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**Chemistry: Atoms First**

Julia Burdge & Jason Overby Chapter 1 Chemistry: The Science of Change Kent L. McCorkle Cosumnes River College Sacramento, CA 1 1

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**Chemistry: The Science of Change**

1 Chemistry: The Science of Change 1.1 The Study of Chemistry Chemistry You May Already Know The Scientific Method 1.2 Classification of Matter States of Matter Mixtures 1.3 The Properties of Matter Physical Properties Chemical Properties Extensive and Intensive Properties 1.4 Scientific Measurement SI Base Units Mass Temperature Derived Units: Volume and Density 1.5 Uncertainty in Measurement Significant Figures Calculations with Measured Numbers Accuracy and Precision 1.6 Using Units and Solving Problems Conversion Factors Dimensional Analysis Tracking Units 2

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The Study of Chemistry 1.1 Chemistry is the study of matter and the changes that matter undergoes. Matter is anything that has mass and occupies space. 3

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The Study of Chemistry Scientists follow a set of guidelines known as the scientific method: gather data via observations and experiments identify patterns or trends in the collected data summarize their findings with a law formulate a hypothesis with time a hypothesis may evolve into a theory 4

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**Classification of Matter**

1.2 Chemists classify matter as either a substance or a mixture of substances. A substance is a form of matter that has definite composition and distinct properties. Examples: salt (sodium chloride), iron, water, mercury, carbon dioxide, and oxygen Substances differ from one another in composition and may be identified by appearance, smell, taste, and other properties. A mixture is a physical combination of two or more substances. A homogeneous mixture is uniform throughout. Also called a solution. Examples: seawater, apple juice A heterogeneous mixture is not uniform throughout. Examples: trail mix, chicken noodle soup 5

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**Classification of Matter**

All substances can, in principle, exist as a solid, liquid or gas. We can convert a substance from one state to another without changing the identity of the substance. 6

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**Classification of Matter**

Solid particles are held closely together in an ordered fashion. Solids do not conform to the shape of their container. Liquids do conform to the shape of their container. Liquid particles are close together but are not held rigidly in position. Gases assume both the shape and volume of their container. Gas particles have significant separation from each other and move freely. 7

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**Classification of Matter**

A mixture can be separated by physical means into its components without changing the identities of the components. 8

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**1.3 The Properties of Matter**

There are two general types of properties of matter: 1) Quantitative properties are measured and expressed with a number. 2) Qualitative properties do not require measurement and are usually based on observation. 9

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**The Properties of Matter**

A physical property is one that can be observed and measured without changing the identity of the substance. Examples: color, melting point, boiling point A physical change is one in which the state of matter changes, but the identity of the matter does not change. Examples: changes of state (melting, freezing, condensation) 10

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**The Properties of Matter**

A chemical property is one a substance exhibits as it interacts with another substance. Examples: flammability, corrosiveness A chemical change is one that results in a change of composition; the original substances no longer exist. Examples: digestion, combustion, oxidation 11

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**The Properties of Matter**

An extensive property depends on the amount of matter. Examples: mass, volume An intensive property does not depend on the amount of matter. Examples: temperature, density 12

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**1.4 Scientific Measurement**

Properties that can be measured are called quantitative properties. A measured quantity must always include a unit. The English system has units such as the foot, gallon, pound, etc. The metric system includes units such as the meter, liter, kilogram, etc. 13

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**There are seven SI base units**

The revised metric system is called the International System of Units (abbreviated SI Units) and was designed for universal use by scientists. There are seven SI base units 14

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SI Base Units The magnitude of a unit may be tailored to a particular application using prefixes. 15

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**Mass is a measure of the amount of matter in an object or sample. **

Because gravity varies from location to location, the weight of an object varies depending on where it is measured. But mass doesn’t change. The SI base unit of mass is the kilogram (kg), but in chemistry the smaller gram (g) is often used. 1 kg = 1000 g = 1×103 g Atomic mass unit (amu) is used to express the masses of atoms and other similar sized objects. 1 amu = ×10-24 g 16

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**There are two temperature scales used in chemistry: **

The Celsius scale (°C) Freezing point (pure water): 0°C Boiling point (pure water): 100°C The Kelvin scale (K) The “absolute” scale Lowest possible temperature: 0 K (absolute zero) K = °C 17

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Worked Example 1.1 Normal human body temperature can range over the course of a day from about 36°C in the early morning to about 37°C in the afternoon. Express these two temperatures and the range that they span using the Kelvin scale. Strategy Use K = °C to convert temperatures from Celsius to Kelvin. Solution 36°C = 309 K 37°C = 310 K What range do they span? 310 K K = 1 K Depending on the precision required, the conversion from °C to K is often simply done by adding 273, rather than Think About It Remember that converting a temperature from °C to K is different from converting a range or difference in temperature from °C to K. 18

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**Temp in °F = ( ×temp in °C ) + 32°F**

Temperature The Fahrenheit scale is common in the United States. Freezing point (pure water): 32°C Boiling point (pure water): 212°C There are 180 degrees between freezing and boiling in Fahrenheit (212°F-32°F) but only 100 degrees in Celsius (100°C-0°C). The size of a degree on the Fahrenheit scale is only of a degree on the Celsius scale. Temp in °F = ( ×temp in °C ) + 32°F 19

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**Temp in °F = ( × temp in °C ) + 32°F**

Worked Example 1.2 A body temperature above 39°C constitutes a high fever. Convert this temperature to the Fahrenheit scale. Strategy We are given a temperature and asked to convert it to degrees Fahrenheit. We will use the equation below: Temp in °F = ( × temp in °C ) + 32°F Solution Temp in °F = ( × 39°C ) + 32°F Temp in °F = 102°F Think About It Knowing that normal body temperature on the Fahrenheit scale is approximately 98.6°F, 102°F seems like a reasonable answer. 20

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**Derived Units: Volume and Density**

There are many units (such as volume) that require units not included in the base SI units. The derived SI unit for volume is the meter cubed (m3). A more practical unit for volume is the liter (L). 1 dm3 = 1 L 1 cm3 = 1 mL Comp: Replace with new Figure 1.8 21

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**Derived Units: Volume and Density**

The density of a substance is the ratio of mass to volume. d = density m = mass V = volume SI-derived unit: kilogram per cubic meter (kg/m3) Other common units: g/cm3 (solids) g/mL (liquids) g/L (gases) 22

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Worked Example 1.3 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 0°C, 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 0°C. Strategy (a) Determine density by dividing mass by volume, and (b) use the calculated density to determine the volume occupied by the given mass. Solution (a) A cube has three equal sides so the volume is (2.0 cm)3, or 8.0 cm3 d = (b) Rearranging d = m/V to solve for volume gives V = m/d V = 7.36 g 8.0 cm3 = 0.92 g/cm3 23 g 0.92 g/cm3 = 25 cm3 Think About It For a sample with a density less than 1 g/cm3, the number of cubic centimeters should be greater than the number of grams. In this case, 25 cm3 > 23 g. 23

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**1.5 Uncertainty in Measurement**

There are two types of numbers used in chemistry: 1) Exact numbers: are those that have defined values 1 kg = 1000 g 1 dozen = 12 objects are those determined by counting 28 students in a class 2) Inexact numbers: measured by any method other than counting length, mass, volume, time, speed, etc. 24

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**Uncertainty in Measurement**

An inexact number must be reported so as to indicate its uncertainty. Significant figures are the meaningful digits in a reported number. The last digit in a measured number is referred to as the uncertain digit. When using the top ruler to measure the memory card, we could estimate 2.5 cm. We are certain about the 2, but we are not certain about the 5. The uncertainty is generally considered to be + 1 in the last digit. cm Comp: Replace with new Fig 1.9 25

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**Uncertainty in Measurement**

When using the bottom ruler to measure the memory card, we might record 2.45 cm. Again, we estimate one more digit than we are certain of. Comp: Replace with new Fig 1.9 cm 26

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**1) Any nonzero digit is significant.**

Significant Figures The number of significant figures can be determined using the following guidelines: 1) Any nonzero digit is significant. 2) Zeros between nonzero digits are significant. 3) Zeros to the left of the first nonzero digit are not significant. 112.1 4 significant figures 305 3 significant figures 50.08 4 significant figures 0.0023 2 significant figure 1 significant figure 27

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Significant Figures The number of significant figures can be determined using the following guidelines: 4) Zeros to the right of the last nonzero digit are significant if a decimal is present. 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. 1.200 4 significant figures 100 1, 2, or 3 – ambiguous 28

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Worked Example 1.4 Determine the number of significant figures in the following measurements: (a) 443 cm, (b) g, (c) kg, (d) 3.000×10-7 L, (e) 50 mL, (f) m. Strategy Zeros are significant between nonzero digits or after a nonzero digit with a decimal. Zeros may or may not be significant if they appear to the right of a nonzero digit without a decimal. Solution (a) 443 cm (b) g (c) kg (d) x 10-7 L (e) 50 mL (f) m 3 S.F. 4 S.F. 3 S.F. 4 S.F. 1 or 2, ambiguous 4 S.F. Think About It Be sure that you have identified zeros correctly as either significant or not significant. They are significant in (b) and (d); they are not significant in (c); it is not possible to tell in (e); and the number in (f) contains one zero that is significant, and one that is not. 29

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**Calculations with Measured Numbers**

In addition and subtraction, the answer cannot have more digits to the right of the decimal point than any of the original numbers. 102.50 143.29 123.19 ← two digits after the decimal point ← three digits after the decimal point ← round to two digits after the decimal point, ← two digits after the decimal point ← one digit after the decimal point ← round to one digit after the decimal point, 123.2 30

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**Calculations with Measured Numbers**

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. 1.4×8.011 = 11.57/ = ← fewest significant figures is 2, so round to 11 2 S.F. 4 S.F. ← fewest significant figures is 4, so round to 4 S.F. 5 S.F. 31

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**Calculations with Measured Numbers**

Exact numbers can be considered to have an infinite number of significant figures and do not limit the number of significant figures in a result. Example: Three pennies each have a mass of 2.5 g. What is the total mass? 3×2.5 = 7.5 g Exact (counting number) Inexact (measurement) 32

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**Rounding after each step**

Calculations with Measured Numbers In calculations with multiple steps, round at the end of the calculation to reduce any rounding errors. Do not round after each step. Compare the following: Rounding after each step Rounding at end 1) 3.66×8.45 = 30.9 2) 30.9×2.11 = 65.2 1) 3.66×8.45 = 30.93 2) 30.93×2.11 = 65.3 In general, keep at least one extra digit until the end of a multistep calculation. 33

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Worked Example 1.5 Perform the following arithmetic operations and report the result to the proper number of significant figures: (a) mL mL, (b) L – L, (c) 13.5 g ÷ L, (d) 6.25 cm x cm, (e) 5.46x102 g x103 g Strategy Apply the rules for significant figures in calculations, and round each answer to the appropriate number of digits. Solution (a) mL mL mL (b) L L L ← round to mL ← round to L 34

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Worked Example 1.5 (cont.) Perform the following arithmetic operations and report the result to the proper number of significant figures: (a) mL mL, (b) L – L, (c) 13.5 g ÷ L, (d) 6.25 cm x cm, (e) 5.46x102 g x103 g Strategy Apply the rules for significant figures in calculations, and round each answer to the appropriate number of digits. 3 S.F. Solution (c) 13.5 g 45.18 L (d) 6.25 cm×1.175 cm = g/L ← round to g/L 4 S.F. = cm2 ← round to 7.34 cm2 3 S.F. 4 S.F. 35

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Worked Example 1.5 (cont.) Perform the following arithmetic operations and report the result to the proper number of significant figures: (a) mL mL, (b) L – L, (c) 13.5 g ÷ L, (d) 6.25 cm x cm, (e) 5.46x102 g x103 g Strategy Apply the rules for significant figures in calculations, and round each answer to the appropriate number of digits. Solution (e) x 102 g x 102 g 55.37 x 102 g = x 103 g Think About It Changing the answer to correct scientific notation doesn’t change the number of significant figures, but in this case it changes the number of places past the decimal place. 36

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Worked Example 1.6 An empty container with a volume of x 102 cm3 is weighed and found to have a mass of g. The container is filled with a gas and reweighed. The mass of the container and the gas is g. Determine the density of the gas to the appropriate number of significant figures. 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. Solution g – g mass of gas = g density = ← one place past the decimal point (two sig figs) 1.9 g 9.850 x 102 cm3 = g/cm3 ← round to g/cm3 Think About It In this case, although each of the three numbers we started with has four significant figures, the solution only has two significant figures. 37

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**Accuracy and Precision**

Accuracy tells us how close a measurement is to the true value. Precision tells us how close a series of replicate measurements are to one another. Good accuracy and good precision Poor accuracy but good precision 38 Poor accuracy and poor precision

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**Accuracy and Precision**

Three students were asked to find the mass of an aspirin tablet. The true mass of the tablet is g. Student A: Results are precise but not accurate Student B: Results are neither precise nor accurate Student C: Results are both precise and accurate 39

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**1.6 Using Units and Solving Problems**

A conversion factor is a fraction in which the same quantity is expressed one way in the numerator and another way in the denominator. For example, 1 in = 2.54 cm, may be written: 1 in 2.54 cm 2.54 cm 1 in or 40

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**Dimensional Analysis – Tracking Units**

The use of conversion factors in problem solving is called dimensional analysis or the factor-label method. Example: Convert inches to meters. 12.00 in × Which conversion factor will cancel inches and give us centimeters? The result contains 4 sig figs because the conversion, a definition, is exact. = cm 1 in 2.54 cm 2.54 cm 1 in or 41

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Worked Example 1.7 The Food and Drug Administration (FDA) recommends that dietary sodium intake be no more than 2400 mg per day. Strategy The necessary conversion factors are derived from the equalities 1 g = 1000 mg and 1 lb = g. 1 g 1000 mg 1000 mg 1 g 1 lb 453.6 g 453.6 g 1 lb or or Solution 2400 mg × 1 g 1000 mg 1 lb 453.6 g × = lb Think About It Make sure that the magnitude of the result is reasonable and that the units have canceled properly. If we had mistakenly multiplied by 1000 and instead of dividing by them, the result (2400 mg×1000 mg/g×453.6 g/lb = 1.089×109 mg2/lb) would be unreasonably large and the units would not have canceled properly. 42

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Worked Example 1.8 An average adult has 5.2 L of blood. What is the volume of blood in cubic meters? Strategy 1 L = 1000 cm3 and 1 cm = 1x10-2 m. 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. Solution 5.2 L × 3 1000 cm3 1 L 1 x 10-2 m 1 cm × = 5.2 x 10-3 m3 Think About It Based on the preceding conversion factors, 1 L = 1×10-3 m3. Therefore, 5 L of blood would be equal to 5×10-3 m3, which is close to the calculated answer. 43

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**1 Chapter Summary: Key Points The Scientific Method States of Matter**

Substances Mixtures Physical Properties Chemical Properties Extensive and Intensive Properties SI Base Units Mass Temperature Volume and Density Significant Figures 44

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**12 inches = 1 foot (exactly) 1 mile = 5280 feet (exactly)**

Group Quiz #1 Dimensional Analysis: One lap in an olympic swimming pool is 50 meters exactly (2 sig figs). If an athlete swims 81 laps in one practice, how far did he/she swim (in miles)? 1 inch = 2.54 cm (exactly) 12 inches = 1 foot (exactly) 1 mile = 5280 feet (exactly) 45 45

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