Chemistry Workbook For Dummies®, 3rd Edition with Online Practice

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Library of Congress Control Number: 2017932047

ISBN 978-1-119-35745-2 (pbk); ISBN 978-1-119-35746-9 (ebk); ISBN 978-1-119-35747-6 (ebk)

About This Book

When you’re fixed in the thickets of stoichiometry or bogged down by buffered solutions, you’ve got little use for rapturous poetry about the atomic splendor of the universe. What you need is a little practical assistance. Subject by subject, problem by problem, this book extends a helping hand to pull you out of the thickets and bogs.

The topics covered in this book are the topics most often covered in a first-year chemistry course in high school or college. The focus is on problems — problems like the ones you may encounter in homework or on exams. We give you just enough theory to grasp the principles at work in the problems. Then we tackle example problems. Then you tackle practice problems. The best way to succeed at chemistry is to practice. Practice more. And then practice even more. Watching your teacher do the problems or reading about them isn’t enough. Michael Jordan didn’t develop a jump shot by watching other people shoot a basketball. He practiced. A lot. Using this workbook, you can, too (but chemistry, not basketball).

This workbook is modular. You can pick and choose those chapters and types of problems that challenge you the most; you don’t have to read this book cover to cover if you don’t want to. If certain topics require you to know other topics in advance, we tell you so and point you in the right direction. Most importantly, we provide a worked-out solution and explanation for every problem.

Icons Used in This Book

You’ll find a selection of helpful icons nicely nestled along the margins of this workbook. Think of them as landmarks, familiar signposts to guide you as you cruise the highways of chemistry.

Within already pithy summaries of chemical concepts, passages marked by this icon represent the pithiest must-know bits of information. You’ll need to know this stuff to solve problems.

Sometimes there’s an easy way and a hard way. This icon alerts you to passages intended to highlight an easier way. It’s worth your while to linger for a moment. You may find yourself nodding quietly as you jot down a grateful note or two.

Chemistry may be a practical science, but it also has its pitfalls. This icon raises a red flag to direct your attention to easily made errors or other tricky items. Pay attention to this material to save yourself from needless frustration.

Within each section of a chapter, this icon announces, “Here ends theory” and “Let the practice begin.” Alongside the icon is an example problem that employs the very concept covered in that section. An answer and explanation accompany each practice problem.

Where to Go from Here

Where you go from here depends on your situation and your learning style:

• If you’re currently enrolled in a chemistry course, you may want to scan the table of contents to determine what material you’ve already covered in class and what you’re covering right now. Use this book as a supplement to clarify things you don’t understand or to practice concepts that you’re struggling with.
• If you’re brushing up on forgotten chemistry, scan the chapters for example problems. As you read through them, you’ll probably have one of two responses: 1) “Ahhh, yes … I remember that” or 2) “Oooh, no … I so do not remember that.” Let your responses guide you.
• If you’re just beginning a chemistry course, you can follow along in this workbook, using the practice problems to supplement your homework or as extra pre-exam practice. Alternatively, you can use this workbook to preview material before you cover it in class, sort of like a spoonful of sugar to help the medicine go down.
• If you bought this book a week before your final exam and are just now trying to figure out what this whole “chemistry” thing is about, well, good luck. The best way to start in that case is to determine what exactly is going to be on your exam and to study only those parts of this book. Due to time constraints or the proclivities of individual teachers/professors, not everything is covered in every chemistry class.

No matter the reason you have this book in your hands now, there are three simple steps to remember:

1. Don’t just read it; do the practice problems.
2. Don’t panic.
3. Do more practice problems.

Anyone can do chemistry given enough desire, focus, and time. Keep at it, and you’ll get an element on the periodic table named after you soon enough.

Using Exponential and Scientific Notation to Report Measurements

Because chemistry concerns itself with ridiculously tiny things like atoms and molecules, chemists often find themselves dealing with extraordinarily small or extraordinarily large numbers. Numbers describing the distance between two atoms joined by a bond, for example, run in the ten-billionths of a meter. Numbers describing how many water molecules populate a drop of water run into the trillions of trillions.

To make working with such extreme numbers easier, chemists turn to scientific notation, which is a special kind of exponential notation. Exponential notation simply means writing a number in a way that includes exponents. In scientific notation, every number is written as the product of two numbers, a coefficient and a power of 10. In plain old exponential notation, a coefficient can be any value of a number multiplied by a power with a base of 10 (such as 10⁴). But scientists have rules for coefficients in scientific notation. In scientific notation, the coefficient is always at least 1 and always less than 10. For example, the coefficient could be 7, 3.48, or 6.0001.

To convert a very large or very small number to scientific notation, move the decimal point so it falls between the first and second digits. Count how many places you moved the decimal point to the right or left, and that’s the power of 10. If you moved the decimal point to the left, the exponent on the 10 is positive; to the right, it’s negative. (Here’s another easy way to remember the sign on the exponent: If the initial number value is greater than 1, the exponent will be positive; if the initial number value is between 0 and 1, the exponent will be negative.)

To convert a number written in scientific notation back into decimal form, just multiply the coefficient by the accompanying power of 10.

Multiplying and Dividing in Scientific Notation

A major benefit of presenting numbers in scientific notation is that it simplifies common arithmetic operations. The simplifying abilities of scientific notation are most evident in multiplication and division. (As we note in the next section, addition and subtraction benefit from exponential notation but not necessarily from strict scientific notation.)

To multiply two numbers written in scientific notation, multiply the coefficients and then add the exponents. To divide two numbers, simply divide the coefficients and then subtract the exponent of the denominator (the bottom number) from the exponent of the numerator (the top number).

Using Exponential Notation to Add and Subtract

Addition or subtraction gets easier when you express your numbers as coefficients of identical powers of 10. To wrestle your numbers into this form, you may need to use coefficients less than 1 or greater than 10. So scientific notation is a bit too strict for addition and subtraction, but exponential notation still serves you well.

To add two numbers easily by using exponential notation, first express each number as a coefficient and a power of 10, making sure that 10 is raised to the same exponent in each number. Then add the coefficients. To subtract numbers in exponential notation, follow the same steps but subtract the coefficients.

Distinguishing between Accuracy and Precision

Accuracy and precision, precision and accuracy … same thing, right? Chemists everywhere gasp in horror, reflexively clutching their pocket protectors — accuracy and precision are different!

• Accuracy: Accuracy describes how closely a measurement approaches an actual, true value.
• Precision: Precision, which we discuss more in the next section, describes how close repeated measurements are to one another, regardless of how close those measurements are to the actual value. The bigger the difference between the largest and smallest values of a repeated measurement, the less precision you have.

The two most common measurements related to accuracy are error and percent error:

• Error: Error measures accuracy, the difference between a measured value and the actual value:

  

• Percent error: Percent error compares error to the size of the thing being measured:

  

  

  Being off by 1 meter isn’t such a big deal when measuring the altitude of a mountain, but it’s a shameful amount of error when measuring the height of an individual mountain climber.

Expressing Precision with Significant Figures

When you know how to express your numbers in scientific notation and how to distinguish between precision and accuracy (we cover both topics earlier in this chapter), you can bask in the glory of a new skill: using scientific notation to express precision. The beauty of this system is that simply by looking at a measurement, you know just how precise that measurement is.

When you report a measurement, you should include digits only if you’re really confident about their values. Including a lot of digits in a measurement means something — it means that you really know what you’re talking about — so we call the included digits significant figures. The more significant figures (sig figs) in a measurement, the more accurate that measurement must be. The last significant figure in a measurement is the only figure that includes any uncertainty, because it’s an estimate. Here are the rules for deciding what is and what isn’t a significant figure:

• Any nonzero digit is significant. So 6.42 contains three significant figures.
• Zeros sandwiched between nonzero digits are significant. So 3.07 contains three significant figures.
• Zeros on the left side of the first nonzero digit are not significant. So 0.0642 and 0.00307 each contain three significant figures.
• One or more final zeros (zeros that end the measurement) used after the decimal point are significant. So 1.760 has four significant figures, and 1.7600 has five significant figures. The number has only four significant figures because the first zeros are not final.

• When a number has no decimal point, any zeros after the last nonzero digit may or may not be significant. So in a measurement reported as 1,370, you can’t be certain whether the 0 is a certain value or is merely a placeholder.

  Be a good chemist. Report your measurements in scientific notation to avoid such annoying ambiguities. (See the earlier section “Using Exponential and Scientific Notation to Report Measurements” for details on scientific notation.)

• If a number is already written in scientific notation, then all the digits in the coefficient are significant. So the number has five significant figures due to the five digits in the coefficient.
• Numbers from counting (for example, 1 kangaroo, 2 kangaroos, 3 kangaroos) or from defined quantities (say, 60 seconds per 1 minute) are understood to have an unlimited number of significant figures. In other words, these values are completely certain.

The number of significant figures you use in a reported measurement should be consistent with your certainty about that measurement. If you know your speedometer is routinely off by 5 miles per hour, then you have no business protesting to a policeman that you were going only 63.2 mph in a 60 mph zone.

Doing Arithmetic with Significant Figures

Doing chemistry means making a lot of measurements. The point of spending a pile of money on cutting-edge instruments is to make really good, really precise measurements. After you’ve got yourself some measurements, you roll up your sleeves, hike up your pants, and do some math.

When doing math in chemistry, you need to follow some rules to make sure that your sums, differences, products, and quotients honestly reflect the amount of precision present in the original measurements. You can be honest (and avoid the skeptical jeers of surly chemists) by taking things one calculation at a time, following a few simple rules. One rule applies to addition and subtraction, and another rule applies to multiplication and division.

• Adding or subtracting: Round the sum or difference to the same number of decimal places as the measurement with the fewest decimal places. Rounding like this is honest, because you’re acknowledging that your answer can’t be any more precise than the least-precise measurement that went into it.
• Multiplying or dividing: Round the product or quotient so that it has the same number of significant figures as the least-precise measurement — the measurement with the fewest significant figures.

Notice the difference between the two rules. When you add or subtract, you assign significant figures in the answer based on the number of decimal places in each original measurement. When you multiply or divide, you assign significant figures in the answer based on the smallest number of significant figures from your original set of measurements.

Caught up in the breathless drama of arithmetic, you may sometimes perform multi-step calculations that include addition, subtraction, multiplication, and division, all in one go. No problem. Follow the normal order of operations, doing multiplication and division first, followed by addition and subtraction. At each step, follow the simple significant-figure rules, and then move on to the next step.

Answers to Questions on Noting Numbers Scientifically

The following are the answers to the practice problems in this chapter.

1. . Move the decimal point immediately after the 2 to create a coefficient between 1 and 10. Because you’re moving the decimal point five places to the left, multiply the coefficient, 2, by the power 10⁵.
2. . Move the decimal point immediately after the 8 to create a coefficient between 1 and 10. You’re moving the decimal point four places to the left, so multiply the coefficient, 8.0736, by the power 10⁴.
3. . Move the decimal point immediately after the 2 to create a coefficient between 1 and 10. You’re moving the decimal point five spaces to the right, so multiply the coefficient, 2, by the power 10^–5.
4. 690.3. You need to understand scientific notation to change the number back to regular decimal form. Because 10² equals 100, multiply the coefficient, 6.903, by 100. This moves the decimal point two spaces to the right.
5. . First, multiply the coefficients: . Then multiply the powers of 10 by adding the exponents: . The raw calculation yields , which converts to the given answer when you express it in scientific notation.
6. . The ease of math with scientific notation shines through in this problem. Dividing the coefficients yields a coefficient quotient of , and dividing the powers of 10 (by subtracting their exponents) yields a quotient of . Marrying the two quotients produces the given answer, already in scientific notation.
7. 1.8. First, convert each number to scientific notation: and . Next, multiply the coefficients: . Then add the exponents on the powers of 10: . Finally, join the new coefficient with the new power: . Expressed in scientific notation, this answer is . Looking back at the original numbers, you see that both factors have only two significant figures; therefore, you have to round your answer to match that number of sig figs, making it 1.8.
8. . First, convert each number to scientific notation: and . Then divide the coefficients: . Next, subtract the exponent on the denominator from the exponent of the numerator to get the new power of 10: . Join the new coefficient with the new power: . Finally, express gratitude that the answer is already conveniently expressed in scientific notation.
9. . Because the numbers are each already expressed with identical powers of 10, you can simply add the coefficients: . Then join the new coefficient with the original power of 10.
10. . Because the numbers are each expressed with the same power of 10, you can simply subtract the coefficients: . Then join the new coefficient with the original power of 10.
11. (or an equivalent expression). First, convert the numbers so they each use the same power of 10: and . Here, we use 10^–3, but you can use a different power as long as the power is the same for each number. Next, add the coefficients: . Finally, join the new coefficient with the shared power of 10.
12. (or an equivalent expression). First, convert the numbers so each uses the same power of 10: and . Here, we’ve picked 10², but any power is fine as long as the two numbers have the same power. Then subtract the coefficients: . Finally, join the new coefficient with the shared power of 10.
13. Reginald’s measurement incurred the greater magnitude of error, and Dagmar’s measurement incurred the greater percent error. Reginald’s scale reported with an error of , and Dagmar’s scale reported with an error of . Comparing the magnitudes of error, you see that 19 pounds is greater than 12 pounds. However, Reginald’s measurement had a percent error of , while Dagmar’s measurement had a percent error of .

14. Jeweler A’s official average measurement was 0.864 grams, and Jeweler B’s official measurement was 0.856 grams. You determine these averages by adding up each jeweler’s measurements and then dividing by the total number of measurements, in this case 3. Based on these averages, Jeweler B’s official measurement is more accurate because it’s closer to the actual value of 0.856 grams.

    However, Jeweler A’s measurements were more precise because the differences between A’s measurements were much smaller than the differences between B’s measurements. Despite the fact that Jeweler B’s average measurement was closer to the actual value, the range of his measurements (that is, the difference between the largest and the smallest measurements) was 0.041 grams (). The range of Jeweler A’s measurements was 0.010 grams ().

    This example shows how low-precision measurements can yield highly accurate results through averaging of repeated measurements. In the case of Jeweler A, the error in the official measurement was . The corresponding percent error was . In the case of Jeweler B, the error in the official measurement was . Accordingly, the percent error was 0%.

15. The correct number of significant figures is as follows for each measurement: a) 5, b) 3, and c) 4.

16. a) “ gram” is an improperly reported measurement because the reported value, 893.7, suggests that the measurement is certain to within a few tenths of a gram. The reported error is known to be greater, at gram. The measurement should be reported as “ gram.”

    b) “ gram” is improperly reported because the reported value, 342, gives the impression that the measurement becomes uncertain at the level of grams. The reported error makes clear that uncertainty creeps into the measurement only at the level of hundredths of a gram. The measurement should be reported as “ gram.”

17. 114.36 seconds. The trick here is remembering to convert all measurements to the same power of 10 before comparing decimal places for significant figures. Doing so reveals that seconds goes to the hundredths of a second, despite the fact that the measurement contains only two significant figures. The raw calculation yields 114.359 seconds, which rounds properly to the hundredths place (taking significant figures into account) as 114.36 seconds, or seconds in scientific notation.

18. inches. Here, you have to recall that defined quantities (1 foot is defined as 12 inches) have unlimited significant figures. So your calculation is limited only by the number of significant figures in the measurement 345.6 feet. When you multiply 345.6 feet by 12 inches per foot, the feet cancel, leaving units of inches:

    

    The raw calculation yields 4,147.2 inches, which rounds properly to four significant figures as 4,147 inches, or inches in scientific notation.

19. minutes. Here, it helps here to convert all measurements to the same power of 10 so you can more easily compare decimal places in order to assign the proper number of significant figures. Doing so reveals that minutes goes to the hundred-thousandths of a minute, and 0.009 minutes goes to the thousandths of a minute. The raw calculation yields minutes, which rounds properly to the thousandths place (taking significant figures into account) as minutes, or minutes in scientific notation.

20. 2.81 feet. Following standard order of operations, you can do this problem in two main steps, first performing multiplication and division and then performing addition and subtraction.

    Following the rules of significant-figure math, the first step yields . Each product or quotient contains the same number of significant figures as the number in the calculation with the fewest number of significant figures.

    After completing the first step, divide by 10.0 feet to finish the problem:

    

    You write the answer with three sig figs because the measurement 10.0 feet contains three sig figs, which is the smallest available between the two numbers.

Building Derived Units from Base Units

Chemists aren’t satisfied with measuring length, mass, temperature, and time alone. On the contrary, chemistry often deals in calculated quantities. These kinds of quantities are expressed with derived units, which are built from combinations of base units.

• Area (for example, catalytic surface): , and area has units of length squared (square meters, or m², for example).

• Volume (of a reaction vessel, for example): You calculate volume by using the familiar formula . Because length, width, and height are all length units, you end up with , or a length cubed (for example, cubic meters, or m³).

  The most common way of representing volume in chemistry is by using liters (L). You can treat the liter like you would any other metric base unit by adding prefixes to it, such as milli- or deci-.

• Density (of an unidentified substance): Density, arguably the most important derived unit to a chemist, is built by using the basic formula .

  In the SI system, mass is measured in kilograms. The standard SI units for mass and length were chosen by the Scientific Powers That Be because many objects that you encounter in everyday life have masses between 1 and 100 kilograms and have dimensions on the order of 1 meter. Chemists, however, are most often concerned with very small masses and dimensions; in such cases, grams and centimeters are much more convenient. Therefore, the standard unit of density in chemistry is grams per cubic centimeter (g/cm³) rather than kilograms per cubic meter.

  The cubic centimeter is exactly equal to 1 milliliter, so densities are also often expressed in grams per milliliter (g/mL).

• Pressure (of gaseous reactants, for example): Pressure units are derived using the formula . The SI units for force and area are newtons (N) and square meters (m²), so the SI unit of pressure, the pascal (Pa), can be expressed as .