Chapter 1

Chapter 1

Chemistry Fourth Edition Julia Burdge Lecture PowerPoints Chapter 1 Chemistry: The Central Science Copyright McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. CHAPTER 1 Chemistry: The Central Science

1.1The Study of Chemistry 1.2Classification of Matter 1.3Scientific Measurement 1.4The Properties of Matter 1.5Uncertainty in Measurement 1.6Using Units and Solving Problems 2 Copyright McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 1.1 The Study of Chemistry Topics Chemistry You May Already Know

The Scientific Method 3 Copyright McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 1.1 The Study of Chemistry (1) Chemistry You May Already Know Chemistry is the study of matter and the changes that matter undergoes. Matter is what makes up our bodies, our belongings, our physical environment, and in fact our universe. Matter is anything that has mass and occupies space. Copyright McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 4

1.1 The Study of Chemistry (2) Chemistry You May Already Know Steve Allen/Getty The McGraw-Hill Companies, Inc./Charles D. Winters, photographer Stockbyte/PunchStock Copyright McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 5 1.1 The Study of Chemistry (3) The Scientific Method

Copyright McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 6 1.1 The Study of Chemistry (4) The Scientific Method Copyright McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 7 1.1 The Study of Chemistry (5)

The Scientific Method Copyright McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 8 1.2 Classification of Matter Topics States of Matter Elements Compounds Mixtures Copyright McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 9

1.2 Classification of Matter (1) States of Matter Chemists classify matter as either a substance or a mixture of substances. A substance may be further categorized as either an element or a compound. A substance is a form of matter that has a definite (constant) composition and distinct properties. Examples are salt (sodium chloride), iron, water, mercury, carbon dioxide, and oxygen. Copyright McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 10 1.2 Classification of Matter (2)

States of Matter Substances can be either elements (such as iron, mercury, and oxygen) or compounds (such as salt, water, and carbon dioxide). Copyright McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 11 1.2 Classification of Matter (3) States of Matter All substances can, in principle, exist as a solid, a liquid, and a gas, the three physical states . Solids and liquids sometimes are referred to collectively as the condensed phases. Liquids and gases sometimes are referred to collectively as

fluids. Copyright McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 12 1.2 Classification of Matter (4) States of Matter The McGraw-Hill Companies, Inc./Charles D. Winters, photographer Copyright McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 13 1.2

Classification of Matter (5) Elements An element is a substance that cannot be separated into simpler substances by chemical means. Copyright McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 14 1.2 Classification of Matter (6) Compounds Most elements can combine with other elements to form compounds. A compound is a substance composed

of atoms of two or more elements chemically united in fixed proportions. A compound cannot be separated into simpler substances by any physical process. Copyright McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 15 1.2 Classification of Matter (7) Mixtures A mixture is a combination of two or more substances in which the substances retain their distinct identities.

Like pure substances, mixtures can be solids, liquids, or gases. Copyright McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 16 1.2 Classification of Matter (8) Mixtures Mixtures are either homogeneous or heterogeneous. When we dissolve a teaspoon of sugar in a glass of water, we get a homogeneous mixture because the composition of the mixture is uniform throughout. If we mix sand with iron filings, however, the sand and the

iron filings remain distinct and discernible from each other. This type of mixture is called a heterogeneous mixture because the composition is not uniform. Copyright McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 17 1.2 Classification of Matter (9) Mixtures Copyright McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 18

1.3 Scientific Measurement Topics SI Base Units Mass Temperature Derived Units: Volume and Density Copyright McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 19 1.3 Scientific Measurement (1) SI Base Units TABLE 1.2

Base SI Units Base Quantity Name of Unit Symbol Length meter m Mass

kilogram kg Time second s Electric current ampere A

Temperature kelvin K Amount of substance mole mol Luminous intensity candela

cd Copyright McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 20 1.3 Scientific Measurement (2) SI Base Units TABLE1.3Prefixes Used with SI Units Prefix Symbol Meaning Example

Tera- T (1,000,000,000,000) 1 teragram (Tg) = g Giga- G (1,000,000,000) 1 gigawatt (GW) = W

Mega- M (1,000,000) 1 megahertz (MHz) =Hz Kilo- k (1,000) 1 kilometer (km) = m

Deci- d (0.1) 1 deciliter (dL) = L Centi- c (0.01) 1 centimeter (cm) = m

Milli- m (0.001) 1 millimeter (mm) = m (0.000001) 1 microliter () = L MicroNano- n

1 (0.000000001) 1 nanosecond (ns) = s Pico- P (0.000000000001) 1 picogram (pg) = g Copyright McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 21

1.3 Scientific Measurement (3) Mass Mass is a measure of the amount of matter in an object or sample. 3 1 kg=1000 g=1 10 g Copyright McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 22 1.3 Scientific Measurement (4) Temperature

There are two temperature scales used in chemistry. The Celsius scale was originally defined using the freezing point and the boiling point of pure water at sea level. The SI base unit of temperature is the kelvin. Kelvin is known as the absolute temperature scale, meaning that the lowest temperature possible is 0 K, a temperature referred to as absolute zero. Copyright McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 23 1.3 Scientific Measurement (5) Temperature Units of the Celsius and Kelvin scales are equal in magnitude, so a degree Celsius is equivalent to a kelvin.

K = C +273.15 Copyright McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 24 SAMPLE PROBLEM 1.1 Strategy Normal human body temperature can range over the course of the day from about in the early morning to about in the afternoon. Express these two temperatures and the range that they span using the Kelvin scale.

Strategy Use to convert temperatures from the Celsius scale to the Kelvin scale. Then convert the range of temperatures from degrees Celsius to kelvin, keeping in mind that is equivalent to 1 K. Copyright McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 25 SAMPLE PROBLEM 1.1 Solution Solution The range of is equal to a range of 1 K.

Copyright McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 26 1.3 Scientific Measurement(6) Temperature 5C temperatureCelsius=(temperatureFahrenheit 32 F) 9 F 9F temperatureFahrenheit= (temperaturedegreesCelsius)+32 F 5C

Copyright McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 27 SAMPLE PROBLEM 1.2 Strategy A body temperature above constitutes a high fever. Convert this temperature to the Fahrenheit scale. Strategy We are given a temperature in Celsius and are asked to convert it to Fahrenheit. Setup

9 F temperatureFahrenheit= (temperatureCelsius)+32 F 5C Copyright McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 28 SAMPLE PROBLEM 1.2 Solution Solution

9 F temperatureFahrenheit= 39 C +32=102.2 F 5C Copyright McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 29 1.3 Scientific Measurement (7) Derived Units: Volume and Density There are many quantities, such as volume and density, that require units not included in the base SI units. In these cases, we must combine base units to derive appropriate units for the quantity. The derived SI unit for volume, the meter cubed (m3), is a

larger volume than is practical in most laboratory settings. Copyright McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 30 1.3 Scientific Measurement (8) Derived Units: Volume and Density The more commonly used metric unit, the liter (L), is derived by cubing the decimeter (one-tenth of a meter) and is therefore also

referred to as the cubic decimeter (dm3). Copyright McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 31 1.3 Scientific Measurement (9) Derived Units: Volume and Density Density is the ratio of mass to volume. Copyright McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 32 SAMPLE PROBLEM

1.3Strategy Ice cubes float in a glass of water because solid water is less dense than liquid water. (a) Calculate the density of ice given that, at , a cube that is 2.0 cm on each side has a mass of 7.36 g, and (b) determine the volume occupied by 23 g of ice at . Strategy (c) Determine density by dividing mass by volume. (d) use the calculated density to determine the volume occupied by the given mass. Copyright McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 33

SAMPLE PROBLEM 1.3 Setup Setup (a) We are given the mass of the ice cube, but we must calculate its volume from the dimensions given. The volume of the ice cube is , or . (b) Rearranging the density equation to solve for volume gives . Copyright McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 34

SAMPLE PROBLEM 1.3 Solution Solution (a) or (b) or Copyright McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 35

1.4 The Properties of Matter Topics Physical Properties Chemical Properties Extensive and Intensive Properties Copyright McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 36 1.4 The Properties of Matter (1) Physical Properties Substances are identified by their properties as well as by their composition. Properties of a sub- stance may be quantitative (measured

and expressed with a number) or qualitative (not requiring explicit measurement). A physical property is one that can be observed and measured without changing the identity of a substance. Copyright McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 37 1.4 The Properties of Matter (2) Physical Properties Melting is a physical change; one in which the state of matter changes, but the identity of the matter does not change. We can recover the original ice by cooling the water until it freezes. Therefore, the melting point of a substance is a physical

property. Copyright McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 38 1.4 The Properties of Matter (3) Chemical Properties The statement Hydrogen gas burns in oxygen gas to form water describes a chemical property of hydrogen, because to observe this property we must carry out a chemical change burning in oxygen (combustion), in this case. After a chemical change, the original substance (hydrogen gas

in this case) will no longer exist. What remains is a different substance (water, in this case). We cannot recover the hydrogen gas from the water by means of a physical process, such as boiling or freezing. Copyright McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 39 1.4 The Properties of Matter (4) Extensive and Intensive Properties All properties of matter are either extensive or intensive. The measured value of an extensive property depends on the amount of matter.

Mass is an extensive property. The value of an intensive property does not depend on the amount of matter. Density and temperature are intensive properties. Copyright McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 40 SAMPLE PROBLEM 1.4 The diagram in (a) shows a compound made up of atoms of two elements (represented by the green and red spheres) in the liquid state. Which of the diagrams in (b) to (d) represent a physical

change, and which diagrams represent a chemical change? Copyright McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 41 SAMPLE PROBLEM 1.4 Strategy Strategy A physical change does not change the identity of a substance, whereas a chemical change does change the identity of a substance. Copyright McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.

42 SAMPLE PROBLEM 1.4Solution Solution Diagrams (b) and (c) represent chemical changes. Diagram (d) represents a physical change. Copyright McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 43 1.5 Uncertainty in Measurement

Topics Significant Figures Calculations with Measured Numbers Accuracy and Precision 44 Copyright McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 1.5 Uncertainty in Measurement (1) Significant Figures Chemistry makes use of two types of numbers: exact and inexact. Exact numbers include numbers with defined values, such as 2.54 in the definition 1 inch (in) = 2.54 cm 1000 in the definition 1 kg = 1000 g 12 in the definition 1 dozen = 12 objects.

Numbers measured by any method other than counting are inexact. Copyright McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 45 1.5 Uncertainty in Measurement (2) Significant Figures An inexact number must be reported in such a way as to indicate the uncertainty in its value. This is done using significant figures. Significant figures are the meaningful digits in a reported number.

Copyright McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 46 1.5 Uncertainty in Measurement (3) Significant Figures The number of significant figures in any number can be determined using the following guidelines: 1. Any digit that is not zero is significant (112.1 has four significant figures). 2. Zeros located between nonzero digits are significant (305 has three significant figures, and 50.08 has four significant figures). Copyright McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.

47 1.5 Uncertainty in Measurement (4) Significant Figures The number of significant figures in any number can be determined using the following guidelines: 3. Zeros to the left of the first nonzero digit are not significant (0.0023 has two significant figures, and 0.000001 has one significant figure). 4. Zeros to the right of the last nonzero digit are significant if the number contains a decimal point (1.200 has four significant figures Copyright McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 48

1.5 Uncertainty in Measurement (5) Significant Figures The number of significant figures in any number can be determined using the following guidelines: 5. Zeros to the right of the last nonzero digit in a number that does not contain a decimal point may or may not be significant (100 may have one, two, or three significant figuresit is impossible to tell without additional information. Copyright McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 49

1.5 Uncertainty in Measurement(6) Significant Figures To avoid ambiguity in such cases, it is best to express such numbers using scientific notation [Appendix 1]. two significant figures three significant figures Copyright McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 50 SAMPLE PROBLEM 1.5

Determine the number of significant figures in the following measurements: (a) (b) (c) (d) (e) (f) 443 cm 15.03 g 0.0356 kg 3.000 3 L 50 mL 0.9550 m

Copyright McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 51 SAMPLE PROBLEM 1.5 Strategy Strategy All nonzero digits are significant, so the goal will be to determine which of the zeros is significant. Setup Zeros are significant if they appear between nonzero digits or if they appear after a nonzero digit in a number that contains a decimal point. Zeros may or may not be significant if they appear to the right

of the last nonzero digit in a number that does not contain a decimal point. Copyright McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 52 SAMPLE PROBLEM Solution (a) (b) (c) (d) (e) (f) 1.5

Solution 443 cm 15.03 g 0.0356 kg 3.000 3 L 50 mL 0.9550 m (a) 3; (b) 4; (c) 3; (d) 4; (e) 1 or 2, an ambiguous case; (f) 4 Copyright McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 53

1.5 Uncertainty in Measurement (7) Calculations with Measured Numbers 1. In addition and subtraction, the answer cannot have more digits to the right of the decimal point than the original number with the smallest number of digits to the right of the decimal point. Copyright McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 54 1.5 Uncertainty in Measurement (8) Calculations with Measured Numbers If the leftmost digit to be dropped is less than 5, round down. If the leftmost digit to be dropped is equal to or greater than

5, round up. Copyright McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 55 1.5 Uncertainty in Measurement (9) Calculations with Measured Numbers 2. In multiplication and division, the number of significant figures in the final product or quotient is determined by the original number that has the smallest number of significant figures. Copyright McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 56

1.5 Uncertainty in Measurement (10) Calculations with Measured Numbers 3. Exact numbers can be considered to have an infinite number of significant figures and do not limit the number of significant figures in a calculated result. 3 2.5 g=7.5 g Copyright McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 57

1.5 Uncertainty in Measurement (11) Calculations with Measured Numbers 4. In calculations with multiple steps, rounding the result of each step can result in rounding error. In general, it is best to retain at least one extra digit until the end of a multistep calculation to minimize rounding error. Copyright McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 58 SAMPLE PROBLEM

1.6 Strategy Perform the following arithmetic operations and report the result to the proper number of significant figures: (a) (b) (c) (d) 317.5 mL + 0.675 mL 47.80 L 2.075 L 13.5 g 45.18 L 6.25 cm 1.175 cm

Strategy Apply the rules for significant figures in calculations, and round each answer to the appropriate number of digits. Copyright McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 59 SAMPLE PROBLEM 1.6 Setup Setup (a)

(b) (c) (d) 317.5 mL + 0.675 mL 47.80 L 2.075 L 13.5 g 45.18 L 6.25 cm 1.175 cm (a) The answer will contain one digit to the right of the decimal point to match 317.5, which has the fewest digits to the right of the decimal point. (b) The answer will contain two digits to the right of the decimal point to match 47.80. Copyright McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.

60 SAMPLE PROBLEM 1.6 Setup, Cont. Setup (a) (b) (c) (d) 317.5 mL + 0.675 mL 47.80 L 2.075 L 13.5 g 45.18 L 6.25 cm 1.175 cm

(c) The answer will contain three significant figures to match 13.5, which has the fewest number of significant figures in the calculation. (d) The answer will contain three significant figures to match 6.25. Copyright McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 61 SAMPLE PROBLEM 1.6Setup, Cont.1 Setup (a)

(b) (c) (d) 317.5 mL + 0.675 mL 47.80 L 2.075 L 13.5 g 45.18 L 6.25 cm 1.175 cm (e) To add numbers expressed in scientific notation, first write both numbers to the same power of 10. That is, = , so the answer will contain two digits to the right of the decimal point (when multiplied by ) to match both 5.46 and 49.91. Copyright McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.

62 SAMPLE PROBLEM 1.6 Solution Solution (a) 317.5 mL (b) 47.80 L 075 L (c) (d) Copyright McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.

63 SAMPLE PROBLEM 1.6 Solution, Cont. Solution (e) Copyright McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 64 SAMPLE PROBLEM

1.7 An empty container with a volume of is weighed and found to have a mass of 124.6 g. The container is filled with a gas and reweighed. The mass of the container and the gas is 126.5 g. Determine the density of the gas to the appropriate number of significant figures. Copyright McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 65 SAMPLE PROBLEM

1.7 Strategy Strategy This problem requires two steps: subtraction to determine the mass of the gas, and division to determine its density. Apply the corresponding rule regarding significant figures to each step. Setup Thus, in the division of the mass of the gas by the volume of the container, the result can have only two significant figures. Copyright McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.

66 SAMPLE PROBLEM 1.7Solution Solution mass of gas= Copyright McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 67 1.5

Uncertainty in Measurement (12) Accuracy and Precision Accuracy tells us how close a measurement is to the true value. Precision tells us how close multiple measurements of the same thing are to one another. Copyright McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 68 1.5 Uncertainty in Measurement (13)

Accuracy and Precision Copyright McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 69 1.5 Uncertainty in Measurement (14) Accuracy and Precision Copyright McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 70

1.6 Using Units and Solving Problems Topics Conversion Factors Dimensional AnalysisTracking Units 71 Copyright McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 1.6 Using Units and Solving Problem (1) Conversion Factors A conversion factor is a fraction in which the same quantity is expressed one way in the numerator and another way in the denominator. Because both forms of this conversion factor are equal to 1, we can multiply a quantity by either form without changing

the value of that quantity. Copyright McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 72 1.6 Using Units and Solving Problems (2) Conversion Factors 2.54 cm 12.00 1=30.48 cm Copyright McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 73

1.6 Using Units and Solving Problems (3) Dimensional AnalysisTracking Units The use of conversion factors in problem solving is called dimensional analysis or the factor-label method. 2.54 cm 12.00 1m 1 =0.3048 m 100 cm Copyright McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 74

SAMPLE PROBLEM 1.8 Strategy The Food and Drug Administration (FDA) recommends that dietary sodium intake be no more than 2400 mg per day. What is this mass in pounds (lb), if 1 lb = 453.6 g? Strategy This problem requires a two-step dimensional analysis, because we must convert milligrams to grams and then grams to pounds. Assume the number 2400 has four significant figures. Copyright McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 75

SAMPLE PROBLEM 1.8 Setup Setup The necessary conversion factors are derived from the equalities 1 g = 1000 mg and 1 lb = 453.6 g. or and or Solution

Copyright McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 76 SAMPLE PROBLEM 1.9Strategy An average adult has 5.2 L of blood. What is the volume of blood in cubic meters? Strategy Convert liters to cubic centimeters and then cubic centimeters to cubic meters. Setup When a unit is raised to a power, the corresponding conversion factor must also be raised to that power in order

for the units to cancel appropriately. Copyright McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 77 SAMPLE PROBLEM 1.9Solution Solution Copyright McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 78

SAMPLE PROBLEM 1.4 - Appendix The diagram in (a) shows a compound made up of atoms of two elements (represented by the green and red spheres) in the liquid state. Which of the diagrams in (b) to (d) represent a physical change, and which diagrams represent a chemical change? Copyright McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 79 1.5 Uncertainty in Measurement (12) Appendix Accuracy and Precision

Accuracy tells us how close a measurement is to the true value. Precision tells us how close multiple measurements of the same thing are to one another. Copyright McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 80

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