analysis?

Classify each statement as an observation, a law, or a theory. MISSED THIS? Read Section 1.2 a. All matter is made of tiny, indestructible particles called atoms. b. When iron rusts in a closed container, the mass of the container and its contents does not change. c. In chemical reactions, matter is neither created nor destroyed. d. When a match burns, heat is released.

Classify each statement as an observation, a law, or a theory. a. Chlorine is a highly reactive gas. b. If elements are listed in order of increasing mass of their atoms, their chemical reactivities follow a repeating pattern. c. Neon is an inert (or nonreactive) gas. d. The reactivity of elements depends on the arrangement of their electrons.

A chemist decomposes several samples of carbon monoxide into carbon and oxygen and weighs the resultant elements. The results are shown in the table. MISSED THIS? Read Section 1.2 $$\begin{array}{ccc}\text { Sample } & \text { Mass of Carbon (g) } & \text { Mass of Oxygen (g) } \\\hline 1 & 6 & 8 \\ \hline 2 & 12 & 16 \\\hline 3 & 18 & 24 \\\hline\end{array}$$ a. Do you notice a pattern in these results? Next, the chemist decomposes several samples of hydrogen peroxide into hydrogen and oxygen. The results are shown in the table. $$\begin{array}{ccc}\text { Sample } & \text { Mass of Hydrogen (g) } & \text { Mass of Oxygen (g) } \\\hline 1 & 0.5 & 8 \\\hline 2 & 1 & 16 \\\hline 3 & 1.5 & 24 \\\hline\end{array}$$ b. Do you notice a similarity between these results and those for carbon monoxide in part a? c. Can you formulate a law from your observations in a and b? d. Can you formulate a hypothesis that might explain your law in c?

When astronomers observe distant galaxies, they can tell that most of them are moving away from one another. In addition, the more distant the galaxies, the more rapidly they are likely to be moving away from each other. Can you devise a hypothesis to explain these observations?

Classify each substance as a pure substance or a mixture. If it is a pure substance, classify it as an element or a compound. If it is a mixture, classify it as homogeneous or heterogeneous. MISSED THIS? Read Section 1.3; Watch KCV 1.3 a. sweat b. carbon dioxide c. aluminum d. vegetable soup

Classify each substance as a pure substance or a mixture. If it is a pure substance, classify it as an element or a compound. If it is a mixture, classify it as homogeneous or heterogeneous. a. wine b. beef stew c. iron d. carbon monoxide

Complete the table. MISSED THIS? Read Section 1.3; Watch $\mathrm{KCV} 1.3$

Complete the table.

Determine whether each molecular diagram represents a pure substance or a mixture. If it represents a pure substance, classify the substance as an element or a compound. If it represents a mixture, classify the mixture as homogeneous or heterogeneous. MISSED THIS? Read Section 1.3; Watch KCV 1.3

Determine whether each molecular diagram represents a pure substance or a mixture. If it represents a pure substance, classify the substance as an element or a compound. If it represents a mixture, classify the mixture as homogeneous or heterogeneous.

Classify each of the listed properties of isopropyl alcohol (also known as rubbing alcohol) as physical or chemical. MISSED THIS? Read Section 1.4 a. colorless b. flammable c. liquid at room temperature d. density $=0.79 \mathrm{~g} / \mathrm{mL}$ e. mixes with water

Classify each of the listed properties of ozone (a pollutant in the lower atmosphere but part of a protective shield against UV light in the upper atmosphere) as physical or chemical. a. bluish color b. pungent odor c. very reactive d. decomposes on exposure to ultraviolet light e. gas at room temperature

Classify each property as physical or chemical. MISSED THIS? Read Section 1.4 a. the tendency of ethyl alcohol to burn b. the shine on silver c. the odor of paint thinner d. the flammability of propane gas

Classify each property as physical or chemical. a. the boiling point of ethyl alcohol b. the temperature at which dry ice evaporates c. the tendency of iron to rust d. the color of gold

Classify each change as physical or chemical. MISSED THIS? Read Section 1.4 a. Natural gas burns in a stove. b. The liquid propane in a gas grill evaporates because the valve was left open. c. The liquid propane in a gas grill burns in a flame. d. A bicycle frame rusts on repeated exposure to air and water.

Classify each change as physical or chemical. a. Sugar burns when heated in a skillet. b. Sugar dissolves in water. c. A platinum ring becomes dull because of continued abrasion. d. A silver surface becomes tarnished after exposure to air for a long period of time.

Based on the molecular diagram, classify each change as physical or chemical. MISSED THIS? Read Section 1.4

Based on the molecular diagram, classify each change as physical or chemical.

Convert each temperature. MISSED THIS? Read Section 1.6; Watch $\mathrm{KCV} 1.6$ a. $32^{\circ} \mathrm{F}$ to ${ }^{\circ} \mathrm{C}$ (temperature at which water freezes) b. $77 \mathrm{~K}$ to ${ }^{\circ} \mathrm{F}$ (temperature of liquid nitrogen) c. $-109^{\circ} \mathrm{F}$ to ${ }^{\circ} \mathrm{C}$ (temperature of dry ice) d. $98.6^{\circ} \mathrm{F}$ to $\mathrm{K}$ (body temperature)

Convert each temperature. a. $212^{\circ} \mathrm{F}$ to ${ }^{\circ} \mathrm{C}$ (temperature of boiling water at sea level) b. $22^{\circ} \mathrm{C}$ to $\mathrm{K}$ (approximate room temperature) c. $0.00 \mathrm{~K}$ to ${ }^{\circ} \mathrm{F}$ (coldest temperature possible, also known as absolute zero) d. $2.735 \mathrm{~K}$ to ${ }^{\circ} \mathrm{C}$ (average temperature of the universe as measured from background black body radiation)

The coldest ground-level temperature ever measured on Earth is $-128.6^{\circ} \mathrm{F},$ recorded on July $21,1983,$ in Antarctica. Convert that temperature to ${ }^{\circ} \mathrm{C}$ and $\mathrm{K}$. MISSED THIS? Read Section 1.6; Watch $\mathrm{KCV} 1.6$.

The warmest temperature ever measured in the United States is $134^{\circ} \mathrm{F},$ recorded on July $10,1913,$ in Death Valley, California. Convert that temperature to ${ }^{\circ} \mathrm{C}$ and $\mathrm{K}$.

Use the prefix multipliers to express each measurement without exponents. MISSED THIS? Read Section 1.6; Watch $\mathrm{KCV} 1.6$ a. $1.2 \times 10^{-9} \mathrm{~m}$ b. $22 \times 10^{-15} \mathrm{~s}$ c. $1.5 \times 10^{9} \mathrm{~g}$ d. $3.5 \times 10^{6} \mathrm{~L}$

Use prefix multipliers to express each measurement without exponents. a. $38.8 \times 10^{5} \mathrm{~g}$ b. $55.2 \times 10^{-10} \mathrm{~s}$ c. $23.4 \times 10^{11} \mathrm{~m}$ d. $87.9 \times 10^{-7} \mathrm{~L}$

Use scientific notation to express each quantity with only base units (no prefix multipliers). MISSED THIS? Read Section 1.6; Watch KCV 1.6 a. $4.5 \mathrm{~ns}$ b. 18 fs c. $128 \mathrm{pm}$ d. $35 \mu \mathrm{m}$

Use scientific notation to express each quantity with only base units (no prefix multipliers). a. $35 \mu \mathrm{L}$ b. $225 \mathrm{Mm}$ c. $133 \mathrm{Tg}$ d. $1.5 \mathrm{cg}$

Complete the table. MISSED THIS? Read Section 1.6; Watch $\mathrm{KCV} 1.6$ a. $1245 \mathrm{~kg} \quad 1.245 \times 10^{6} \mathrm{~g} \quad 1.245 \times 10^{9} \mathrm{mg}$ b. $515 \mathrm{~km}$ _____ dm _____cm c. $122.355 \mathrm{~s}$ _____ms ____ks d. $3.345 \mathrm{~kJ}$ _____J ____mJ

Complete the table. a. $355 \mathrm{~km} / \mathrm{s}$ _____cm/s _____s/ms b. $1228 \mathrm{~g} / \mathrm{L}$ _____g/mL ______ kg/mL c. $554 \mathrm{mK} / \mathrm{s}$ _____K/s _____ $\mu \mathrm{K} / \mathrm{ms}$ d. $2.554 \mathrm{mg} / \mathrm{mL}$ _____g/L _____$\mu \mathrm{g} / \mathrm{mL}$

Express the quantity $254,998 \mathrm{~m}$ in each unit. MISSED THIS? Read Section 1.6; Watch KCV 1.6 a. $\mathrm{km}$ b. $\mathrm{Mm}$ c. $\mathrm{mm}$ d. $\mathrm{cm}$

Express the quantity $556.2 \times 10^{-12} \mathrm{~s}$ in each unit. a. ms b. ns c. ps d. fs

How many $1-\mathrm{cm}$ squares would it take to construct a square that is $1 \mathrm{~m}$ on each side? MISSED THIS? Read Section 1.6

How many $1-\mathrm{cm}$ cubes would it take to construct a cube that is $4 \mathrm{~cm}$ on edge?

A new penny has a mass of $2.49 \mathrm{~g}$ and a volume of $0.349 \mathrm{~cm}^{3}$. Is the penny made of pure copper? Explain your answer. MISSED THIS? Read Section 1.6; Watch KCV 1.6.

A titanium bicycle frame displaces $0.314 \mathrm{~L}$ of water and has a mass of 1.41 kg. What is the density of the titanium in $g / \mathrm{cm}^{3} ?$

Glycerol is a syrupy liquid often used in cosmetics and soaps. A $3.25 \mathrm{~L}$ sample of pure glycerol has a mass of $4.10 \times 10^{3} \mathrm{~g}$. What is the density of glycerol in $\mathrm{g} / \mathrm{cm}^{3}$ ? MISSED THIS? Read Section 1.6; Watch KCV 1.6

A supposedly gold nugget displaces $19.3 \mathrm{~mL}$ of water and has a mass of 371 g. Could the nugget be made of gold?

Ethylene glycol (antifreeze) has a density of $1.11 \mathrm{~g} / \mathrm{cm}^{3}$ MISSED THIS? Read Section 1.6; Watch $\mathrm{KCV} 1.6,$ IWE 1.10 a. What is the mass in g of $417 \mathrm{~mL}$ of ethylene glycol? b. What is the volume in $\mathrm{L}$ of $4.1 \mathrm{~kg}$ of ethylene glycol?

Acetone (nail polish remover) has a density of $0.7857 \mathrm{~g} / \mathrm{cm}^{3} .$ a. What is the mass in g of $28.56 \mathrm{~mL}$ of acetone? b. What is the volume in $\mathrm{mL}$ of $6.54 \mathrm{~g}$ of acetone?

A small airplane takes on 245 L of fuel. If the density of the fuel is $0.821 \mathrm{~g} / \mathrm{mL},$ what mass of fuel has the airplane taken on? MISSED THIS? Read Section 1.6; Watch KCV 1.6, IWE 1.10

Human fat has a density of $0.918 \mathrm{~g} / \mathrm{cm}^{3}$. How much volume (in $\mathrm{cm}^{3}$ ) is gained by a person who gains 10.0 lb of pure fat?

Read each measurement to the correct number of significant figures. Laboratory glassware should always be read from the bottom of the meniscus. MISSED THIS? Read Section 1.7

Read each measurement to the correct number of significant figures. Laboratory glassware should always be read from the bottom of the meniscus. Digital balances normally display mass to the correct number of significant figures for that particular balance.

For each number, underline the zeroes that are significant and draw an $\mathbf{x}$ through the zeroes that are not. MISSED THIS? Read Section 1.7; Watch $\mathrm{KCV} 1.6,$ IWE 1.5 a. $1,050,501 \mathrm{~km}$ b. $0.0020 \mathrm{~m}$ c. $0.000000000000002 \mathrm{~s}$ d. $0.001090 \mathrm{~cm}$

For each number, underline the zeroes that are significant and draw an $\mathbf{x}$ through the zeroes that are not. a. $180,701 \mathrm{mi}$ b. $0.001040 \mathrm{~m}$ c. $0.005710 \mathrm{~km}$ d. $90,201 \mathrm{~m}$

How many significant figures are in each number? MISSED THIS? Read Section 1.7; Watch KCV $1.6,$ IWE 1.5 a. $0.000312 \mathrm{~m}$ b. $312,000 \mathrm{~s}$ c. $3.12 \times 10^{5} \mathrm{~km}$ d. 13,127 s e. 2000

How many significant figures are in each number? a. 0.1111 s b. $0.007 \mathrm{~m}$ c. $108,700 \mathrm{~km}$ d. $1.563300 \times 10^{11} \mathrm{~m}$ e. 30,800

Which numbers are exact (and therefore have an unlimited number of significant figures)? MISSED THIS? Read Section 1.7; Watch KCV 1.6, IWE 1.5 a. $\pi=3.14$ b. 12 in $=1 \mathrm{ft}$ c. EPA gas mileage rating of 26 miles per gallon d. 1 gross $=144$

Indicate the number of significant figures in each number. If the number is an exact number, indicate an unlimited number of significant figures. a. 325,365,189 (July 4,2017 U.S. population) b. $2.54 \mathrm{~cm}=1$ in c. $11.4 \mathrm{~g} / \mathrm{cm}^{3}$ (density of lead) d. $12=1$ dozen

Round each number to four significant figures. MISSED THIS? Read Section 1.7; Watch $\mathrm{KCV} 1.7$ a. 156.852 b. 156.842 c. 156.849 d. 156.899

Round each number to three significant figures. a. 79,845.82 b. $1.548937 \times 10^{7}$ c. 2.3499999995 d. 0.000045389

Calculate to the correct number of significant figures. MISSED THIS? Read Section 1.7; Watch KCVs 1.6, 1.7, IWEs 1.5, 1.6 a. $9.15 \div 4.970$ b. $1.54 \times 0.03060 \times 0.69$ c. $27.5 \times 1.82 \div 100.04$ d. $\left(2.290 \times 10^{6}\right) \div\left(6.7 \times 10^{4}\right)$

Calculate to the correct number of significant figures. a. $89.3 \times 77.0 \times 0.08$ b. $\left(5.01 \times 10^{5}\right) \div\left(7.8 \times 10^{2}\right)$ c. $4.005 \times 74 \times 0.007$ d. $453 \div 2.031$

Calculate to the correct number of significant figures. MISSED THIS? Read Section 1.7; Watch KCVs $1.6,1.7,$ IWEs 1.5,1.6 a. $43.7-2.341$ b. $17.6+2.838+2.3+110.77$ c. $19.6+58.33-4.974$ d. $5.99-5.572$

Calculate to the correct number of significant figures. a. $0.004+0.09879$ b. $1239.3+9.73+3.42$ c. $2.4-1.777$ d. $532+7.3-48.523$

Calculate to the correct number of significant figures. MISSED THIS? Read Section 1.7; Watch KCVs 1.6, 1.7, IWEs 1.5, 1.6 a. $(24.6681 \times 2.38)+332.58$ b. $(85.3-21.489) \div 0.0059$ c. $(512 \div 986.7)+5.44$ d. $\left[\left(28.7 \times 10^{5}\right) \div 48.533\right]+144.99$

Calculate to the correct number of significant figures. a. $\left[\left(1.7 \times 10^{6}\right) \div\left(2.63 \times 10^{5}\right)\right]+7.33$ b. $(568.99-232.1) \div 5.3$ c. $(9443+45-9.9) \times 8.1 \times 10^{6}$ d. $(3.14 \times 2.4367)-2.34$

A flask containing $11.7 \mathrm{~mL}$ of a liquid weighs $132.8 \mathrm{~g}$ with the liquid in the flask and $124.1 \mathrm{~g}$ when empty. Calculate the density of the liquid in $\mathrm{g} / \mathrm{mL}$ to the correct number of significant digits. MISSED THIS? Read Section 1.6; Watch KCV 1.7, IWE 1.6

A flask containing $9.55 \mathrm{~mL}$ of a liquid weighs $157.2 \mathrm{~g}$ with the liquid in the flask and $148.4 \mathrm{~g}$ when empty. Calculate the density of the liquid in $\mathrm{g} / \mathrm{mL}$ to the correct number of significant digits.

Perform each unit conversion. MISSED THIS? Read Section 1.8; Watch $K C V 1.8,$ IWE 1.8 a. $27.8 \mathrm{~L}$ to $\mathrm{cm}^{3}$ b. $1898 \mathrm{mg}$ to $\mathrm{kg}$ c. $198 \mathrm{~km}$ to $\mathrm{cm}$

Perform each unit conversion. a. $28.9 \mathrm{nm}$ to $\mu \mathrm{m}$ b. $1432 \mathrm{~cm}^{3}$ to $\mathrm{L}$ c. 1211 Tm to Gm

Perform each unit conversion. MISSED THIS? Read Section 1.8; Watch $\mathrm{KCV} 1.8, \mathrm{IWE} 1.8$ a. $154 \mathrm{~cm}$ to in b. $3.14 \mathrm{~kg}$ to $\mathrm{g}$ c. $3.5 \mathrm{~L}$ to $\mathrm{qt}$ d. $109 \mathrm{~mm}$ to in

Perform each unit conversion. a. 1.4 in to $\mathrm{mm}$ b. $116 \mathrm{ft}$ to $\mathrm{cm}$ c. $1845 \mathrm{~kg}$ to $1 \mathrm{~b}$ d. 815 yd to $\mathrm{km}$

A runner wants to run $10.0 \mathrm{~km} .$ Her running pace is $7.5 \mathrm{mi}$ per hour. How many minutes must she run? MISSED THIS? Read Section 1.8; Watch KCV 1.8, IWE 1.8

A cyclist rides at an average speed of $18 \mathrm{mi}$ per hour. If she wants to bike $212 \mathrm{~km}$, how long (in hours) must she ride?

A certain European automobile has a gas mileage of $17 \mathrm{~km} / \mathrm{L}$. What is the gas mileage in miles per gallon? MISSED THIS? Read Section 1.8; Watch $\mathrm{KCV} 1.8, \mathrm{IWE} 1.8$

A gas can holds 5.0 gal of gasoline. Express this quantity in $\mathrm{cm}^{3}$.

A house has an area of $195 \mathrm{~m}^{2}$. What is its area in each unit? MISSED THIS? Read Section 1.8; Watch KCV 1.8, IWE 1.9 a. $\mathrm{km}^{2}$ b. $\mathrm{dm}^{2}$ c. $\mathrm{cm}^{2}$

Problem 100

A bedroom has a volume of $115 \mathrm{~m}^{3} .$ What is its volume in each unit? a. $\mathrm{km}^{3}$ b. $\mathrm{dm}^{3}$ c. $\mathrm{cm}^{3}$

Problem 101

The average U.S. farm occupies 435 acres. How many square miles is this? $\left(1\right.$ acre $\left.=43,560 \mathrm{ft}^{2}, 1 \mathrm{mile}=5280 \mathrm{ft}\right)$ MISSED THIS? Read Section 1.8; Watch $\mathrm{KCV} 1.8,$ IWE 1.9

Problem 102

Total U.S. farmland occupies 954 million acres. How many square miles is this? (1 acre $=43,560 \mathrm{ft}^{2}, 1 \mathrm{mi}=5280 \mathrm{ft}$ ). Total U.S. land area is 3.537 million square miles. What percentage of U.S. land is farmland?

Problem 103

An acetaminophen suspension for infants contains $80 \mathrm{mg} / 0.80 \mathrm{~mL}$ suspension. The recommended dose is $15 \mathrm{mg} / \mathrm{kg}$ body weight. How many $\mathrm{mL}$ of this suspension should be given to an infant weighing 14 lb? (Assume two significant figures.) MISSED THIS? Read Section 1.8; Watch $\mathrm{KCV} 1.8, \mathrm{IWE} 1.8$

Problem 104

An ibuprofen suspension for infants contains $100 \mathrm{mg} / 5.0 \mathrm{~mL}$ suspension. The recommended dose is $10 \mathrm{mg} / \mathrm{kg}$ body weight. How many $\mathrm{mL}$ of this suspension should be given to an infant weighing 18 lb? (Assume two significant figures.)

Problem 105

There are exactly 60 seconds in a minute, exactly 60 minutes in an hour, exactly 24 hours in a mean solar day, and 365.24 solar days in a solar year. How many seconds are in a solar year? Give your answer with the correct number of significant figures.

Problem 106

Determine the number of picoseconds in 2.0 hours.

Problem 107

Classify each property as intensive or extensive. a. volume b. boiling point c. temperature d. electrical conductivity e. energy

Problem 108

At what temperatures are the readings on the Fahrenheit and Celsius thermometers the same?

Problem 109

Suppose you design a new thermometer called the X thermometer. On the X scale the boiling point of water is $130^{\circ} \mathrm{X}$, and the freezing point of water is $10^{\circ} \mathrm{X}$. At what temperature are the readings on the Fahrenheit and X thermometers the same?

Problem 110

On a new Jekyll temperature scale, water freezes at $17^{\circ} \mathrm{J}$ and boils at $97^{\circ} \mathrm{J} .$ On another new temperature scale, the Hyde scale, water freezes at $0^{\circ} \mathrm{H}$ and boils at $120^{\circ} \mathrm{H}$. If methyl alcohol boils at 84 ${ }^{\circ} \mathrm{H},$ what is its boiling point on the Jekyll scale?

Problem 111

Force is defined as mass times acceleration. Starting with SI base units, derive a unit for force. Using SI prefixes, suggest a convenient unit for the force resulting from a collision with a 10 -ton trailer truck moving at 55 mi per hour and for the force resulting from the collision of a molecule of mass around $10^{-20} \mathrm{~kg}$ moving almost at the speed of light $\left(3 \times 10^{8} \mathrm{~m} / \mathrm{s}\right)$ with the wall of its container. (Assume a 1 -second deceleration time for both collisions.)

Problem 112

A temperature measurement of $25^{\circ} \mathrm{C}$ has three significant figures, while a temperature measurement of $-196^{\circ} \mathrm{C}$ has only two significant figures. Explain.

Problem 113

Do each calculation without your calculator and give the answers to the correct number of significant figures. a. $1.76 \times 10^{-3} / 8.0 \times 10^{2}$ b. $1.87 \times 10^{-2}+2 \times 10^{-4}-3.0 \times 10^{-3}$ c. $\left[\left(1.36 \times 10^{5}\right)(0.000322) / 0.082\right](129.2)$

Problem 114

The value of the euro was recently $\$ 1.15$ U.S., and the price of 1 liter of gasoline in France is 1.42 euro. What is the price of 1 gallon of gasoline in U.S. dollars in France?

Problem 115

A thief uses a can of sand to replace a solid gold cylinder that sits on a weight-sensitive, alarmed pedestal. The can of sand and the gold cylinder have exactly the same dimensions (length $=22$ and radius $=3.8 \mathrm{~cm}$ ). a. Calculate the mass of each cylinder (ignore the mass of 1 the can itself). (density of gold $=19.3 \mathrm{~g} / \mathrm{cm}^{3},$ density of sand $\left.=3.00 \mathrm{~g} / \mathrm{cm}^{3}\right)$ b. Does the thief set off the alarm? Explain.

Problem 116

The proton has a radius of approximately $1.0 \times 10^{-13} \mathrm{~cm}$ and a mass of $1.7 \times 10^{-24} \mathrm{~g} .$ Determine the density of a proton. For a sphere, $V=(4 / 3) \pi r^{3}$.

Problem 117

The density of titanium is $4.51 \mathrm{~g} / \mathrm{cm}^{3} .$ What is the volume (in cubic inches) of 3.5 lb of titanium?

Problem 118

The density of iron is $7.86 \mathrm{~g} / \mathrm{cm}^{3}$. What is its density in pounds per cubic inch ( $\left(\mathrm{lb} / \mathrm{in}^{3}\right) ?$

Problem 119

A steel cylinder has a length of 2.16 in, a radius of 0.22 in, and a mass of $41 \mathrm{~g}$. What is the density of the steel in $\mathrm{g} / \mathrm{cm}^{3} ?$

Problem 120

A solid aluminum sphere has a mass of 85 g. Use the density of aluminum to find the radius of the sphere in inches.

Problem 121

A backyard swimming pool holds 185 cubic yards $\left(\mathrm{yd}^{3}\right)$ of water. What is the mass of the water in pounds?

Problem 122

An iceberg has a volume of $7655 \mathrm{ft}^{2}$. What is the mass of the ice (in kg) composing the iceberg (at $0^{\circ} \mathrm{C}$ )?

Problem 123

The Toyota Prius, a hybrid electric vehicle, has an EPA gas mileage rating of $52 \mathrm{mi} /$ gal in the city. How many kilometers can the Prius travel on 15 L of gasoline?

Problem 124

The Honda Insight, a hybrid electric vehicle, has an EPA gas mileage rating of $41 \mathrm{mi} /$ gal in the city. How many kilometers can the Insight travel on the amount of gasoline that would fit in a soda can? The volume of a soda can is $355 \mathrm{~mL}$.

Problem 125

The single proton that forms the nucleus of the hydrogen atom has a radius of approximately $1.0 \times 10^{-13} \mathrm{~cm} .$ The hydrogen atom itself has a radius of approximately $52.9 \mathrm{pm} .$ What fraction of the space within the atom is occupied by the nucleus?

Problem 126

A sample of gaseous neon atoms at atmospheric pressure and $0^{\circ} \mathrm{C}$ contains $2.69 \times 10^{22}$ atoms per liter. The atomic radius of neon is $69 \mathrm{pm} .$ What fraction of the space do the atoms themselves occupy? What does this reveal about the separation between atoms in the gaseous phase?

Problem 127

The diameter of a hydrogen atom is $212 \mathrm{pm}$. Find the length in kilometers of a row of $6.02 \times 10^{23}$ hydrogen atoms. The diameter of a ping pong ball is $4.0 \mathrm{~cm} .$ Find the length in kilometers of a row of $6.02 \times 10^{23}$ ping pong balls.

Problem 128

The world record in the men's 100-m dash is $9.58 \mathrm{~s}$, and in the 100-yd dash it is 9.07 s. Find the speed in $\mathrm{mi} / \mathrm{hr}$ of the runners who set these records. (Assume three significant figures for $100 \mathrm{~m}$ and 100 yd. $)$

Problem 129

Table salt contains $39.33 \mathrm{~g}$ of sodium per $100 \mathrm{~g}$ of salt. The U.S. Food and Drug Administration (FDA) recommends that adults consume less than $2.40 \mathrm{~g}$ of sodium per day. A particular snack mix contains $1.25 \mathrm{~g}$ of salt per $100 \mathrm{~g}$ of the mix. What mass of the snack mix can an adult consume and still be within the FDA limit? (Assume three significant figures for 100 g.)

Problem 130

Lead metal can be extracted from a mineral called galena, which contains $86.6 \%$ lead by mass. A particular ore contains $68.5 \%$ galena by mass. If the lead can be extracted with $92.5 \%$ efficiency, what mass of ore is required to make a lead sphere with a $5.00-\mathrm{cm}$ radius?

Problem 131

A length of #8 copper wire (radius $=1.63 \mathrm{~mm}$ ) has a mass of $24.0 \mathrm{~kg}$ and a resistance of 2.061 ohm per $\mathrm{km}(\Omega / \mathrm{km}) .$ What is the overall resistance of the wire?

Problem 132

Rolls of aluminum foil are $304 \mathrm{~mm}$ wide and $0.016 \mathrm{~mm}$ thick. What maximum length of aluminum foil can be made from $1.10 \mathrm{~kg}$ of aluminum?

Problem 133

Liquid nitrogen has a density of $0.808 \mathrm{~g} / \mathrm{mL}$ and boils at $77 \mathrm{~K}$. Researchers often purchase liquid nitrogen in insulated $175 \mathrm{~L}$ tanks. The liquid vaporizes quickly to gaseous nitrogen (which has a density of $1.15 \mathrm{~g} / \mathrm{L}$ at room temperature and atmospheric pressure) when the liquid is removed from the tank. Suppose that all $175 \mathrm{~L}$ of liquid nitrogen in a tank accidentally vaporized in a lab that measured $10.00 \mathrm{~m} \times 10.00 \mathrm{~m} \times 2.50 \mathrm{~m} .$ What maximum fraction of the air in the room could be displaced by the gaseous nitrogen?

Problem 134

Mercury is often used in thermometers. The mercury sits in a bulb on the bottom of the thermometer and rises up a thin capillary as the temperature rises. Suppose a mercury thermometer contains $3.380 \mathrm{~g}$ of mercury and has a capillary that is $0.200 \mathrm{~mm}$ in diameter. How far does the mercury rise in the capillary when the temperature changes from $0.0^{\circ} \mathrm{C}$ to $25.0^{\circ} \mathrm{C}$ ? The density of mercury respectively.

Problem 135

A force of $2.31 \times 10^{4} \mathrm{~N}$ is applied to a diver's face mask that has an area of $125 \mathrm{~cm}^{2}$. Find the pressure in atm on the face mask.

Problem 136

The SI unit of force is the newton, derived from the base units by using the definition of force, $F=m a$. The dyne is a non-SI unit of force in which mass is measured in grams and time is measured in seconds. The relationship between the two units is 1 dyne $=10^{-5} \mathrm{~N}$. Find the unit of length used to define the dyne.

Problem 137

Kinetic energy can be defined as $\frac{1}{2} m v^{2}$ or as $\frac{3}{2} P V .$ Show that the derived SI units of each of these terms are those of energy. (Pressure is force/area and force is mass $\times$ acceleration.)

Problem 138

In 1999 , scientists discovered a new class of black holes with masses 100 to 10,000 times the mass of our sun that occupy less space than our moon. Suppose that one of these black holes has a mass of $1 \times 10^{3}$ suns and a radius equal to one-half the radius of our moon. What is the density of the black hole in $\mathrm{g} / \mathrm{cm}^{3}$ ? The radius of our sun is $7.0 \times 10^{5} \mathrm{~km}$, and it has an average density of $1.4 \times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$. The diameter of the moon is $2.16 \times 10^{3} \mathrm{mi}$.

Problem 139

Suppose that polluted air has carbon monoxide (CO) levels of 15.0 ppm. An average human inhales about $0.50 \mathrm{~L}$ of air per breath and takes about 20 breaths per minute. How many milligrams of carbon monoxide does the average person inhale in an 8 -hour period at this level of carbon monoxide pollution? Assume that the carbon monoxide has a density of $1.2 \mathrm{~g} / \mathrm{L} .$ (Hint: 15.0 ppm CO means $15.0 \mathrm{~L}$ CO per $10^{6} \mathrm{~L}$ air. $)$

Problem 140

Nanotechnology, the field of building ultrasmall structures one atom at a time, has progressed in recent years. One potential application of nanotechnology is the construction of artificial cells. The simplest cells would probably mimic red blood cells, the body's oxygen transporters. Nanocontainers, perhaps constructed of carbon, could be pumped full of oxygen and injected into a person's bloodstream. If the person needed additional oxygen - due to a heart attack perhaps, or for the purpose of space travel-these containers could slowly release oxygen into the blood, allowing tissues that would otherwise die to remain alive. Suppose that the nanocontainers were cubic and had an edge length of $25 \mathrm{nm}$. a. What is the volume of one nanocontainer? (Ignore the thickness of the nanocontainer's wall.) b. Suppose that each nanocontainer could contain pure oxygen pressurized to a density of $85 \mathrm{~g} / \mathrm{L}$. How many grams of oxygen could each nanocontainer contain? c. Air typically contains about 0.28 g of oxygen per liter. An average human inhales about $0.50 \mathrm{~L}$ of air per breath and takes about 20 breaths per minute. How many grams of oxygen does a human inhale per hour? (Assume two significant figures.) d. What is the minimum number of nanocontainers that a person would need in his or her bloodstream to provide 1 hour's worth of oxygen? e. What is the minimum volume occupied by the number of nanocontainers calculated in part d? Is such a volume feasible, given that total blood volume in an adult is about $5 \mathrm{~L} ?$

Problem 141

Approximate the percent increase in waist size that occurs when a 155 -lb person gains 40.0 lb of fat. Assume that the volume of the person can be modeled by a cylinder that is $4.0 \mathrm{ft}$ tall. The average density of a human is about $1.0 \mathrm{~g} / \mathrm{cm}^{3}$, and the density of fat is $0.918 \mathrm{~g} / \mathrm{cm}^{3}$.

Problem 142

A box contains a mixture of small copper spheres and small lead spheres. The total volume of both metals is measured by the displacement of water to be $427 \mathrm{~cm}^{3},$ and the total mass is $4.36 \mathrm{~kg}$. What percentage of the spheres are copper?

Problem 143

A volatile liquid (one that easily evaporates) is put into a jar, and the jar is then sealed. Does the mass of the sealed jar and its contents change upon the vaporization of the liquid?

Problem 144

The diagram shown first represents solid carbon dioxide, also known as dry ice. Which of the other diagrams best represents the dry ice after it has sublimed into a gas?

Problem 145

A cube has an edge length of $7 \mathrm{~cm} .$ If it is divided into $1-\mathrm{cm}$ cubes, how many $1-\mathrm{cm}$ cubes are there?

Problem 146

Substance A has a density of $1.7 \mathrm{~g} / \mathrm{cm}^{3}$. Substance $\mathrm{B}$ has a density of $1.7 \mathrm{~kg} / \mathrm{m}^{3} .$ Without doing any calculations, determine which substance is more dense.

Problem 147

For each box, examine the blocks attached to the balances. Based on their positions and sizes, determine which block is more dense (the dark block or the lighter-colored block), or if the relative densities cannot be determined. (Think carefully about the information being shown.)

Problem 148

Let a triangle represent atoms of element $\mathrm{A}$ and a circle represent atoms of element $\mathrm{B}$. a. Draw an atomic-level view of a homogeneous mixture of elements A and B. b. Draw an atomic view of the compound $\mathrm{AB}$ in a liquid state (molecules close together). c. Draw an atomic view of the compound AB after it has undergone a physical change (such as evaporation). d. Draw an atomic view of the compound after it has undergone a chemical change (such as decomposition of AB into A and B).

Problem 149

Identify each statement as being most like an observation, a law, or a theory. a. All coastal areas experience two high tides and two low tides each day. b. The tides in Earth's oceans are caused mainly by the gravitational attraction of the moon. c. Yesterday, high tide in San Francisco Bay occurred at 2: 43 A.M. and 3: 07 P.M. d. Tides are higher at the full moon and new moon than at other times of the month.

Problem 150

Using white and black circles to represent different kinds of atoms, make a drawing that accurately represents each sample of matter: a solid element, a liquid compound, and a heterogeneous mixture. Make a drawing (clearly showing before and after) depicting your liquid compound undergoing a physical change. Make a drawing depicting your solid element undergoing a chemical change.

Problem 151

Look up the measurement of the approximate thickness of a human hair. a. Convert the measurement to an SI unit (if it isn't already). b. Write it in scientific notation. c. Write it without scientific notation. d. Write it with an appropriate prefix on a base unit. Now repeat these steps using the distance from Earth to the sun.

Problem 152

The following statements are all true. a. Jessica's house is $5 \mathrm{~km}$ from the grocery store. b. Jessica's house is $4.73 \mathrm{~km}$ from the grocery store. c. Jessica's house is $4.73297 \mathrm{~km}$ from the grocery store. How can all the statements be true? What does the number of digits in each statement communicate? What sort of device would Jessica need to make the measurement in each statement?

Problem 153

One inch is equal to $2.54 \mathrm{~cm}$. Draw a line that is 1 in long, and mark the centimeters on the line. Draw a cube that is 1 in on each side. Draw lines on each face of the cube that are $1 \mathrm{~cm}$ apart. How many cubic centimeters are there in 1 in $^{3}$ ?

Problem 154

Convert the height of each member in your group from feet and inches to meters. Once you have your heights in meters, calculate the sum of all the heights. Use appropriate rules for significant figures at each step.

Problem 155

The density of a substance can change with temperature. The graph that follows displays the density of water from $-150^{\circ} \mathrm{C}$ to $100^{\circ} \mathrm{C} .$ Examine the graph and answer the questions. a. Water undergoes a large change in density at $0^{\circ} \mathrm{C}$ as it freezes to form ice. Calculate the percent change in density that occurs when liquid water freezes to ice at $0^{\circ} \mathrm{C}$. $$\text { (Hint: \% change } \left.=\frac{\text { final value - initial value }}{\text { initial value }} \times 100 \%\right)$$ b. Calculate the volume (in $\mathrm{cm}^{3}$ ) of $54 \mathrm{~g}$ of water at $1^{\circ} \mathrm{C}$ and the volume of the same mass of ice at $-1^{\circ} \mathrm{C}$. What is the change in volume? c. Antarctica contains 26.5 million cubic kilometers of ice. Assume the temperature of the ice is $-20^{\circ} \mathrm{C}$. If all of this ice were heated to $1^{\circ} \mathrm{C}$ and melted to form water, what volume of liquid water would form? d. A 1.00-L sample of water is heated from $1^{\circ} \mathrm{C}$ to $100^{\circ} \mathrm{C}$. What is the volume of the water after it is heated?

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1.8: Solving Chemical Problems

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  Learning Objectives

• Explain the dimensional analysis (factor label) approach to mathematical calculations involving quantities.
• Describe how to use dimensional analysis to carry out unit conversions for a given property and computations involving two or more properties.
• Convert between the three main temperature units: Fahrenheit, Celsius, and Kelvin.

It is often the case that a quantity of interest may not be easy (or even possible) to measure directly but instead must be calculated from other directly measured properties and appropriate mathematical relationships. For example, consider measuring the average speed of an athlete running sprints. This is typically accomplished by measuring the time required for the athlete to run from the starting line to the finish line, and the distance between these two lines, and then computing speed from the equation that relates these three properties:

\[\mathrm{speed=\dfrac{distance}{time}} \nonumber \]

An Olympic-quality sprinter can run 100 m in approximately 10 s, corresponding to an average speed of

\[\mathrm{\dfrac{100\: m}{10\: s}=10\: m/s} \nonumber \]

Note that this simple arithmetic involves dividing the numbers of each measured quantity to yield the number of the computed quantity (100/10 = 10) and likewise dividing the units of each measured quantity to yield the unit of the computed quantity (m/s = m/s). Now, consider using this same relation to predict the time required for a person running at this speed to travel a distance of 25 m. The same relation between the three properties is used, but in this case, the two quantities provided are a speed (10 m/s) and a distance (25 m). To yield the sought property, time, the equation must be rearranged appropriately:

\[\mathrm{time=\dfrac{distance}{speed}} \nonumber \]

The time can then be computed as:

\[\mathrm{\dfrac{25\: m}{10\: m/s}=2.5\: s} \nonumber \]

Again, arithmetic on the numbers (25/10 = 2.5) was accompanied by the same arithmetic on the units (m/m/s = s) to yield the number and unit of the result, 2.5 s. Note that, just as for numbers, when a unit is divided by an identical unit (in this case, m/m), the result is “1”—or, as commonly phrased, the units “cancel.”

These calculations are examples of a versatile mathematical approach known as dimensional analysis (or the factor-label method ). Dimensional analysis is based on this premise: the units of quantities must be subjected to the same mathematical operations as their associated numbers . This method can be applied to computations ranging from simple unit conversions to more complex, multi-step calculations involving several different quantities.

Conversion Factors and Dimensional Analysis

A ratio of two equivalent quantities expressed with different measurement units can be used as a unit conversion factor . For example, the lengths of 2.54 cm and 1 in. are equivalent (by definition), and so a unit conversion factor may be derived from the ratio,

\[\mathrm{\dfrac{2.54\: cm}{1\: in.}\:(2.54\: cm=1\: in.)\: or\: 2.54\:\dfrac{cm}{in.}} \nonumber \]

Several other commonly used conversion factors are given in Table \(\PageIndex{1}\).

When we multiply a quantity (such as distance given in inches) by an appropriate unit conversion factor, we convert the quantity to an equivalent value with different units (such as distance in centimeters). For example, a basketball player’s vertical jump of 34 inches can be converted to centimeters by:

\[\mathrm{34\: \cancel{in.} \times \dfrac{2.54\: cm}{1\:\cancel{in.}}=86\: cm} \nonumber \]

Since this simple arithmetic involves quantities , the premise of dimensional analysis requires that we multiply both numbers and units . The numbers of these two quantities are multiplied to yield the number of the product quantity, 86, whereas the units are multiplied to yield

\[\mathrm{\dfrac{in.\times cm}{in.}}. \nonumber \]

Just as for numbers, a ratio of identical units is also numerically equal to one,

\[\mathrm{\dfrac{in.}{in.}=1} \nonumber \]

and the unit product thus simplifies to cm . (When identical units divide to yield a factor of 1, they are said to “cancel.”) Using dimensional analysis, we can determine that a unit conversion factor has been set up correctly by checking to confirm that the original unit will cancel, and the result will contain the sought (converted) unit.

Example \(\PageIndex{1}\): Using a Unit Conversion Factor

The mass of a competition Frisbee is 125 g. Convert its mass to ounces using the unit conversion factor derived from the relationship 1 oz = 28.349 g (Table \(\PageIndex{1}\)).

If we have the conversion factor, we can determine the mass in kilograms using an equation similar the one used for converting length from inches to centimeters.

\[x\:\mathrm{oz=125\: g\times unit\: conversion\: factor}\nonumber \]

We write the unit conversion factor in its two forms:

\[\mathrm{\dfrac{1\: oz}{28.349\: g}\:and\:\dfrac{28.349\: g}{1\: oz}}\nonumber \]

The correct unit conversion factor is the ratio that cancels the units of grams and leaves ounces.

\[\begin{align*} x\:\ce{oz}&=\mathrm{125\:\cancel{g}\times \dfrac{1\: oz}{28.349\:\cancel{g}}}\\ &=\mathrm{\left(\dfrac{125}{28.349}\right)\:oz}\\ &=\mathrm{4.41\: oz\: (three\: significant\: figures)} \end{align*} \nonumber \]

Exercise \(\PageIndex{1}\)

Convert a volume of 9.345 qt to liters.

Beyond simple unit conversions, the factor-label method can be used to solve more complex problems involving computations. Regardless of the details, the basic approach is the same—all the factors involved in the calculation must be appropriately oriented to insure that their labels (units) will appropriately cancel and/or combine to yield the desired unit in the result. This is why it is referred to as the factor-label method. As your study of chemistry continues, you will encounter many opportunities to apply this approach.

Example \(\PageIndex{2}\): Computing Quantities from Measurement Results

What is the density of common antifreeze in units of g/mL? A 4.00-qt sample of the antifreeze weighs 9.26 lb.

Since \(\mathrm{density=\dfrac{mass}{volume}}\), we need to divide the mass in grams by the volume in milliliters. In general: the number of units of B = the number of units of A \(\times\) unit conversion factor. The necessary conversion factors are given in Table 1.7.1: 1 lb = 453.59 g; 1 L = 1.0567 qt; 1 L = 1,000 mL. We can convert mass from pounds to grams in one step:

\[\mathrm{9.26\:\cancel{lb}\times \dfrac{453.59\: g}{1\:\cancel{lb}}=4.20\times 10^3\:g}\nonumber \]

We need to use two steps to convert volume from quarts to milliliters.

• Convert quarts to liters.

\[\mathrm{4.00\:\cancel{qt}\times\dfrac{1\: L}{1.0567\:\cancel{qt}}=3.78\: L}\nonumber \]

• Convert liters to milliliters.

\[\mathrm{3.78\:\cancel{L}\times\dfrac{1000\: mL}{1\:\cancel{L}}=3.78\times10^3\:mL}\nonumber \]

\[\mathrm{density=\dfrac{4.20\times10^3\:g}{3.78\times10^3\:mL}=1.11\: g/mL}\nonumber \]

Alternatively, the calculation could be set up in a way that uses three unit conversion factors sequentially as follows:

\[\mathrm{\dfrac{9.26\:\cancel{lb}}{4.00\:\cancel{qt}}\times\dfrac{453.59\: g}{1\:\cancel{lb}}\times\dfrac{1.0567\:\cancel{qt}}{1\:\cancel{L}}\times\dfrac{1\:\cancel{L}}{1000\: mL}=1.11\: g/mL}\nonumber \]

Exercise \(\PageIndex{2}\)

What is the volume in liters of 1.000 oz, given that 1 L = 1.0567 qt and 1 qt = 32 oz (exactly)?

\(\mathrm{2.956\times10^{-2}\:L}\)

Example \(\PageIndex{3}\): Computing Quantities from Measurement Results

While being driven from Philadelphia to Atlanta, a distance of about 1250 km, a 2014 Lamborghini Aventador Roadster uses 213 L gasoline.

• What (average) fuel economy, in miles per gallon, did the Roadster get during this trip?
• If gasoline costs $3.80 per gallon, what was the fuel cost for this trip?

(a) We first convert distance from kilometers to miles:

\[\mathrm{1250\: km\times\dfrac{0.62137\: mi}{1\: km}=777\: mi}\nonumber \]

and then convert volume from liters to gallons:

\[\mathrm{213\:\cancel{L}\times\dfrac{1.0567\:\cancel{qt}}{1\:\cancel{L}}\times\dfrac{1\: gal}{4\:\cancel{qt}}=56.3\: gal}\nonumber \]

\[\mathrm{(average)\: mileage=\dfrac{777\: mi}{56.3\: gal}=13.8\: miles/gallon=13.8\: mpg}\nonumber \]

Alternatively, the calculation could be set up in a way that uses all the conversion factors sequentially, as follows:

\[\mathrm{\dfrac{1250\:\cancel{km}}{213\:\cancel{L}}\times\dfrac{0.62137\: mi}{1\:\cancel{km}}\times\dfrac{1\:\cancel{L}}{1.0567\:\cancel{qt}}\times\dfrac{4\:\cancel{qt}}{1\: gal}=13.8\: mpg}\nonumber \]

(b) Using the previously calculated volume in gallons, we find:

\[\mathrm{56.3\: gal\times\dfrac{$3.80}{1\: gal}=$214}\nonumber \]

Exercise \(\PageIndex{3}\)

A Toyota Prius Hybrid uses 59.7 L gasoline to drive from San Francisco to Seattle, a distance of 1300 km (two significant digits).

• What (average) fuel economy, in miles per gallon, did the Prius get during this trip?
• If gasoline costs $3.90 per gallon, what was the fuel cost for this trip?

Conversion of Temperature Units

We use the word temperature to refer to the hotness or coldness of a substance. One way we measure a change in temperature is to use the fact that most substances expand when their temperature increases and contract when their temperature decreases. The mercury or alcohol in a common glass thermometer changes its volume as the temperature changes. Because the volume of the liquid changes more than the volume of the glass, we can see the liquid expand when it gets warmer and contract when it gets cooler.

To mark a scale on a thermometer, we need a set of reference values: Two of the most commonly used are the freezing and boiling temperatures of water at a specified atmospheric pressure. On the Celsius scale, 0 °C is defined as the freezing temperature of water and 100 °C as the boiling temperature of water. The space between the two temperatures is divided into 100 equal intervals, which we call degrees. On the Fahrenheit scale, the freezing point of water is defined as 32 °F and the boiling temperature as 212 °F. The space between these two points on a Fahrenheit thermometer is divided into 180 equal parts (degrees).

Defining the Celsius and Fahrenheit temperature scales as described in the previous paragraph results in a slightly more complex relationship between temperature values on these two scales than for different units of measure for other properties. Most measurement units for a given property are directly proportional to one another (y = mx). Using familiar length units as one example:

\[\mathrm{length\: in\: feet=\left(\dfrac{1\: ft}{12\: in.}\right)\times length\: in\: inches} \nonumber \]

• y = length in feet,
• x = length in inches, and
• the proportionality constant, m, is the conversion factor.

The Celsius and Fahrenheit temperature scales, however, do not share a common zero point, and so the relationship between these two scales is a linear one rather than a proportional one (\(y = mx + b\)). Consequently, converting a temperature from one of these scales into the other requires more than simple multiplication by a conversion factor, m, it also must take into account differences in the scales’ zero points (\(b\)).

The linear equation relating Celsius and Fahrenheit temperatures is easily derived from the two temperatures used to define each scale. Representing the Celsius temperature as \(x\) and the Fahrenheit temperature as \(y\), the slope, \(m\), is computed to be:

\[\begin{align*} m &=\dfrac{\Delta y}{\Delta x} \\[4pt] &= \mathrm{\dfrac{212\: ^\circ F - 32\: ^\circ F}{100\: ^\circ C-0\: ^\circ C}} \\[4pt] &= \mathrm{\dfrac{180\: ^\circ F}{100\: ^\circ C}} \\[4pt] &= \mathrm{\dfrac{9\: ^\circ F}{5\: ^\circ C} }\end{align*} \nonumber \]

The y-intercept of the equation, b , is then calculated using either of the equivalent temperature pairs, (100 °C, 212 °F) or (0 °C, 32 °F), as:

\[\begin{align*} b&=y-mx \\[4pt] &= \mathrm{32\:^\circ F-\dfrac{9\:^\circ F}{5\:^\circ C}\times0\:^\circ C} \\[4pt] &= \mathrm{32\:^\circ F} \end{align*} \nonumber \]

The equation relating the temperature scales is then:

\[\mathrm{\mathit{T}_{^\circ F}=\left(\dfrac{9\:^\circ F}{5\:^\circ C}\times \mathit{T}_{^\circ C}\right)+32\:^\circ C} \nonumber \]

An abbreviated form of this equation that omits the measurement units is:

\[\mathrm{\mathit{T}_{^\circ F}=\dfrac{9}{5}\times \mathit{T}_{^\circ C}+32} \nonumber \]

Rearrangement of this equation yields the form useful for converting from Fahrenheit to Celsius:

\[\mathrm{\mathit{T}_{^\circ C}=\dfrac{5}{9}(\mathit{T}_{^\circ F}+32)} \nonumber \]

As mentioned earlier in this chapter, the SI unit of temperature is the kelvin (K). Unlike the Celsius and Fahrenheit scales, the kelvin scale is an absolute temperature scale in which 0 (zero) K corresponds to the lowest temperature that can theoretically be achieved. The early 19th-century discovery of the relationship between a gas's volume and temperature suggested that the volume of a gas would be zero at −273.15 °C. In 1848, British physicist William Thompson, who later adopted the title of Lord Kelvin, proposed an absolute temperature scale based on this concept (further treatment of this topic is provided in this text’s chapter on gases).

The freezing temperature of water on this scale is 273.15 K and its boiling temperature 373.15 K. Notice the numerical difference in these two reference temperatures is 100, the same as for the Celsius scale, and so the linear relation between these two temperature scales will exhibit a slope of \(\mathrm{1\:\dfrac{K}{^\circ\:C}}\). Following the same approach, the equations for converting between the kelvin and Celsius temperature scales are derived to be:

\[T_{\ce K}=T_{\mathrm{^\circ C}}+273.15 \nonumber \]

\[T_\mathrm{^\circ C}=T_{\ce K}-273.15 \nonumber \]

The 273.15 in these equations has been determined experimentally, so it is not exact. Figure \(\PageIndex{1}\) shows the relationship among the three temperature scales. Recall that we do not use the degree sign with temperatures on the kelvin scale.

Although the kelvin (absolute) temperature scale is the official SI temperature scale, Celsius is commonly used in many scientific contexts and is the scale of choice for nonscience contexts in almost all areas of the world. Very few countries (the U.S. and its territories, the Bahamas, Belize, Cayman Islands, and Palau) still use Fahrenheit for weather, medicine, and cooking.

Example \(\PageIndex{4}\): Conversion from Celsius

Normal body temperature has been commonly accepted as 37.0 °C (although it varies depending on time of day and method of measurement, as well as among individuals). What is this temperature on the kelvin scale and on the Fahrenheit scale?

\[\mathrm{K= {^\circ C}+273.15=37.0+273.2=310.2\: K}\nonumber \]

\[\mathrm{^\circ F=\dfrac{9}{5}\:{^\circ C}+32.0=\left(\dfrac{9}{5}\times 37.0\right)+32.0=66.6+32.0=98.6\: ^\circ F}\nonumber \]

Exercise \(\PageIndex{4}\)

Convert 80.92 °C to K and °F.

354.07 K, 177.7 °F

Example \(\PageIndex{5}\): Conversion from Fahrenheit

Baking a ready-made pizza calls for an oven temperature of 450 °F. If you are in Europe, and your oven thermometer uses the Celsius scale, what is the setting? What is the kelvin temperature?

\[\mathrm{^\circ C=\dfrac{5}{9}(^\circ F-32)=\dfrac{5}{9}(450-32)=\dfrac{5}{9}\times 418=232 ^\circ C\rightarrow set\: oven\: to\: 230 ^\circ C}\hspace{20px}\textrm{(two significant figures)}\nonumber \]

\[\mathrm{K={^\circ C}+273.15=230+273=503\: K\rightarrow 5.0\times 10^2\,K\hspace{20px}(two\: significant\: figures)}\nonumber \]

Exercise \(\PageIndex{5}\)

Convert 50 °F to °C and K.

10 °C, 280 K

Measurements are made using a variety of units. It is often useful or necessary to convert a measured quantity from one unit into another. These conversions are accomplished using unit conversion factors, which are derived by simple applications of a mathematical approach called the factor-label method or dimensional analysis. This strategy is also employed to calculate sought quantities using measured quantities and appropriate mathematical relations.

Key Equations

• \(T_\mathrm{^\circ C}=\dfrac{5}{9}\times T_\mathrm{^\circ F}-32\)
• \(T_\mathrm{^\circ F}=\dfrac{9}{5}\times T_\mathrm{^\circ C}+32\)
• \(T_\ce{K}={^\circ \ce C}+273.15\)
• \(T_\mathrm{^\circ C}=\ce K-273.15\)

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NEW  |  50 Interactive Sample Exercise s bring key Sample Exercises in the text to life through animation and narration. Author Matt Stoltzfus uses the text’s Analyze/Plan/Solve/Check technique to guide students through the problem-solving process. Play icons within the text identify each Interactive Sample Exercise. Clicking the icon in the eText launches a visual and conceptual presentation which goes beyond the static page. The Practice Exercises within each Sample Exercise can also be assigned in Mastering Chemistry where students will receive answer-specific feedback.

Updated table of contents: energy now serves as a unifying theme throughout the narrative

Chapter 1 NEW | Section 1.4: The Nature of Energy  provides a much earlier introduction to work, heat, and energy—all key topics that run throughout the course—so that energy can serve as a unifying theme throughout the narrative.

Chapter 5  Section 5.1  now has a tighter focus on chemical energy and the relationship between electrostatic potential energy and bonds. This section builds upon the basic concepts introduced now in  Section 1.4.   NEW | Section 5.8: Bond Enthalpies  offers an earlier introduction to this topic.

Chapter 8 REVISED | Section 8.8  now builds on the bond enthalpy discussion from Section 5.8  and expands the discussion to consider the strengths and lengths of covalent bonds.

Visual enhancements help students build general chemistry knowledge and understanding

The style of the art has been revised throughout for enhanced clarity and a cleaner more relevant look. This includes new white-background annotation boxes with crisp, thin leaders; richer and more saturated colors in the art; and expanded use of 3D renderings.  Before/after photos  now more clearly show characteristics of endothermic and exothermic reactions. Added reaction equations connect the chemistry to what’s happening in the photos.

Design an Experiment Exercises take students beyond recall

Design an Experiment  features provide a departure from the usual kinds of end-of-chapter exercises with an inquiry-based, open-ended approach that tries to stimulate the student to “think like a scientist.” Designed to foster critical thinking, each exercise presents the student with a scenario in which various unknowns require investigation. The student is called upon to ponder how experiments might be set up to provide answers to particular questions about observations. These exercises can be found at the end of the chapter in print and are also assignable within Mastering Chemistry.

Updated features encourage students to think about the practical, real-world use of chemistry

The author team utilized Mastering metadata to edit and clarify in-chapter Go Figure and Give It Some Thought  questions, as well as end-of-chapter problems. User data helped them to identify ‘problematic’ questions and then modify, replace, or delete-resulting in a more diverse and polished set of problems.

Reach every student by pairing this text with Mastering Chemistry.

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Pearson eText is a simple-to-use, mobile-optimized, personalized reading experience available within Mastering. It allows students to easily highlight, take notes, and review key vocabulary all in one place–even when offline. Seamlessly integrated videos and other rich media engage students and give them access to the help they need, when they need it. 

• NEW - Give It Some Thought (GIST) are now interactive in the eText, giving students seamless access to these i nformal, sharply focused exercises that test just how well they’re “getting it” as they move through the course.
• NEW - Learning Outcomes now appear at the section and chapter levels, giving students access as they move through the material rather than at the end of chapters. Self-assessment exercises allow students to check their mastery of the material and to focus on smaller pieces of information and skills they should be able to perform. Students can access through embedded eText links and the Study Area of Mastering Chemistry, and instructors can assign in Mastering.
• NEW - Ready-to-Go Study Tools in the Mastering Chemistry Study Area help students master the toughest topics (as identified by professors and fellow students completing homework and practicing for exams). Key Concept Videos, Interactive Worked Examples, and problem sets are all-on-one, easy-to-navigate tools with answer-specific feedback that keep students focused and give them the scaffolded support needed to succeed. Students can use the modules on their own, even when their professor doesn’t assign them.
• NEW - Dynamic Study Modules are now specific to Chemistry: The Central Science. The assignable modules pose a series of question sets about a course topic. The questions adapt to each student’s performance and offer personalized, targeted feedback to help them master key concepts. As a result, students build the confidence they need to deepen their understanding, participate meaningfully, and perform better – in and out of class. Students can use their computer or the MyLab and Mastering app to access Dynamic Study Modules. Available for select titles. 
• NEW - Curated list of author-recommended Mastering assignments is available for instructors to use in the Mastering Item Library and appears in each section of the eText.  Assignments include select End-of-Chapter exercises, Tutorials, and Dynamic Study Modules.
• NEW - Self-assessment exercises are a series of questions at the end of each section, allowing students to assess their understanding of the content. These come complete with author-written, answer-specific feedback.and are assignable in Mastering Chemistry.
• ENHANCED - 10 End-of-Chapter problem sets are revised with real data, modern applications, and creative new problems, providing instructors with alternate chemistry problems.

Hallmark features of Chemistry: The Central Science

Learning beyond knowledge recall

• Smart Figures walk students through complex visual representations, dispelling common misconceptions before they take root by animating a continuous process rather than relying on discrete time points. Students receive answer-specific video feedback from the author team that validates correct responses or helps get them back on track.  
• Integrative Exercises connect concepts in the current chapter with those from previous chapters and serve as an overall review of key concepts, helping students gain a deeper understanding of how chemistry fits together. Sample Integrative Exercises in many chapters show how to analyze and solve problems encompassing more than one concept.
• Design An Experiment activities provide an inquiry-based, open-ended approach that stimulates a student to “think like a scientist.” Designed to foster critical thinking, each exercise presents the student with a scenario in which various unknowns require investigation. Students are called upon to ponder how experiments might be set up as they provide answers to particular questions about observations.
• A Closer Look essays and features cover high-interest topics, reflect recent news and discoveries in the field of chemistry, and provide relevance and applications for students. 
• Chemistry and Life, and Chemistry Put to Work help students connect chemistry to world events, scientific discoveries, and medical breakthroughs.
• Go Figure questions encourage students to stop and take time to analyze the artwork to make sure they understand the concept behind it. 

Applying and practicing problem solving

• How To features offer step-by-step guidance for solving specific types of problems such as Drawing Lewis Structures, Balancing Redox Equations, Naming Acids, etc. These features, with numbered steps wrapped by a thin rule, are integrated into the main discussion and easy to find.
• Analyze/Plan/Solve/Check is the unique problem-solving process used consistently throughout the text and guides students in practicing problem solving. The process helps students to understand what they are being asked as they plan how to solve a problem, work their way through the solution, and check their answers.
• Selected sample exercises use a dual-column problem-solving strategy approach to show students the thought process involved in each step of a mathematical calculation.
• 50 Interactive Sample Exercises bring key Sample Exercises to life through animation and narration. Author Matt Stoltzfus uses the Analyze/Plan/Solve/Check technique to guide students through the problem-solving process. Students can access the visual and conceptual presentations in the eText, or instructors can assign them in Mastering Chemistry where students receive answer-specific feedback.
• Practice Exercises test mastery of key concepts and touch on the most common misconceptions based on the authors consulting the ACS Chemistry Concept inventory before writing the questions. Second Practice Exercises are multiple-choice and accompany each Sample Exercise within the chapters. Specific wrong answer feedback, written by the authors, is available in Mastering Chemistry .
• Strategies for Success essays encourage students to think like chemists and aid students in analyzing information and organizing thoughts as a means to improve problem solving and critical thinking.

Visualizing for conceptual understanding

• Visualizing Concepts exercises help students develop a conceptual understanding of the key ideas in the chapter by asking them to consider concepts through the use of models, graphs, and other visual materials. Visualizing Concepts exercises precede the end-of-chapter exercises and in the end-of-chapter material.
• Molecular illustrations help students see what is happening on a molecular level in the sample exercises. Computer-generated molecular illustrations provide visual representations of matter at the atomic level.
• Multi-Focus Graphics provide a variety of perspectives including macroscopic, microscopic, and symbolic to portray various chemical concepts to help students develop a more complete understanding of the topic being presented. 
• Conceptual Questions developed around the GIST and Go Figure questions are integrated with classroom clicker questions. In turn, these questions are integrated into Mastering Chemistry.

Hallmark features of Mastering Chemistry.  Learn more about Mastering Chemistry . 

Teach your course your way: 

• With Learning Catalytics , you will hear from every student when it matters most. You pose a variety of questions that help students recall ideas, apply concepts, and develop critical-thinking skills. Your students respond using their own smartphones, tablets, or laptops.  You can monitor responses with real-time analytics and find out what your students do – and don’t – understand. Then, you can adjust your teaching accordingly and even facilitate peer-to-peer learning, helping students stay motivated and engaged. Open-ended questions help students develop critical thinking skills around structure and reactivity in general chemistry with Learning Catalytics questions for each chapter of Chemistry: The Central Science .
• Ready-to-Go Teaching Modules provide organized material for every tough topic in General Chemistry enabling you as the instructor to expose your students to the best content. Created for and by instructors, the modules provide a guide for easy-to-use assignments for before and after class plus in-class activities with clicker questions and questions in Learning Catalytics™. Modules can be easily accessed via Mastering Chemistry. 
• Adaptive Follow-Up Assignments allow instructors to deliver content to students–automatically personalized for each individual based on the strengths and weaknesses identified by his or her performance on initial Mastering Chemistry assignments.

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• The Chemistry Primer helps students remediate their chemistry math skills and prepare for their first college chemistry course.
• Pre-built Assignments get students up to speed at the beginning of the course.
• Math is covered in the context of chemistry, basic chemical literacy, balancing chemical equations, mole theory, and stoichiometry.
• Scaled to students’ needs , remediation is only suggested to students that perform poorly on initial assessment.
• Remediation includes tutorials, wrong-answer specific feedback, video instruction, and step-wise scaffolding to build students’ abilities.
• Simulations (including PhET simulations) are interactive simulations that foster conceptual understanding and active learning, and are complemented by tutorials developed to make these powerful visuals assignable.
• Pause and Predict Video Quizzes bring chemistry to life with lab demonstrations that illustrate key topics in general chemistry. Students predict the outcome of experiments as they watch the videos; follow-up multiple-choice questions challenge students to apply the concepts from videos to related scenarios.

Deliver trusted content: 

• 50 Interactive Sample Exercises bring key Sample Exercises in the text to life through animation and narration. Author Matt Stoltzfus uses the text’s Analyze/Plan/Solve/Check technique to guide students through the problem solving process. Students can seamlessly access the visual and conceptual presentations in the eText. The Practice Exercises within each Sample Exercise can also be assigned in Mastering Chemistry where students will receive answer-specific feedback. Second Practice Exercises are multiple-choice and accompany each Sample Exercise within the chapters. Specific wrong answer feedback, written by the authors, is available in Mastering Chemistry. 
• 27 SmartFigures walk students through complex visual representations, dispelling common misconceptions before they take root. Each SmartFigure converts a static in-text figure into a dynamic process narrated by one of the authors. Students can work through SmartFigures in the eText, and instructors can assign SmartFigures in Mastering Chemistry, where they are accompanied by a multiple-choice question with answer specific video feedback. Selecting the correct answer launches a brief wrap up video that highlights the key concepts behind the answer.

Improve student results: When you teach with Mastering, student performance often improves. That’s why instructors have chosen Mastering for over 15 years, touching the lives of over 20 million students.  Learn more in this efficacy report.

New to This Edition

Pearson eText is a simple-to-use, mobile-optimized, personalized reading experience available within Mastering. It allows students to easily highlight, take notes, and review key vocabulary all in one place—even when offline. Seamlessly integrated videos and other rich media engage students and give them access to the help they need, when they need it. 

• Give It Some Thought (GIST) are now interactive in the eText, giving students seamless access to these i nformal, sharply focused exercises that test just how well they’re “getting it” as they move through the course.
• Learning Outcomes now appear at the section and chapter levels, giving students access as they move through the material rather than at the end of chapters. Self-assessment exercises allow students to check their mastery of the material and to focus on smaller pieces of information and skills they should be able to perform. Students can access through embedded eText links and the Study Area of Mastering Chemistry, and instructors can assign in Mastering.
• Ready-to-Go Study Tools in the Mastering Chemistry Study Area help students master the toughest topics (as identified by professors and fellow students completing homework and practicing for exams). Key Concept Videos, Interactive Worked Examples, and problem sets are all-on-one, easy-to-navigate tools with answer-specific feedback that keep students focused and give them the scaffolded support needed to succeed. Students can use the modules on their own, even when their professor doesn’t assign them.
• Dynamic Study Modules are now specific to Chemistry: The Central Science. The assignable modules pose a series of question sets about a course topic. The questions adapt to each student’s performance and offer personalized, targeted feedback to help them master key concepts. As a result, students build the confidence they need to deepen their understanding, participate meaningfully, and perform better — in and out of class. Students can use their computer or the MyLab and Mastering app to access Dynamic Study Modules. Available for select titles. 
• Curated list of author-recommended Mastering assignments is available for instructors to use in the Mastering Item Library and appears in each section of the eText.  Assignments include select End-of-Chapter exercises, Tutorials, and Dynamic Study Modules.
• Self-assessment exercises are a series of questions at the end of each section, allowing students to assess their understanding of the content. These come complete with author-written, answer-specific feedback.and are assignable in Mastering Chemistry.

Table of Contents

BRIEF CONTENTS

1. Introduction: Matter, Energy, and Measurement

2. Atoms, Molecules, and Ions

3. Chemical Reactions and Reaction Stoichiometry

4. Reactions in Aqueous Solution

5. Thermochemistry 

6. Electronic Structure of Atoms

7. Periodic Properties of the Elements

8. Basic Concepts of Chemical Bonding 

9. Molecular Geometry and Bonding Theories 

10.   Gases

11.   Liquids and Intermolecular Forces      

12.   Solids and Modern Materials 

13.   Properties of Solutions

14.   Chemical Kinetics 

15.   Chemical Equilibrium

16.   Acid—Base Equilibria 

17.   Additional Aspects of Aqueous Equilibria 

18.   Chemistry of the Environment

19.   Chemical Thermodynamics

20.   Electrochemistry      

21.   Nuclear Chemistry

22.   Chemistry of the Nonmetals

23.   Transition Metals and Coordination Chemistry

24.   The Chemistry of Life: Organic and Biological Chemistry       

Mathematical Operations

Properties of Water

Thermodynamic Quantities for Selected Substances at 298.15 K (25 ο C)             

Aqueous Equilibrium Constants      

Standard Reduction Potentials at 25 ο C

Answers to Selected Exercises

Answers to Give It Some Thought

Answers to Go Figure

Answer to Selected Practice Exercises

Photo and Art Credits

DETAILED CONTENTS

1 Introduction: Matter, Energy, and Measurement

1.1   The Study of Chemistry

The Atomic and Molecular Perspective of Chemistry

Why Study Chemistry?

1.2   Classifications of Matter

States of Matter

Pure Substances

1.3   Properties of Matter

Physical and Chemical Changes

Separation of Mixtures

1.4   The Nature of Energy 

Kinetic Energy and Potential Energy   

1.5   Units of Measurement

SI Units  

Length and Mass  

Temperature

Derived SI Units    

Volume   

Density   

Units of Energy

1.6   Uncertainty in Measurement  

Precision and Accuracy  

Significant Figures 

Significant Figures in Calculations 

1.7   Dimensional Analysis 

Conversion Factors

Using Two or More Conversion Factors 

Conversions Involving Volume

Chemistry Put To Work Chemistry and the Chemical Industry         

A Closer Look The Scientific Method 

Chemistry Put To Work Chemistry in the News

Strategies For Success Estimating Answers   

Strategies For Success The Importance of Practice  

Strategies For Success The Features of This Book 

2 Atoms, Molecules, and Ions

2.1   The Atomic Theory of Matter  

2.2   The Discovery of Atomic Structure

Cathode Rays and Electrons

Radioactivity

The Nuclear Model of the Atom 

2.3   The Modern View of Atomic Structure 

Atomic Numbers, Mass Numbers, and Isotopes 

2.4   Atomic Weights 

The Atomic Mass Scale  

Atomic Weight 

2.5   The Periodic Table 

2.6   Molecules and Molecular Compounds 

Molecules and Chemical Formulas

Molecular and Empirical Formulas 

Picturing Molecules

2.7   Ions and Ionic Compounds

Predicting Ionic Charges

Ionic Compounds  

2.8   Naming Inorganic Compounds 

Names and Formulas of Ionic Compounds  

Names and Formulas of Acids 

Names and Formulas of Binary Molecular Compounds

2.9   Some Simple Organic Compounds    

Alkanes  

Some Derivatives of Alkanes

A Closer Look Basic Forces

A Closer Look The Mass Spectrometer

A Closer Look What Are Coins Made Of?  

Chemistry and Life Elements Required by Living Organisms  

Strategies For Success How to Take a Test  

3 Chemical Reactions and Reaction Stoichiometry

3.1   Chemical Equations   

Balancing Equations

A Step-by-Step Example of Balancing a Chemical Equation               

Indicating the States of Reactants and Products

3.2   Simple Patterns of Chemical Reactivity

Combination and Decomposition Reactions 

Combustion Reactions

3.3   Formula Weights

Formula and Molecular Weights

Percentage Composition from Chemical Formulas

3.4   Avogadro’s Number and the Mole 

Molar Mass 

Interconverting Masses and Moles

Interconverting Masses and Numbers of Particles

3.5   Empirical Formulas from Analyses

Molecular Formulas from Empirical Formulas

Combustion Analysis

3.6   Quantitative Information from Balanced Equations      

3.7   Limiting Reactants 

Theoretical and Percent Yields

Strategies For Success Problem Solving  

Chemistry and Life Glucose Monitoring

Strategies For Success Design an Experiment  

4 Reactions in Aqueous Solution 

4.1   General Properties of Aqueous Solutions 

Electrolytes and Nonelectrolytes

How Compounds Dissolve in Water    

Strong and Weak Electrolytes 

4.2   Precipitation Reactions 

Solubility Guidelines for Ionic Compounds

Exchange (Metathesis) Reactions 

Ionic Equations and Spectator Ions

4.3   Acids, Bases, and Neutralization Reactions  

Strong and Weak Acids and Bases

Identifying Strong and Weak Electrolytes

Neutralization Reactions and Salts

Neutralization Reactions with Gas Formation

4.4   Oxidation-Reduction Reactions

Oxidation and Reduction

Oxidation Numbers

Oxidation of Metals by Acids and Salts

The Activity Series 

4.5   Concentrations of Solutions   

Molarity  

Expressing the Concentration of an Electrolyte  

Interconverting Molarity, Moles, and Volume 

Dilution   

4.6   Solution Stoichiometry and Chemical Analysis

Titrations 

Chemistry Put To Work Antacids

Strategies For Success Analyzing Chemical Reactions  

5 Thermochemistry  

5.1   The Nature of Chemical Energy 

5.2   The First Law of Thermodynamics

System and Surroundings    

Internal Energy

Relating  E to Heat and Work

Endothermic and Exothermic Processes

State Functions

5.3   Enthalpy

Pressure—Volume Work  

Enthalpy Change  

5.4   Enthalpies of Reaction 

5.5   Calorimetry

Heat Capacity and Specific Heat

Constant-Pressure Calorimetry 

Bomb Calorimetry (Constant-Volume Calorimetry)

5.6   Hess’s Law

5.7   Enthalpies of Formation 

Using Enthalpies of Formation to Calculate Enthalpies of Reaction  

5.8   Bond Enthalpies 

Bond Enthalpies and the Enthalpies of Reactions 

5.9   Foods and Fuels 

Other Energy Sources

A Closer Look Energy, Enthalpy, and P-V Work

A Closer Look Using Enthalpy as a Guide 

Chemistry and Life The Regulation of Body Temperature   

Chemistry Put To Work The Scientific and Political Challenges of Biofuels 

6 Electronic Structure of Atoms

6.1   The Wave Nature of Light 

6.2   Quantized Energy and Photons 

Hot Objects and the Quantization of Energy 

The Photoelectric Effect and Photons  

6.3   Line Spectra and the Bohr Model 

Line Spectra

Bohr’s Model

The Energy States of the Hydrogen Atom 

Limitations of the Bohr Model

6.4   The Wave Behavior of Matter 

The Uncertainty Principle

6.5   Quantum Mechanics and Atomic Orbitals 

Orbitals and Quantum Numbers

6.6   Representations of Orbitals    

The s Orbitals  

The  Orbitals

The  and  Orbitals  

6.7   Many-Electron Atoms 

Orbitals and Their Energies  

Electron Spin and the Pauli Exclusion Principle  

6.8   Electron Configurations

Hund’s Rule 

Condensed Electron Configurations    

Transition Metals   

The Lanthanides and Actinides

6.9   Electron Configurations and the Periodic Table 

Anomalous Electron Configurations    

A Closer Look Measurement and the Uncertainty Principle

A Closer Look Thought Experiments and Schrödinger’s Cat

A Closer Look Probability Density and Radial Probability Functions   

Chemistry and Life Nuclear Spin and Magnetic Resonance Imaging 

7 Periodic Properties of the Elements 

7.1   Development of the Periodic Table

7.2   Effective Nuclear Charge  

7.3   Sizes of Atoms and Ions 

Periodic Trends in Atomic Radii 

Periodic Trends in Ionic Radii

7.4   Ionization Energy

Variations in Successive Ionization Energies

Periodic Trends in First Ionization Energies  

Electron Configurations of Ions

7.5   Electron Affinity 

Periodic Trends in Electron Affinity 

7.6   Metals, Nonmetals, and Metalloids

Metals    

Nonmetals 

Metalloids 

7.7   Trends for Group 1A and Group 2A Metals    

Group 1A: The Alkali Metals 

Group 2A: The Alkaline Earth Metals   

7.8   Trends for Selected Nonmetals

Group 6A: The Oxygen Group 

Group 7A: The Halogens

Group 8A: The Noble Gases 

A Closer Look Effective Nuclear Charge

Chemistry Put To Work Ionic Size and Lithium-Ion Batteries  

Chemistry and Life The Improbable Development of Lithium Drugs 

8 Basic Concepts of Chemical Bonding

8.1   Lewis Symbols and the Octet Rule

The Octet Rule

8.2   Ionic Bonding  

Energetics of Ionic Bond Formation

Electron Configurations of Ions of the s - and p -Block Elements  

Transition Metal Ions

8.3   Covalent Bonding  

Lewis Structures   

Multiple Bonds 

8.4   Bond Polarity and Electronegativity   

Electronegativity   

Electronegativity and Bond Polarity

Dipole Moments    

Comparing Ionic and Covalent Bonding 

8.5   Drawing Lewis Structures 

Formal Charge and Alternative Lewis Structures

8.6   Resonance Structures

Resonance in Benzene  

8.7   Exceptions to the Octet Rule  

Odd Number of Electrons

Less Than an Octet of Valence Electrons 

More Than an Octet of Valence Electrons 

8.8   Strengths and Lengths of Covalent Bonds

A Closer Look Calculation of Lattice Energies: The Born—Haber Cycle

A Closer Look Oxidation Numbers, Formal Charges, and Actual Partial Charges  

9 Molecular Geometry and Bonding Theories  

9.1  Molecular Shapes  

Applying the VSEPR Model to Determine Molecular Shapes

Effect of Nonbonding Electrons and Multiple Bonds on Bond Angles

Molecules with Expanded Valence Shells 

Shapes of Larger Molecules 

9.2  The VSEPR Model

Shapes of Larger Molecules

9.3  Molecular Shape and Molecular Polarity  

9.4  Covalent Bonding and Orbital Overlap

9.5  Hybrid Orbitals

sp Hybrid Orbitals  

sp 2 and sp 3 Hybrid Orbitals   

Hypervalent Molecules

Hybrid Orbital Summary 

9.6  Multiple Bonds

Resonance Structures, Delocalization, and p Bonding   

General Conclusions about s and p  

9.7  Molecular Orbitals 

Molecular Orbitals of the Hydrogen Molecule

Bond Order 

9.8  Bonding in Period 2 Diatomic Molecules  

Molecular Orbitals for  Li 2 and Be 2

Molecular Orbitals from 2 p Atomic Orbitals

Electron Configurations for B 2 through Ne 2

Electron Configurations and Molecular Properties 

Heteronuclear Diatomic Molecules

Chemistry and Life The Chemistry of Vision    

A Closer Look Phases in Atomic and Molecular Orbitals     

Chemistry Put To Work Orbitals and Energy   

10.1  Characteristics of Gases

10.2  Pressure 

Atmospheric Pressure and the Barometer

10.3  The Gas Laws

The Pressure—Volume Relationship: Boyle’s Law

The Temperature—Volume Relationship: Charles’s Law

The Quantity—Volume Relationship: Avogadro’s Law  

10.4  The Ideal-Gas Equation 

Relating the Ideal-Gas Equation and the Gas Laws 

 10.5  Further Applications of the Ideal-Gas Equation 

Gas Densities and Molar Mass

Volumes of Gases in Chemical Reactions 

 10.6  Gas Mixtures and Partial Pressures  

Partial Pressures and Mole Fractions  

 10.7  The Kinetic-Molecular Theory of Gases 

Distributions of Molecular Speed

Application of Kinetic-Molecular Theory to the Gas Laws      

10.8  Molecular Effusion and Diffusion

Graham’s Law of Effusion    

Diffusion and Mean Free Path 

10.9  Real Gases: Deviations from Ideal Behavior 

The van der Waals Equation 

Strategies for Success Calculations Involving Many Variables

A Closer Look The Ideal-Gas Equation

Chemistry Put To Work Gas Separations  

11 Liquids and Intermolecular Forces

  11.1   A Molecular Comparison of Gases, Liquids, and Solids

  11.2   Intermolecular Forces 

Dispersion Forces 

Dipole—Dipole Interactions   

Hydrogen Bonding 

Ion—Dipole Forces 

Comparing Intermolecular Forces 

  11.3   Select Properties of Liquids   

Viscosity 

Surface Tension    

Capillary Action

  11.4   Phase Changes

Energy Changes Accompany Phase Changes   

Heating Curves

Critical Temperature and Pressure

  11.5   Vapor Pressure 

Volatility, Vapor Pressure, and Temperature 

Vapor Pressure and Boiling Point  

  11.6   Phase Diagrams 

The Phase Diagrams of  and 

  11.7   Liquid Crystals

Types of Liquid Crystals 

Chemistry Put To Work Ionic Liquids

A Closer Look The Clausius—Clapeyron Equation 

12 Solids and Modern Materials

12.1   Classification of Solids 

12.2   Structures of Solids

Crystalline and Amorphous Solids 

Unit Cells and Crystal Lattices 

Filling the Unit Cell 

12.3   Metallic Solids 

The Structures of Metallic Solids

Close Packing 

12.4   Metallic Bonding 

Electron-Sea Model 

Molecular Orbital Model 

12.5   Ionic Solids

Structures of Ionic Solids

12.6   Molecular Solids 

12.7   Covalent-Network Solids

Semiconductors    

Semiconductor Doping

12.8   Polymers 

Making Polymers  

Structure and Physical Properties of Polymers   

12.9   Nanomaterials

Semiconductors on the Nanoscale

Metals on the Nanoscale

Carbon on the Nanoscale

A Closer Look X-ray Diffraction

Chemistry Put To Work Alloys of Gold

Chemistry Put To Work Solid-State Lighting   

Chemistry Put To Work Modern Materials in the Automobile  

Chemistry Put To Work Microporous and Mesoporous Materials  

13 Properties of Solutions

13.1   The Solution Process 

The Natural Tendency toward Mixing  

The Effect of Intermolecular Forces on Solution Formation    

Energetics of Solution Formation  

Solution Formation and Chemical Reactions

13.2   Saturated Solutions and Solubility

13.3   Factors Affecting Solubility

Solute—Solvent Interactions  

Pressure Effects    

Temperature Effects 

13.4   Expressing Solution Concentration    

Mass Percentage, ppm, and ppb  

Mole Fraction, Molarity, and Molality   

Converting Concentration Units 

13.5   Colligative Properties 

Vapor—Pressure Lowering    

Boiling-Point Elevation

Freezing-Point Depression   

Osmosis 

Determination of Molar Mass from Colligative Properties  

13.6   Colloids 

Hydrophilic and Hydrophobic Colloids 

Colloidal Motion in Liquids   

Chemistry and Life Fat-Soluble and Water-Soluble Vitamins  

Chemistry and Life Blood Gases and Deep-Sea Diving      

A Closer Look Ideal Solutions with Two or More Volatile Components

A Closer Look The van’t Hoff Factor  

Chemistry and Life Sickle-Cell Anemia

14 Chemical Kinetics  

14.1   Factors That Affect Reaction Rates   

14.2   Reaction Rates 

Change of Rate with Time    

Instantaneous Rate

Reaction Rates and Stoichiometry 

14.3   Concentration and Rate Laws

Reaction Orders: The Exponents in the Rate Law 

Magnitudes and Units of Rate Constants

Using Initial Rates to Determine Rate Laws  

14.4   The Change of Concentration with Time

First-Order Reactions 

Second-Order Reactions

Zero-Order Reactions 

Half-Life  

14.5   Temperature and Rate

The Collision Model 

The Orientation Factor

Activation Energy  

The Arrhenius Equation  

Determining the Activation Energy 

14.6   Reaction Mechanisms

Elementary Reactions 

Multistep Mechanisms

Rate Laws for Elementary Reactions  

The Rate-Determining Step for a Multistep Mechanism

Mechanisms with a Slow Initial Step   

Mechanisms with a Fast Initial Step

14.7   Catalysis 

Homogeneous Catalysis 

Heterogeneous Catalysis

A Closer Look Using Spectroscopic Methods to Measure Reaction Rates: Beer’s Law

Chemistry Put To Work Methyl Bromide in the Atmosphere 

Chemistry Put To Work Catalytic Converters  

Chemistry and Life Nitrogen Fixation and Nitrogenase   

15 Chemical Equilibrium

15.1   The Concept of Equilibrium    

15.2   The Equilibrium Constant  

Evaluating K c    

Equilibrium Constants in Terms of Pressure, K p

Equilibrium Constants and Units

15.3   Understanding and Working with Equilibrium Constants  

The Magnitude of Equilibrium Constants

The Direction of the Chemical Equation and K   

Relating Chemical Equation Stoichiometry and Equilibrium Constants

15.4   Heterogeneous Equilibria  

15.5   Calculating Equilibrium Constants

15.6   Applications of Equilibrium Constants

Predicting the Direction of Reaction

Calculating Equilibrium Concentrations

15.7   Le Châtelier’s Principle

Change in Reactant or Product Concentration   

Effects of Volume and Pressure Changes 

Effect of Temperature Changes 

The Effect of Catalysts

Chemistry Put To Work The Haber Process    

A Closer Look Temperature Changes and Le Châtelier’s Principle

Chemistry Put To Work Controlling Nitric Oxide Emissions 

16 Acid—Base Equilibria 

16.1   Arrhenius Acids and Bases

16.2   Brønsted—Lowry Acids and Bases

The H + Ion in Water

Proton-Transfer Reactions   

Conjugate Acid—Base Pairs  

Relative Strengths of Acids and Bases

16.3   The Autoionization of Water   

The Ion Product of Water

16.4   The pH Scale  

pOH and Other “p” Scales    

Measuring pH 

16.5   Strong Acids and Bases 

Strong Acids

Strong Bases  

16.6   Weak Acids

Calculating K a from pH

Percent Ionization  

Using K a to Calculate pH

Polyprotic Acids

16.7   Weak Bases   

Types of Weak Bases 

16.8   Relationship Between K a and K b

16.9   Acid—Base Properties of Salt Solutions 

An Anion’s Ability to React with Water  

A Cation’s Ability to React with Water  

Combined Effect of Cation and Anion in Solution

16.10 Acid—Base Behavior and Chemical Structure

Factors That Affect Acid Strength  

Binary Acids 

Carboxylic Acids   

16.11 Lewis Acids and Bases 

A Closer Look Polyprotic Acids

Chemistry Put To Work Amines and Amine Hydrochlorides 

Chemistry and Life The Amphiprotic Behavior of Amino Acids 

17 Additional Aspects of Aqueous Equilibria  

17.1   The Common-Ion Effect 

17.2   Buffers

Composition and Action of Buffers 

Calculating the pH of a Buffer 

Buffer Capacity and pH Range

Addition of Strong Acids or Bases to Buffers 

17.3   Acid—Base Titrations   

Strong Acid—Strong Base Titrations

Weak Acid—Strong Base Titrations 

Titrating with an Acid—Base Indicator   

Titrations of Polyprotic Acids 

17.4   Solubility Equilibria

The Solubility-Product Constant, K sp

Solubility and K sp

17.5   Factors That Affect Solubility  

The Common-Ion Effect 

Solubility and pH   

Formation of Complex Ions  

Amphoterism  

17.6   Precipitation and Separation of Ions  

Selective Precipitation of Ions 

17.7   Qualitative Analysis for Metallic Elements

Chemistry and Life Blood as a Buffered Solution

A Closer Look Limitations of Solubility Products 

Chemistry and Life Tooth Decay and Fluoridation 

A Closer Look Lead Contamination in Drinking Water

18 Chemistry of the Environment

18.1   Earth’s Atmosphere

Composition of the Atmosphere

Photochemical Reactions in the Atmosphere

Ozone in the Stratosphere

18.2   Human Activities and Earth’s Atmosphere

The Ozone Layer and Its Depletion

Sulfur Compounds and Acid Rain

Nitrogen Oxides and Photochemical Smog

Greenhouse Gases: Water Vapor, Carbon Dioxide, and Climate

18.3   Earth’s Water

The Global Water Cycle

Salt Water: Earth’s Oceans and Seas

Freshwater and Groundwater

18.4   Human Activities and Water Quality

Dissolved Oxygen and Water Quality

Water Purification: Desalination

Water Purification: Municipal Treatment

18.5   Green Chemistry

Supercritical Solvents

Greener Reagents and Processes

A Closer Look Other Greenhouse Gases  

A Closer Look The Ogallala Aquifer–A Shrinking Resource

A Closer Look Fracking and Water Quality

Chemistry and Life Ocean Acidification

19 Chemical Thermodynamics

19.1   Spontaneous Processes

Seeking a Criterion for Spontaneity

Reversible and Irreversible Processes 

19.2   Entropy and the Second Law of Thermodynamics        

The Relationship between Entropy and Heat

 S for Phase Changes  

The Second Law of Thermodynamics  

19.3   The Molecular Interpretation of Entropy and the Third Law of Thermodynamics

Expansion of a Gas at the Molecular Level  

Boltzmann’s Equation and Microstates

Molecular Motions and Energy                                                                                  

Making Qualitative Predictions about  S  

The Third Law of Thermodynamics

19.4   Entropy Changes in Chemical Reactions 

Temperature Variation of Entropy  

Standard Molar Entropies

Calculating the Standard Entropy Change for a Reaction      Entropy Changes in the Surroundings 

19.5   Gibbs Free Energy

Standard Free Energy of Formation    

19.6   Free Energy and Temperature 

19.7   Free Energy and the Equilibrium Constant    

Free Energy under Nonstandard Conditions 

Relationship between  G° and K 

A Closer Look The Entropy Change When a Gas Expands Isothermally

Chemistry and Life Entropy and Human Society

A Closer Look What’s “Free” About Free Energy? 

Chemistry and Life Driving Nonspontaneous Reactions: Coupling Reactions

20 Electrochemistry

20.1   Oxidation States and Oxidation—Reduction Reactions  

20.2   Balancing Redox Equations   

Half-Reactions 

Balancing Equations by the Method of Half-Reactions 

Balancing Equations for Reactions Occurring in Basic Solution  

20.3   Voltaic Cells

20.4   Cell Potentials Under Standard Conditions   

Standard Reduction Potentials

Strengths of Oxidizing and Reducing Agents

20.5   Free Energy and Redox Reactions    

Emf, Free Energy, and the Equilibrium Constant 

20.6   Cell Potentials Under Nonstandard Conditions

The Nernst Equation

Concentration Cells

20.7   Batteries and Fuel Cells 

Lead—Acid Battery 

Alkaline Battery

Nickel—Cadmium and Nickel—Metal Hydride Batteries 

Lithium-Ion Batteries

Hydrogen Fuel Cells 

20.8   Corrosion

Corrosion of Iron (Rusting)   

Preventing Corrosion of Iron 

20.9   Electrolysis

Quantitative Aspects of Electrolysis

A Closer Look Electrical Work 

Chemistry and Life Heartbeats and Electrocardiography

Chemistry Put To Work Batteries for Hybrid and Electric Vehicles

Chemistry Put To Work Electrometallurgy of Aluminum  

21 Nuclear Chemistry 

21.1   Radioactivity and Nuclear Equations 

Nuclear Equations 

Types of Radioactive Decay 

21.2   Patterns of Nuclear Stability   

Neutron-to-Proton Ratio 

Radioactive Decay Chains   

Further Observations

21.3   Nuclear Transmutations 

Accelerating Charged Particles 

Reactions Involving Neutrons

Transuranium Elements 

21.4   Rates of Radioactive Decay   

Radiometric Dating

Calculations Based on Half-Life 

21.5   Detection of Radioactivity  

Radiotracers

21.6   Energy Changes in Nuclear Reactions

Nuclear Binding Energies

21.7   Nuclear Power: Fission

Nuclear Reactors  

Nuclear Waste 

21.8   Nuclear Power: Fusion 

21.9   Radiation in the Environment and Living Systems

Radiation Doses   

Chemistry and Life Medical Applications of Radiotracers     

A Closer Look The Dawning of the Nuclear Age

A Closer Look Nuclear Synthesis of the Elements 

Chemistry and Life Radiation Therapy

22 Chemistry of the Nonmetals

22.1   Periodic Trends and Chemical Reactions 

Chemical Reactions 

22.2   Hydrogen

Isotopes of Hydrogen 

Properties of Hydrogen  

Production of Hydrogen  

Uses of Hydrogen  

Binary Hydrogen Compounds 

22.3   Group 8A: The Noble Gases  

Noble-Gas Compounds  

22.4   Group 7A: The Halogens

Properties and Production of the Halogens  

Uses of the Halogens 

The Hydrogen Halides

Interhalogen Compounds

Oxyacids and Oxyanions

22.5   Oxygen 

Properties of Oxygen

Production of Oxygen 

Uses of Oxygen

Ozone    

Oxides   

Peroxides and Superoxides  

22.6   The Other Group 6A Elements: S, Se, Te, and Po

Occurrence and Production of S, Se, and Te

Properties and Uses of Sulfur, Selenium, and Tellurium

Sulfides  

Oxides, Oxyacids, and Oxyanions of Sulfur  

22.7   Nitrogen

Properties of Nitrogen 

Production and Uses of Nitrogen  

Hydrogen Compounds of Nitrogen

Oxides and Oxyacids of Nitrogen  

22.8   The Other Group 5A Elements: P, As, Sb, and Bi 

Occurrence, Isolation, and Properties of Phosphorus  

Phosphorus Halides 

Oxy Compounds of Phosphorus

22.9   Carbon

Elemental Forms of Carbon  

Oxides of Carbon  

Carbonic Acid and Carbonates

Carbides 

22.10 The Other Group 4A Elements: Si, Ge, Sn, and Pb      

General Characteristics of the Group A Elements

Occurrence and Preparation of Silicon 

Silicates  

Silicones 

22.11 Boron  

A Closer Look The Hydrogen Economy 

Chemistry and Life Nitroglycerin, Nitric Oxide, and Heart Disease

Chemistry and Life Arsenic in Drinking Water

Chemistry Put To Work Carbon Fibers and Composites             

23 Transition Metals and Coordination Chemistry

23.1   The Transition Metals

Physical Properties

Electron Configurations and Oxidation States

23.2   Transition-Metal Complexes

The Development of Coordination Chemistry: Werner’s Theory

The Metal—Ligand Bond

Charges, Coordination Numbers, and Geometries

23.3   Common Ligands in Coordination Chemistry

Metals and Chelates in Living Systems

23.4   Nomenclature and Isomerism in Coordination Chemistry

Structural Isomerism

Stereoisomerism

23.5   Color and Magnetism in Coordination Chemistry

Magnetism of Coordination Compounds

23.6   Crystal-field Theory

Electron Configurations in Octahedral Complexes

Tetrahedral and Square-Planar Complexes

Design an Experiment 

A Closer Look Entropy and the Chelate Effect

Chemistry and Life The Battle for Iron in Living Systems

A Closer Look Charge-Transfer Color

24  The Chemistry of Life: Organic and Biological Chemistry

24.1   General Characteristics of Organic Molecules

The Structures of Organic Molecules  

The Stability of Organic Compounds   

Solubility and Acid—Base Properties of Organic Compounds

24.2   Introduction to Hydrocarbons 

Structures of Alkanes

Structural Isomers 

Nomenclature of Alkanes

Cycloalkanes  

Reactions of Alkanes

24.3   Alkenes, Alkynes, and Aromatic Hydrocarbons 

Alkenes  

Alkynes  

Addition Reactions of Alkenes and Alkynes  

Aromatic Hydrocarbons  

Stabilization of p Electrons by Delocalization

Substitution Reactions of Aromatic Hydrocarbons 

24.4   Organic Functional Groups

Alcohols 

Ethers    

Aldehydes and Ketones 

Carboxylic Acids and Esters 

Amines and Amides 

24.5   Chirality in Organic Chemistry

24.6   Introduction to Biochemistry   

24.7   Proteins 

Amino Acids 

Polypeptides and Proteins   

Protein Structure   

24.8   Carbohydrates

Disaccharides 

Polysaccharides    

24.9   Lipids  

Fats  

Phospholipids  

24.10 Nucleic Acids  

Chemistry Put To Work Gasoline

A Closer Look Mechanism of Addition Reactions

STRATEGIES FOR SUCCESS What Now?

Thermodynamic Quantities for Selected Substances at 298.15 K (25 ° C)             

Standard Reduction Potentials at 25 ° C

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The Authors

Brown  |  lemay  |  bursten  |  murphy  |  woodward  |  stoltzfus.

The Brown / Lemay / Bursten / Murphy / Woodward / Stoltzfus author team values collaboration as an integral component to overall success. While each author brings his or her unique talent, research interests, and teaching experiences, the team works together to review and develop the entire text. It is this collaboration that keeps the content ahead of educational trends and contributes to continuous innovations in teaching and learning throughout the text and technology.

Theodore L. Brown

Theodore l. brown received his ph.d. from michigan state university in 1956. .

Since then, he has been a member of the faculty of the University of Illinois, Urbana-Champaign, where he is now Professor of Chemistry, Emeritus. He served as Vice Chancellor for Research, and Dean of The Graduate College, from 1980 to 1986, and as Founding Director of the Arnold and Mabel Beckman Institute for Advanced Science and Technology from 1987 to 1993. Professor Brown has been an Alfred P. Sloan Foundation Research Fellow and has been awarded a Guggenheim Fellowship. In 1972 he was awarded the American Chemical Society Award for Research in Inorganic Chemistry and received the American Chemical Society Award for Distinguished Service in the Advancement of Inorganic Chemistry in 1993. He has been elected a Fellow of the American Association for the Advancement of Science, the American Academy of Arts and Sciences, and the American Chemical Society.

H. Eugene LeMay, Jr.

H. eugene lemay, jr., received his b.s. degree in chemistry from pacific lutheran university (washington) and his ph.d. in chemistry in 1966 from the university of illinois, urbana-champaign..

He then joined the faculty of the University of Nevada, Reno, where he is currently Professor of Chemistry, Emeritus. He has enjoyed Visiting Professorships at the University of North Carolina at Chapel Hill, at the University College of Wales in Great Britain, and at the University of California, Los Angeles. Professor LeMay is a popular and effective teacher, who has taught thousands of students during more than 40 years of university teaching. Known for the clarity of his lectures and his sense of humor, he has received several teaching awards, including the University Distinguished Teacher of the Year Award (1991) and the first Regents’ Teaching Award given by the State of Nevada Board of Regents (1997).

Bruce E. Bursten

Bruce e. bursten received his ph.d. in chemistry from the university of wisconsin in 1978. .

After two years as a National Science Foundation Postdoctoral Fellow at Texas A&M University, he joined the faculty of The Ohio State University, where he rose to the rank of Distinguished University Professor. In 2005, he moved to the University of Tennessee, Knoxville, as Distinguished Professor of Chemistry and Dean of the College of Arts and Sciences. Professor Bursten has been a Camille and Henry Dreyfus Foundation Teacher-Scholar and an Alfred P. Sloan Foundation Research Fellow, and he is a Fellow of both the American Association for the Advancement of Science and the American Chemical Society. At Ohio State he has received the University Distinguished Teaching Award in 1982 and 1996, the Arts and Sciences Student Council Outstanding Teaching Award in 1984, and the University Distinguished Scholar Award in 1990. He received the Spiers Memorial Prize and Medal of the Royal Society of Chemistry in 2003, and the Morley Medal of the Cleveland Section of the American Chemical Society in 2005. He was President of the American Chemical Society for 2008. In addition to his teaching and service activities, Professor Bursten’s research program focuses on compounds of the transition-metal and actinide elements.

Catherine J. Murphy

Catherine j. murphy received two b.s. degrees, one in chemistry and one in biochemistry, from the university of illinois, urbana-champaign, in 1986. she received her ph.d. in chemistry from the university of wisconsin in 1990. .

She was a National Science Foundation and National Institutes of Health Postdoctoral Fellow at the California Institute of Technology from 1990 to 1993. In 1993, she joined the faculty of the University of South Carolina, Columbia, becoming the Guy F. Lipscomb Professor of Chemistry in 2003. In 2009 she moved to the University of Illinois, Urbana-Champaign, as the Peter C. and Gretchen Miller Markunas Professor of Chemistry. Professor Murphy has been honored for both research and teaching as a Camille Dreyfus Teacher-Scholar, an Alfred P. Sloan Foundation Research Fellow, a Cottrell Scholar of the Research Corporation, a National Science Foundation CAREER Award winner, and a subsequent NSF Award for Special Creativity. She has also received a USC Mortar Board Excellence in Teaching Award, the USC Golden Key Faculty Award for Creative Integration of Research and Undergraduate Teaching, the USC Michael J. Mungo Undergraduate Teaching Award, and the USC Outstanding Undergraduate Research Mentor Award. Since 2006, Professor Murphy has served as a Senior Editor for the Journal of Physical Chemistry. In 2008 she was elected a Fellow of the American Association for the Advancement of Science. Professor Murphy’s research program focuses on the synthesis and optical properties of inorganic nanomaterials, and on the local structure and dynamics of the DNA double helix.

Patrick M. Woodward

Patrick m. woodward received b.s. degrees in both chemistry and engineering from idaho state university in 1991. he received a m.s. degree in materials science and a ph.d. in chemistry from oregon state university in 1996..

He spent two years as a postdoctoral researcher in the Department of Physics at Brookhaven National Laboratory. In 1998, he joined the faculty of the Chemistry Department at The Ohio State University where he currently holds the rank of Professor. He has enjoyed visiting professorships at the University of Bordeaux in France and the University of Sydney in Australia. Professor Woodward has been an Alfred P. Sloan Foundation Research Fellow and a National Science Foundation CAREER Award winner. He currently serves as an Associate Editor to the Journal of Solid State Chemistry and as the director of the Ohio REEL program, an NSF-funded center that works to bring authentic research experiments into the laboratories of first- and second-year chemistry classes in 15 colleges and universities across the state of Ohio. Professor Woodward’s research program focuses on understanding the links between bonding, structure, and properties of solid-state inorganic functional materials.

Matthew W. Stoltzfus

Matthew w. stoltzfus received his b.s. degree in chemistry from millersville university in 2002 and his ph. d. in chemistry in 2007 from the ohio state university..

He spent two years as a teaching postdoctoral assistant for the Ohio REEL program, an NSF-funded center that works to bring authentic research experiments into the general chemistry lab curriculum in 15 colleges and universities across the state of Ohio. In 2009, he joined the faculty of Ohio State where he currently holds the position of Chemistry Lecturer. In addition to lecturing general chemistry, Stoltzfus accepted the Faculty Fellow position for the Digital First Initiative, inspiring instructors to offer engaging digital learning content to students through emerging technology. Through this initiative, he developed an iTunes U general chemistry course, which has attracted over 120,000 students from all over the world. Stoltzfus has received several teaching awards, including the inaugural Ohio State University 2013 Provost’s Award for Distinguished Teaching by a Lecturer and he is recognized as an Apple Distinguished Educator.

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About the Author(s)

THEODORE L. BROWN received his Ph.D. from Michigan State University in 1956. Since then, he has been a member of the faculty of the University of Illinois, Urbana-Champaign, where he is now Professor of Chemistry, Emeritus. He served as Vice Chancellor for Research, and Dean of The Graduate College, from 1980 to 1986, and as Founding Director of the Arnold and Mabel Beckman Institute for Advanced Science and Technology from 1987 to 1993. Professor Brown has been an Alfred P. Sloan Foundation Research Fellow and has been awarded a Guggenheim Fellowship. In 1972 he was awarded the American Chemical Society Award for Research in Inorganic Chemistry and received the American Chemical Society Award for Distinguished Service in the Advancement of Inorganic Chemistry in 1993. He has been elected a Fellow of the American Association for the Advancement of Science, the American Academy of Arts and Sciences, and the American Chemical Society.

H. EUGENE LEMAY, JR., received his B.S. degree in Chemistry from Pacific Lutheran University (Washington) and his Ph.D. in Chemistry in 1966 from the University of Illinois, Urbana-Champaign. He then joined the faculty of the University of Nevada, Reno, where he is currently Professor of Chemistry, Emeritus. He has enjoyed Visiting Professorships at the University of North Carolina at Chapel Hill, at the University College of Wales in Great Britain, and at the University of California, Los Angeles. Professor LeMay is a popular and effective teacher, who has taught thousands of students during more than 40 years of university teaching. Known for the clarity of his lectures and his sense of humor, he has received several teaching awards, including the University Distinguished Teacher of the Year Award (1991) and the first Regents’ Teaching Award given by the State of Nevada Board of Regents (1997).

BRUCE E. BURSTEN received his Ph.D. in Chemistry from the University of Wisconsin in 1978. After two years as a National Science Foundation Postdoctoral Fellow at Texas A&M University, he joined the faculty of The Ohio State University, where he rose to the rank of Distinguished University Professor. In 2005, he moved to the University of Tennessee, Knoxville, as Distinguished Professor of Chemistry and Dean of the College of Arts and Sciences. Professor Bursten has been a Camille and Henry Dreyfus Foundation Teacher-Scholar and an Alfred P. Sloan Foundation Research Fellow, and he is a Fellow of both the American Association for the Advancement of Science and the American Chemical Society. At Ohio State he has received the University Distinguished Teaching Award in 1982 and 1996, the Arts and Sciences Student Council Outstanding Teaching Award in 1984, and the University Distinguished Scholar Award in 1990. He received the Spiers Memorial Prize and Medal of the Royal Society of Chemistry in 2003, and the Morley Medal of the Cleveland Section of the American Chemical Society in 2005. He was President of the American Chemical Society for 2008. In addition to his teaching and service activities, Professor Bursten’s research program focuses on compounds of the transition-metal and actinide elements.

CATHERINE J. MURPHY received two B.S. degrees, one in Chemistry and one in Biochemistry, from the University of Illinois, Urbana-Champaign, in 1986. She received her Ph.D. in Chemistry from the University of Wisconsin in 1990. She was a National Science Foundation and National Institutes of Health Postdoctoral Fellow at the California Institute of Technology from 1990 to 1993. In 1993, she joined the faculty of the University of South Carolina, Columbia, becoming the Guy F. Lipscomb Professor of Chemistry in 2003. In 2009 she moved to the University of Illinois, Urbana-Champaign, as the Peter C. and Gretchen Miller Markunas Professor of Chemistry. Professor Murphy has been honored for both research and teaching as a Camille Dreyfus Teacher-Scholar, an Alfred P. Sloan Foundation Research Fellow, a Cottrell Scholar of the Research Corporation, a National Science Foundation CAREER Award winner, and a subsequent NSF Award for Special Creativity. She has also received a USC Mortar Board Excellence in Teaching Award, the USC Golden Key Faculty Award for Creative Integration of Research and Undergraduate Teaching, the USC Michael J. Mungo Undergraduate Teaching Award, and the USC Outstanding Undergraduate Research Mentor Award. Since 2006, Professor Murphy has served as a Senior Editor for the Journal of Physical Chemistry. In 2008 she was elected a Fellow of the American Association for the Advancement of Science. Professor Murphy’s research program focuses on the synthesis and optical properties of inorganic nanomaterials, and on the local structure and dynamics of the DNA double helix.

PATRICK M. WOODWARD received B.S. degrees in both Chemistry and Engineering from Idaho State University in 1991. He received a M.S. degree in Materials Science and a Ph.D. in Chemistry from Oregon State University in 1996. He spent two years as a postdoctoral researcher in the Department of Physics at Brookhaven National Laboratory. In 1998, he joined the faculty of the Chemistry Department at The Ohio State University where he currently holds the rank of Professor. He has enjoyed visiting professorships at the University of Bordeaux in France and the University of Sydney in Australia. Professor Woodward has been an Alfred P. Sloan Foundation Research Fellow and a National Science Foundation CAREER Award winner. He currently serves as an Associate Editor to the Journal of Solid State Chemistry and as the director of the Ohio REEL program, an NSF-funded center that works to bring authentic research experiments into the laboratories of first- and second-year chemistry classes in 15 colleges and universities across the state of Ohio. Professor Woodward’s research program focuses on understanding the links between bonding, structure, and properties of solid-state inorganic functional materials.

MATTHEW W. STOLTZFUS received his B.S. degree in Chemistry from Millersville University in 2002 and his Ph. D. in Chemistry in 2007 from The Ohio State University. He spent two years as a teaching postdoctoral assistant for the Ohio REEL program, an NSF-funded center that works to bring authentic research experiments into the general chemistry lab curriculum in 15 colleges and universities across the state of Ohio. In 2009, he joined the faculty of Ohio State where he currently holds the position of Chemistry Lecturer. In addition to lecturing general chemistry, Stoltzfus accepted the Faculty Fellow position for the Digital First Initiative, inspiring instructors to offer engaging digital learning content to students through emerging technology. Through this initiative, he developed an iTunes U general chemistry course, which has attracted over 120,000 students from all over the world. Stoltzfus has received several teaching awards, including the inaugural Ohio State University 2013 Provost’s Award for Distinguished Teaching by a Lecturer and he is recognized as an Apple Distinguished Educator.

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