CliffsNotes Chemistry Practice Pack (CliffsNotes (Paperback)) - Softcover

Henrickson, Charles H.

Softcover

ISBN 10: 0470495952 ISBN 13: 9780470495957

Publisher: John Wiley & Sons Ltd, 2010

Synopsis

About the Contents: Pretest Helps you pinpoint where you need the most help Topic Area Reviews * Measurement and Units of Measurement * Matter: Elements, Compounds, and Mixtures * Atoms I - The Basics * Formulas and Names of Ionic Compounds, Acids, and Bases * The Mole - Elements and Compounds * Percent Composition and Empirical and Molecular Formulas * Chemical Reactions and Chemical Equations * Calculations Using Balanced Equations * Atoms II - Atomic Structure and Periodic Properties * Chemical Bonding - The Formation of Compounds * Gases and the Gas Laws * The Forces between Molecules - Solids and Liquids * Solutions and Solution Composition * Acids, Bases, and Neutralization Glossary Customized Full-Length Exam Covers all subject areas * Pretest that pinpoints what you need to study most * Clear, concise reviews of every topic * Targeted example problems in every chapter with solutions and explanations * Customized full-length exam that adapts to your skill level

About this title

About the Author

Charles Henrickson, Ph.D., is a retired professor of Chemistry at Western Kentucky University.

Excerpt. © Reprinted by permission. All rights reserved.

CliffsNotes Chemistry Practice Pack

By Charles Henrickson

John Wiley & Sons

Copyright © 2010 John Wiley & Sons, Ltd
All right reserved.
ISBN: 978-0-470-49595-7

Chapter One

Measurement and Units of Measurement

At the core of any science is measurement. Being able to measure volumes, pressures, masses, and temperatures as well as the ability to count atoms and molecules allows chemists to understand nature more precisely. Modern science uses the International System of Units (SI) that was adopted worldwide in 1960. The metric system of measurement, which is consistent with the International System, is widely used in chemistry and is the principal system used in this book.

Chemists often have to work with numbers that are very, very small or very, very large. It is more convenient to express numbers of this kind in scientific notation, so that is the first topic to look at in this chapter.

Writing Numbers in Scientific Notation

It is likely that you have already seen numbers expressed in scientific notation on your calculator. With only 8 or 9 spaces to display numbers, calculators must resort to scientific notation to show very small or very large numbers. In scientific notation a number is expressed in this form

a x [10.sup.p]

where "a" is a number between 1 and 10 (often a decimal number) and "p" is a positive or negative whole number written as an exponent on 10, often called the power of 10. The average distance from the earth to the sun is 93,000,000 miles, a very large number. In scientific notation this would be 9.3 x [10.sup.7] miles. The power of 7 equals the number of places a decimal point would be moved from the right end of 93,000,000 to the left to get an "a" value between 1 and 10 (9.3). The [10.sup.7] term equals 10,000,000 (10 x 10 x 10 x 10 x 10 x 10 x 10) and when multiplied by 9.3 would restate the original number in conventional form.

9.3 x [10.sup.7] miles = 9.3 x 10,000,000 miles = 93,000,000 miles

Likewise, the year 1492 would be written 1.492 x [10.sup.3] in scientific notation.

Small numbers, those less than 1, are handled in a similar way, except the decimal point has to be moved to the right to get an "a" value between 1 and 10, and the "p" exponent is a negative number. For example, an atom of gold has a diameter of 0.000000342 meter. The decimal must be moved 7 places to the right to get 3.42, and the number is stated as 3.42 x [10.sup.-7] meter in scientific notation. The [10.sup.-7] term equals 1 divided by 10,000,000.

3.42 x [10.sup.-7] meter = 3.42 x 1/10,000,000 meter = 0.000000342 meter

Similarly, the number 0.000045 would be written 4.5 x [10.sup.5].

One last thing: If you are given a number between 1 and 10 and need to write it in scientific notation, the power on 10 would be zero. In scientific notation, the number 8 would be written 8 x [10.sup.0]. In mathematics, [10.sup.0] equals 1.

Example Problems

1. Express these numbers in scientific notation.

(a) 22,500,000

Answer: 2.25 x [10.sup.7]

This is a large number, so the decimal is moved 7 places to the left to form 2.25, and 7 is written as a positive exponent on 10.

(b) 0.0006

Answer: 6 x [10.sup.4]

This is a small number, so the decimal must be moved 4 places to the right to form 6, and 4 is written as a negative exponent on 10.

(c) 602,200,000,000,000,000,000,000

Answer: 6.022 x [10.sup.23]

This is a very large number, so the decimal is moved 23 places to the left to form 6.022, and 23 is written as a positive exponent on 10.

2. Express these numbers in conventional form.

(a) 6.35 x [10.sup.5]

Answer: 635,000

The power of 10 is 5, a positive number, so the decimal point is moved 5 places to the right. (b) 2.4 x [10.sup.-3]

Answer: 0.0024

The power of 10 is -3, a negative number, so the decimal point is moved 3 places to the left.

Work Problems

1. Express these numbers in scientific notation.

(a) 1945 (b) 0.00000255 (c) 388000000000 (d) 0.023

2. Express these numbers in conventional form: (a) 7.55 x [10.sup.-4] (b) 8.80 x [10.sup.2]

Worked Solutions

1. (a) 1.945 x [10.sup.3]. Because this is a large number, the decimal is moved 3 places to the left to form 1.945. The exponent on 10 is 3.

(b) 2.55 x [10.sup.-6]. This is a small number, so the decimal is moved 6 places to the right to form 2.55. The exponent on 10 is -6.

(c) 3.88 x [10.sup.11]. This is a large number, so the decimal is moved 11 places to the left to form 3.88. The exponent on 10 is 11.

(d) 2.3 x [10.sup.-2]. Because this is a small number, the decimal is moved 2 places to the right to form 2.3. The exponent on 10 is -2.

2. (a) 0.000755. The power of 10 is -4, a negative number, so the decimal point is moved 4 places to the left.

(b) 880. The power of 10 is 2, a positive number, so the decimal point is moved 2 places to the right.

Significant Figures and Rounding Off Numbers

It is not possible to measure anything exactly; there will always be some amount of uncertainty. In many cases, the tool used to do the measurement causes the uncertainty. An inexpensive laboratory balance, for example, measures the mass of a gold ring to be 2.83 grams, while a more expensive analytical balance measures the mass to a greater accuracy, 2.8275 grams. The greater accuracy of the analytical balance is reflected in the larger number of digits in the numerical value of the mass. In either number, 2.83 or 2.8275, the right-most digit is the only digit that is not known with certainty. The mass of the ring is closer to 2.83 grams than to 2.82 or 2.84 grams on the first balance (2.83 0.01), and closer to 2.8275 grams than to 2.8274 or 2.8276 grams on the second (2.8275 0.0001). In both cases, all the digits are certain except the last one. The number of digits shown in a measured value (the certain digits + the one uncertain digit) indicates the accuracy of that value. These digits are referred to as significant digits or, more commonly, significant figures (sig. figs.).

Counting Significant Figures

You need to know how to count the number of significant figures in a number, because they affect the way answers are stated in calculations. Zeros can be a problem. A zero may or may not be significant depending on how it is used. To handle this "zero problem," follow this set of six rules:

Rule 1. All nonzero digits (1, 2, 3, 4, 5, 6, 7, 8, and 9) are always significant and must be counted.

Rule 2. A zero standing alone to the left of a decimal point is not significant. For example, in 0.63 and 0.0055, the 0 to the left of the decimal only helps you see the decimal point. It has no other use.

Rule 3. For a number less than 1, any zeros between the decimal point and the first nonzero digit are not significant. These zeros are simply placing the decimal point. The zeros in bold type in 0.00457 and 0.0000864 are not significant. Both numbers have three significant figures: 457 in the first number and 864 in the second.

Rule 4. A zero between two nonzero digits is significant. In 2.0056 and 0.0040558, both numbers have 5 significant figures. Because the second number is less than 1, only the 4, 0, 5, 5, and 8 are significant. Rule 5. If the number has a decimal point, any zeros at the end of the number are significant. Both of these numbers have 4 significant figures: 4.500 and 0.01380. Rule 6. If the number does not have a decimal point, like 1,500, the zeros at the end of the number may or may not be significant. If they are significant, place a decimal after the last zero, as in 1,500., or the number could be written in scientific notation, 1.500 x [10.sup.3]. Otherwise, 1,500 means the value is 1,500 100 with 2 significant figures, the 1 and 5. For any number written in scientific notation, all digits in the first part of the number are significant. Both 1,500. and 1.500 x [10.sup.3] show 4 significant figures.

Example Problems

Count the number of significant figures in each of these numbers.

1. 2.054

Answer: 4

The zero between two nonzero digits is counted (Rule 4) along with the 2, 5, and 4.

2. 0.00399

Answer: 3

The zeros between the decimal and the 3 are not counted (Rule 3), so only the 3, 9, and 9 are significant.

3. 0.99800

Answer: 5

The two zeros following the 8 are counted (Rule 5), so five digits are significant.

4. 6.014 x [10.sup.-3]

Answer: 4

The zero is counted (Rule 4), so all four digits are significant.

5. 6,500

Answer: 2

At most, 2 significant figures. 6,500 without a decimal indicates 6,500 100 (Rule 6).

Work Problems

Count the number of significant figures in these numbers.

(a) 93.082 (b) 0.00059 (c) 4.520 (d) 1.0 x [10.sup.6] (e) 120,000.

Worked Solutions

(a) 5. All digits are significant; the zero is counted (Rule 4).

(b) 2. The 5 and 9 are significant; the zeros place the decimal (Rule 3).

(c) 4. All digits are significant; the zero is counted (Rule 5).

(d) 2. All digits in the non-exponential part of a number written in scientific notation are significant (Rule 1 and Rule 5).

(e) 6. The decimal tells us all digits are significant (Rule 6).

Rounding Off Numbers

In calculations, we often obtain answers that have more digits than can be justified considering significant figures. This is a major problem when using calculators. Removing the digits that are not significant from the answer is called rounding off. Here are three rules to guide you:

Rule 1. If the next digit after those you want to retain is 4 or less, drop that digit and all that follow and keep the digits that remain. Rounding to three figures: 3.253 -> 3.25 | 3 -> 3.25 Rule 2. If the next digit after those you want to retain is 5 or greater, drop that digit and all that follow, and then increase the last retained digit by 1. This is sometimes called rounding up. Rounding to three figures: 6.3466 -> 6.34 | 66 -> 6.35 Rule 3. If the number to be rounded is less than 1 with zeros between the decimal point and the first nonzero digit (like 0.0004638), consider only the numerals that follow the zeros when counting digits. Rounding to three figures: 0.0004638 -> 0.000463 | 8 -> 0.000464

Example Problems

1. Round off 45,317 to 2 digits and express the answer in scientific notation.

Answer: 4.5 x [10.sup.4]

Separating the first 2 digits (45|317) shows the next digit to be 3. It and the following digits are dropped (Rule 1), leaving 45,000.

2. Round off 368 to 2 digits and express the answer in scientific notation.

Answer: 3.7 x [10.sup.2]

The digit following the first 2 digits is greater than 5 (36|8). It is dropped, and 6 is increased to 7.

3. Round off 0.00941 to 1 digit and express the answer in scientific notation.

Answer: 9 x [10.sup.3]

Consider only the digits following the zeros. Separating 1 digit from the rest (0.009|41) shows the next digit, 4, and all that follow can be dropped.

Work Problems

Round off each number to the indicated number of significant figures, shown in parentheses, and express the answer in scientific notation.

(a) 55,583 (4) (b) 38,953 (2) (c) 0.007665 (2)

Worked Solutions

(a) 5.558 x [10.sup.4]

55,58 | 3; Rule 1 applies; drop the 3, keep the rest.

(b) 3.9 x [10.sup.4]

38|953; Rule 2 applies; 38 is rounded up to 39 since the next digit is greater than 4.

(c) 7.7 x [10.sup.-3]

0.0076|65; Both Rules 2 and 3 apply, and 0.0076 is rounded up to 0.0077.

Significant Figures in Calculations

Keeping track of the number of significant figures in calculations depends on the kind of calculation you are doing.

Multiplication and division: The product or quotient can have no more significant figures than the number with the smallest number of significant figures used in the calculation.

Addition and subtraction: The sum or difference can have no more places after the decimal than there are in the number with the smallest number of digits after the decimal.

In addition and subtraction, those places after the decimal that are of unknown value (?) negate the numerals in those same places in the other numbers used in the calculation.

Example: 3.45762 <- five places after the decimal are known

+ 4.32??? <- only 2 places after the decimal are known

Here is how these two numbers are added. 3.45762 is rounded off to two places after the decimal: 3.45762 -> 3.45|762 -> 3.46

It is then added to the other number.

3.46 + 4.32 7.78

Example Problems

1. 1,949 6.33 =

Answer: 308

There are 4 significant figures in 1,949 and 3 in 6.33, so the answer can have no more than 3 significant figures.

2. 34.238442 + 9.35 =

Answer: 43.59

The answer can only have 2 digits after the decimal. 34.238442 is rounded up to 34.24 and added to 9.35.

3. 19.42 - (8.5 x [10.sup.-3]) =

Answer: 19.41

Start by writing 8.5 x [10.sup.-3] in conventional form, 0.0085. Only 2 digits after the decimal are allowed. 0.0085 is rounded up to 0.01 and then subtracted from 19.42.

Work Problems

1. 64.33 x 2.1416 =

2. 64.362 - 4.2 =

3. 19 - (3.3 x [10.sup.-2]) =

Worked Solutions

1. 138.0

The 4 significant figures in 64.33 limit the answer to 4 figures.

2. 60.2

Answer is limited to 1 digit after the decimal. 64.362 is rounded up to 64.4, and 4.2 is subtracted from it.

3. 19

3.3 x [10.sup.-2] = 0.033. There are no digits after the decimal in 19, so subtracting 0.033 has no affect on 19.

Calculators and Significant Figures

You use a calculator to do your math chores, but calculators know nothing about significant figures. Calculators blindly grind out all the digits they can show, so it is up to you to get rid of the unnecessary digits and round off the number. If you divide 1.0 by 3.0 (both have 2 significant figures), the calculator gives 0.333333333. You need to round off this answer to 2 significant figures: 0.33|3333333 becomes 0.33, the correct answer with 2 significant figures.

Example Problems

Use your calculator to do each calculation and state the answer in scientific notation with the correct number of significant figures.

1. 600.3 / 0.22 = Answer: 2.7 x [10.sup.3]

Use 2 significant figures. The calculator display, 27|28.636364, becomes 2,700 when rounded to 2 significant figures. The decimal is moved 3 places left to write the answer in scientific notation.

2. 3.1416 6.52 =

Answer: 2.05 x [10.sup.1]

Use 3 significant figures. 2.04|83232 x [10.sup.1] is rounded up to the correct answer.

Work Problems

1. 0.443 9 =

2. 33.0 10.466 =

Worked Solutions

Use your calculator to do each calculation and state the answer in scientific notation with the correct number of significant figures.

1. 5 x [10.sup.-2]

Use 1 significant figure. 0.04|92222222 is rounded up to 0.05, and the decimal moved 2 places right.

2. 3.15 x [10.sup.0]

Use 3 significant figures. 3.15|306707 could be stated correctly as 3.15, forgoing scientific notation.

(Continues...)

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Edition details

• Publisher: John Wiley & Sons Ltd
• Publication date: 2010
• Language: English
• ISBN 10: 0470495952
• ISBN 13: 9780470495957
• Binding: Paperback
• Number of pages: 360