Chemical Calculations Chapter 3 Measurement and Chemical Calculations Presentation Slides to Accompany Cracolice/Peters Introductory Chemistry: An Active Learning Approach, Third Edition Copyright © 2007 Brooks/Cole, a part of the Thomson Corporation.

Section 3.1 Introduction to Measurement Presentation Slides to Accompany Cracolice/Peters Introductory Chemistry: An Active Learning Approach, Third Edition Copyright © 2007 Brooks/Cole, a part of the Thomson Corporation.

Comparison of the dimensions, quantity, or capacity of something Measure: Comparison of the dimensions, quantity, or capacity of something with a standard Presentation Slides to Accompany Cracolice/Peters Introductory Chemistry: An Active Learning Approach, Third Edition Copyright © 2007 Brooks/Cole, a part of the Thomson Corporation.

To answer this question, you compare your height with a standard: How tall are you? To answer this question, you compare your height with a standard: In the United States, feet and inches (centimeters elsewhere in the world) Presentation Slides to Accompany Cracolice/Peters Introductory Chemistry: An Active Learning Approach, Third Edition Copyright © 2007 Brooks/Cole, a part of the Thomson Corporation.

Measurements everywhere in the world, with the exception of the U.S., are made in the metric system SI units are a subset of all metric units SI is an abbreviation for the French name for the International System of Units Presentation Slides to Accompany Cracolice/Peters Introductory Chemistry: An Active Learning Approach, Third Edition Copyright © 2007 Brooks/Cole, a part of the Thomson Corporation.

The SI system is defined by seven base units Examples: mass (weight) length temperature time kilogram meter kelvin second Other measurement units are derived from the base units; accordingly, they are called derived units Presentation Slides to Accompany Cracolice/Peters Introductory Chemistry: An Active Learning Approach, Third Edition Copyright © 2007 Brooks/Cole, a part of the Thomson Corporation.

Section 3.2 Exponential (Scientific) Notation Presentation Slides to Accompany Cracolice/Peters Introductory Chemistry: An Active Learning Approach, Third Edition Copyright © 2007 Brooks/Cole, a part of the Thomson Corporation.

Goal 1 Write in exponential notation a number given in ordinary decimal form; write in ordinary form a number given in exponential notation. Presentation Slides to Accompany Cracolice/Peters Introductory Chemistry: An Active Learning Approach, Third Edition Copyright © 2007 Brooks/Cole, a part of the Thomson Corporation.

Goal 2 Using a calculator, add, subtract, multiply, and divide numbers expressed in exponential notation. Presentation Slides to Accompany Cracolice/Peters Introductory Chemistry: An Active Learning Approach, Third Edition Copyright © 2007 Brooks/Cole, a part of the Thomson Corporation.

Exponentials B B: base p: power or exponent 10 = 10 x 10 x 10 x 10 4 = 10,000 10 = –4 10 4 1 x = 10,000 = 0.0001 Presentation Slides to Accompany Cracolice/Peters Introductory Chemistry: An Active Learning Approach, Third Edition Copyright © 2007 Brooks/Cole, a part of the Thomson Corporation.

usually 1 ≤ coefficient < 10 Exponential Notation a.bcd x 10 e coefficient: a.bcd usually 1 ≤ coefficient < 10 exponent: e a whole number Presentation Slides to Accompany Cracolice/Peters Introductory Chemistry: An Active Learning Approach, Third Edition Copyright © 2007 Brooks/Cole, a part of the Thomson Corporation.

Conversion between decimal numbers and standard exponential notation Convert 724,000 to standard exponential notation 7.24 x 10 e 7 2 4 0 0 0 . 5 places 7.24 x 10 5 Presentation Slides to Accompany Cracolice/Peters Introductory Chemistry: An Active Learning Approach, Third Edition Copyright © 2007 Brooks/Cole, a part of the Thomson Corporation.

standard exponential notation Convert 0.000427 to standard exponential notation 4.27 x 10 e 0 . 0 0 0 4 2 7 4 places 4.27 x 10 –4 Presentation Slides to Accompany Cracolice/Peters Introductory Chemistry: An Active Learning Approach, Third Edition Copyright © 2007 Brooks/Cole, a part of the Thomson Corporation.

Section 3.3 Dimensional Analysis Presentation Slides to Accompany Cracolice/Peters Introductory Chemistry: An Active Learning Approach, Third Edition Copyright © 2007 Brooks/Cole, a part of the Thomson Corporation.

Goal 3 In a problem, identify given and wanted quantities that are related by a PER expression. Set up and solve the problem by dimensional analysis. Presentation Slides to Accompany Cracolice/Peters Introductory Chemistry: An Active Learning Approach, Third Edition Copyright © 2007 Brooks/Cole, a part of the Thomson Corporation.

A quantitative problem-solving technique Dimensional Analysis A quantitative problem-solving technique featuring algebraic cancellation of units and the use of PER expressions. PER Expression A mathematical statement of two quantities that are directly proportional to one another Presentation Slides to Accompany Cracolice/Peters Introductory Chemistry: An Active Learning Approach, Third Edition Copyright © 2007 Brooks/Cole, a part of the Thomson Corporation.

How to Solve a Problem by Dimensional Analysis How many days are in 23 weeks? Step 1: Identify and write down the given quantity. Include units. GIVEN: 23 weeks Presentation Slides to Accompany Cracolice/Peters Introductory Chemistry: An Active Learning Approach, Third Edition Copyright © 2007 Brooks/Cole, a part of the Thomson Corporation.

How many days are in 23 weeks? GIVEN: 23 weeks Step 2: Identify and write down the units of the wanted quantity WANTED: days Presentation Slides to Accompany Cracolice/Peters Introductory Chemistry: An Active Learning Approach, Third Edition Copyright © 2007 Brooks/Cole, a part of the Thomson Corporation.

How many days are in 23 weeks? GIVEN: 23 weeks WANTED: days Step 3: Write down the PER/PATH PATH: weeks days > 7 days/week PER: Presentation Slides to Accompany Cracolice/Peters Introductory Chemistry: An Active Learning Approach, Third Edition Copyright © 2007 Brooks/Cole, a part of the Thomson Corporation.

How many days are in 23 weeks? GIVEN: 23 weeks WANTED: days PATH: weeks days > 7 days/week PER: Step 4: Write down the calculation setup. 23 weeks x 7 days week = Presentation Slides to Accompany Cracolice/Peters Introductory Chemistry: An Active Learning Approach, Third Edition Copyright © 2007 Brooks/Cole, a part of the Thomson Corporation.

How many days are in 23 weeks? GIVEN: 23 weeks WANTED: days PATH: weeks days > 7 days/week PER: 23 weeks x 7 days week = 161 days Step 5: Calculate the answer. Presentation Slides to Accompany Cracolice/Peters Introductory Chemistry: An Active Learning Approach, Third Edition Copyright © 2007 Brooks/Cole, a part of the Thomson Corporation.

How many days are in 23 weeks? GIVEN: 23 weeks WANTED: days PATH: weeks days > 7 days/week PER: 23 weeks x 7 days week = 161 days Step 6: Check the answer to be sure both the number and the units make sense. More days (smaller unit) than weeks (larger unit). OK. Presentation Slides to Accompany Cracolice/Peters Introductory Chemistry: An Active Learning Approach, Third Edition Copyright © 2007 Brooks/Cole, a part of the Thomson Corporation.

Section 3.4 Metric Units Presentation Slides to Accompany Cracolice/Peters Introductory Chemistry: An Active Learning Approach, Third Edition Copyright © 2007 Brooks/Cole, a part of the Thomson Corporation.

Goal 4 Distinguish between mass and weight. Presentation Slides to Accompany Cracolice/Peters Introductory Chemistry: An Active Learning Approach, Third Edition Copyright © 2007 Brooks/Cole, a part of the Thomson Corporation.

Goal 5 Identify the metric units of mass, length, and volume. Presentation Slides to Accompany Cracolice/Peters Introductory Chemistry: An Active Learning Approach, Third Edition Copyright © 2007 Brooks/Cole, a part of the Thomson Corporation.

Mass is a measure of quantity of matter. Mass and Weight Mass is a measure of quantity of matter. Weight is a measure of the force of gravitational attraction. Mass and weight are directly proportional to each other. Presentation Slides to Accompany Cracolice/Peters Introductory Chemistry: An Active Learning Approach, Third Edition Copyright © 2007 Brooks/Cole, a part of the Thomson Corporation.

The SI unit of mass is the kilogram, kg. It is defined as the mass of a platinum-iridium cylinder stored in a vault in France. Presentation Slides to Accompany Cracolice/Peters Introductory Chemistry: An Active Learning Approach, Third Edition Copyright © 2007 Brooks/Cole, a part of the Thomson Corporation.

For most laboratory work, the basic metric mass unit is used: the gram, g. Presentation Slides to Accompany Cracolice/Peters Introductory Chemistry: An Active Learning Approach, Second Edition Copyright © 2004 Brooks/Cole, a division of Thomson Learning, Inc.

For example, the kilo- unit is 1000 times larger than the basic unit. In the metric system, units that are larger than the basic unit are larger by multiples of 10. For example, the kilo- unit is 1000 times larger than the basic unit. Units that are smaller than the basic unit are smaller by fractions that are also multiples of 10. For example, the milli- unit is 1/1000 times smaller than the basic unit. Presentation Slides to Accompany Cracolice/Peters Introductory Chemistry: An Active Learning Approach, Third Edition Copyright © 2007 Brooks/Cole, a part of the Thomson Corporation.

Presentation Slides to Accompany Cracolice/Peters Introductory Chemistry: An Active Learning Approach, Third Edition Copyright © 2007 Brooks/Cole, a part of the Thomson Corporation.

The SI unit of length is the meter, m. It is defined as the distance light travels in a vacuum in 1/299,792,468 second. Presentation Slides to Accompany Cracolice/Peters Introductory Chemistry: An Active Learning Approach, Third Edition Copyright © 2007 Brooks/Cole, a part of the Thomson Corporation.

One inch is defined as 2.54 centimeters Presentation Slides to Accompany Cracolice/Peters Introductory Chemistry: An Active Learning Approach, Second Edition Copyright © 2004 Brooks/Cole, a division of Thomson Learning, Inc.

The SI unit of volume is the cubic meter, m3. A more practical unit for laboratory work is the cubic centimeter, cm3. Presentation Slides to Accompany Cracolice/Peters Introductory Chemistry: An Active Learning Approach, Third Edition Copyright © 2007 Brooks/Cole, a part of the Thomson Corporation.

One liter (L) is defined as exactly 1000 cubic centimeters 1 mL = 0.001 L = 1 cm3 Presentation Slides to Accompany Cracolice/Peters Introductory Chemistry: An Active Learning Approach, Third Edition Copyright © 2007 Brooks/Cole, a part of the Thomson Corporation.

Goal 6 State and write with appropriate metric prefixes the relationship between any metric unit and its corresponding kilounit, centiunit, and milliunit. Presentation Slides to Accompany Cracolice/Peters Introductory Chemistry: An Active Learning Approach, Third Edition Copyright © 2007 Brooks/Cole, a part of the Thomson Corporation.

Goal 7 Using Table 3.2, state and write with appropriate metric prefixes the relationship between any metric unit and other larger and smaller metric units. Presentation Slides to Accompany Cracolice/Peters Introductory Chemistry: An Active Learning Approach, Third Edition Copyright © 2007 Brooks/Cole, a part of the Thomson Corporation.

Goal 8 Given a mass, length, or volume expressed in metric units, kilounits, centiunits, or milliunits, express that quantity in the other three units. Presentation Slides to Accompany Cracolice/Peters Introductory Chemistry: An Active Learning Approach, Third Edition Copyright © 2007 Brooks/Cole, a part of the Thomson Corporation.

Metric Relationship Example 1000 units per kilounit 1000 meters per kilometer 1000 m/km 100 centiunits per unit 100 centigrams per gram 100 cg/g 1000 milliunits per unit 1000 milliliters per liter 1000 mL/L Presentation Slides to Accompany Cracolice/Peters Introductory Chemistry: An Active Learning Approach, Third Edition Copyright © 2007 Brooks/Cole, a part of the Thomson Corporation.

How many centigrams are in 0.87 gram? GIVEN: 0.87 g WANTED: cg > PATH: g cg 100 cg/g PER: 0.87 g x 100 cg g = 87 cg More centigrams (smaller unit) than grams (larger unit). OK. Presentation Slides to Accompany Cracolice/Peters Introductory Chemistry: An Active Learning Approach, Third Edition Copyright © 2007 Brooks/Cole, a part of the Thomson Corporation.

How many kilometers are in 2,335 meters? GIVEN: 2335 m WANTED: km PATH: m km > 1000 m/km PER: 2335 m x 1 km 1000 m = 2.335 km More meters (smaller unit) than kilometers (larger unit). OK. Presentation Slides to Accompany Cracolice/Peters Introductory Chemistry: An Active Learning Approach, Third Edition Copyright © 2007 Brooks/Cole, a part of the Thomson Corporation.

How many milliliters are in 0.00339 liter? GIVEN: 0.00339 L WANTED: mL > PATH: L mL 1000 mL/L PER: 0.00339 L x 1000 mL L = 3.39 mL More milliliters (smaller unit) than liters (larger unit). OK. Presentation Slides to Accompany Cracolice/Peters Introductory Chemistry: An Active Learning Approach, Third Edition Copyright © 2007 Brooks/Cole, a part of the Thomson Corporation.

Section 3.5 Significant Figures Presentation Slides to Accompany Cracolice/Peters Introductory Chemistry: An Active Learning Approach, Third Edition Copyright © 2007 Brooks/Cole, a part of the Thomson Corporation.

Goal 9 State the number of significant figures in a given quantity. Presentation Slides to Accompany Cracolice/Peters Introductory Chemistry: An Active Learning Approach, Third Edition Copyright © 2007 Brooks/Cole, a part of the Thomson Corporation.

Uncertainty in Measurement No measurement is exact. In scientific writing, the uncertainty associated with a measured quantity is always included. By convention, a measured quantity is expressed by stating all digits known accurately plus one uncertain digit. Presentation Slides to Accompany Cracolice/Peters Introductory Chemistry: An Active Learning Approach, Third Edition Copyright © 2007 Brooks/Cole, a part of the Thomson Corporation.

Presentation Slides to Accompany Cracolice/Peters Introductory Chemistry: An Active Learning Approach, Second Edition Copyright © 2004 Brooks/Cole, a division of Thomson Learning, Inc.

The bottom board is one meter long. How long is the top board? More than half as long as the meter stick, but less than one meter—about 6/10 of a meter. The uncertain digit is the last digit written. 0.6 m Presentation Slides to Accompany Cracolice/Peters Introductory Chemistry: An Active Learning Approach, Third Edition Copyright © 2007 Brooks/Cole, a part of the Thomson Corporation.

Now the meter stick has marks every 0.1 m, numbered in centimeters. How long is the board? Between 0.6 m and 0.7 m (with certainty), and the uncertain digit must be estimated. 0.64 m Presentation Slides to Accompany Cracolice/Peters Introductory Chemistry: An Active Learning Approach, Third Edition Copyright © 2007 Brooks/Cole, a part of the Thomson Corporation.

The measuring device now has centimeter marks. How long is the board? 0.643 m Presentation Slides to Accompany Cracolice/Peters Introductory Chemistry: An Active Learning Approach, Third Edition Copyright © 2007 Brooks/Cole, a part of the Thomson Corporation.

The measuring device has millimeter marks. We could estimate between the millimeter marks, but alignment of the board and the meter stick has an uncertainty of a millimeter or so. We have reached the limit of this measuring device. 0.643 m Presentation Slides to Accompany Cracolice/Peters Introductory Chemistry: An Active Learning Approach, Third Edition Copyright © 2007 Brooks/Cole, a part of the Thomson Corporation.

Significant figures are applied to measurements and quantities calculated from measurements. They do not apply to exact numbers. An exact number has no uncertainty. Counting numbers Numbers fixed by definition Presentation Slides to Accompany Cracolice/Peters Introductory Chemistry: An Active Learning Approach, Third Edition Copyright © 2007 Brooks/Cole, a part of the Thomson Corporation.

The uncertain digit is the last digit written Significant Figures The number of significant figures in a quantity is the number of digits that are known accurately plus the one that is uncertain—the uncertain digit. The uncertain digit is the last digit written when expressing a scientific measurement. Presentation Slides to Accompany Cracolice/Peters Introductory Chemistry: An Active Learning Approach, Third Edition Copyright © 2007 Brooks/Cole, a part of the Thomson Corporation.

The measurement process, not the units in which Significant Figures The measurement process, not the units in which the result is expressed, determines the number of significant figures in a quantity. The length of the board in the previous illustrations was 0.643 m. Expressed in centimeters, it is 64.3 cm. They are the same measurement with the same uncertainty. Both must have the same number of significant figures. Presentation Slides to Accompany Cracolice/Peters Introductory Chemistry: An Active Learning Approach, Third Edition Copyright © 2007 Brooks/Cole, a part of the Thomson Corporation.

The location of the decimal point has nothing Significant Figures The location of the decimal point has nothing to do with significant figures. The same 0.643 m is 0.000643 km. The three zeros before the decimal point are not significant. Begin counting significant figures at the first nonzero digit, not at the decimal point. Presentation Slides to Accompany Cracolice/Peters Introductory Chemistry: An Active Learning Approach, Third Edition Copyright © 2007 Brooks/Cole, a part of the Thomson Corporation.

The uncertain digit is the last digit written. Significant Figures The uncertain digit is the last digit written. If the uncertain digit is a zero to the right of the decimal point, that zero must be written. If the mass of a sample is shown on the display of a balance as 15.10 g, and the balance is accurate to ±0.01 g, the last digit recorded must be zero to indicate the correct uncertainty. Presentation Slides to Accompany Cracolice/Peters Introductory Chemistry: An Active Learning Approach, Third Edition Copyright © 2007 Brooks/Cole, a part of the Thomson Corporation.

If the length of the 0.643 m board is expressed Significant Figures Exponential notation must be used for very large numbers to show if final zeros are significant. If the length of the 0.643 m board is expressed in micrometers, its length is 643,000 µm. The uncertainty is ±1,000 µm. The ordinary decimal number makes this ambiguous. Writing 6.43 x 105 µm shows clearly the correct location of the uncertain digit. Presentation Slides to Accompany Cracolice/Peters Introductory Chemistry: An Active Learning Approach, Third Edition Copyright © 2007 Brooks/Cole, a part of the Thomson Corporation.

Goal 10 Round off given numbers to a specified number of significant figures. Presentation Slides to Accompany Cracolice/Peters Introductory Chemistry: An Active Learning Approach, Third Edition Copyright © 2007 Brooks/Cole, a part of the Thomson Corporation.

Rounding a Calculated Number If the first digit to be dropped is less than 5, leave the digit before it unchanged. Examples (round to 3 sig figs) 1.743 m 0.04123 kg 1.74 m 0.0412 kg Presentation Slides to Accompany Cracolice/Peters Introductory Chemistry: An Active Learning Approach, Third Edition Copyright © 2007 Brooks/Cole, a part of the Thomson Corporation.

Rounding a Calculated Number If the first digit to be dropped is 5 or more, increase the digit before it by 1. Examples (round to 3 sig figs) 32.88 mL 0.009776 km 32.9 mL 0.00978 km Presentation Slides to Accompany Cracolice/Peters Introductory Chemistry: An Active Learning Approach, Third Edition Copyright © 2007 Brooks/Cole, a part of the Thomson Corporation.

Goal 11 Add or subtract given quantities and express the result in the proper number of significant figures. Presentation Slides to Accompany Cracolice/Peters Introductory Chemistry: An Active Learning Approach, Third Edition Copyright © 2007 Brooks/Cole, a part of the Thomson Corporation.

Significant Figure Rule for Addition and Subtraction Round off the answer to the first column that has an uncertain digit. Presentation Slides to Accompany Cracolice/Peters Introductory Chemistry: An Active Learning Approach, Third Edition Copyright © 2007 Brooks/Cole, a part of the Thomson Corporation.

The following is a list of shipping masses. What is the total shipping mass? Carton: 226 g; Item 1: 33.5 g; Item 2: 589 g; Packaging: 11.88 g 2 2 6 g 3 3 . 5 g 5 8 9 g 1 1 . 8 8 g 8 6 0 . 3 8 g = 860 g = 8.60 x 102 g Presentation Slides to Accompany Cracolice/Peters Introductory Chemistry: An Active Learning Approach, Third Edition Copyright © 2007 Brooks/Cole, a part of the Thomson Corporation.

Goal 12 Multiply or divide given measurements and express the result in the proper number of significant figures. Presentation Slides to Accompany Cracolice/Peters Introductory Chemistry: An Active Learning Approach, Third Edition Copyright © 2007 Brooks/Cole, a part of the Thomson Corporation.

Significant Figure Rule for Multiplication and Division Round off the answer to the same number of significant figures as the smallest number of significant figures in any factor. Presentation Slides to Accompany Cracolice/Peters Introductory Chemistry: An Active Learning Approach, Third Edition Copyright © 2007 Brooks/Cole, a part of the Thomson Corporation.

What is the volume of a cube that is 34.49 cm long, 23.0 cm wide, and 15 cm high? Volume = Length x Width x Height = 34.49 cm x 23.0 cm x 15 cm 4 sf 2 sf 3 sf = 11,899.05 cm3 round to 2 sf = 1.2 x 104 cm3 Presentation Slides to Accompany Cracolice/Peters Introductory Chemistry: An Active Learning Approach, Third Edition Copyright © 2007 Brooks/Cole, a part of the Thomson Corporation.

Section 3.6 Metric—USCS Conversions Presentation Slides to Accompany Cracolice/Peters Introductory Chemistry: An Active Learning Approach, Third Edition Copyright © 2007 Brooks/Cole, a part of the Thomson Corporation.

Goal 13 Given a metric—USCS conversion table and a quantity expressed in any unit in Table 3.3, express that quantity in corresponding units in the other system. Presentation Slides to Accompany Cracolice/Peters Introductory Chemistry: An Active Learning Approach, Third Edition Copyright © 2007 Brooks/Cole, a part of the Thomson Corporation.

Conversions between the United States Customary System (USCS) and the metric system are done by applying dimensional analysis Presentation Slides to Accompany Cracolice/Peters Introductory Chemistry: An Active Learning Approach, Third Edition Copyright © 2007 Brooks/Cole, a part of the Thomson Corporation.

Presentation Slides to Accompany Cracolice/Peters Introductory Chemistry: An Active Learning Approach, Third Edition Copyright © 2007 Brooks/Cole, a part of the Thomson Corporation.

How many milliliters are in 1.0 quart? GIVEN: 1.0 qt WANTED: mL PATH: qt L > 1000 mL/L PER: 1.06 qt/L mL 1.0 qt x 1 L 1.06 qt x 1000 mL L = 9.4 x 102 mL More milliliters (smaller unit) than quarts (larger unit). OK. Presentation Slides to Accompany Cracolice/Peters Introductory Chemistry: An Active Learning Approach, Third Edition Copyright © 2007 Brooks/Cole, a part of the Thomson Corporation.

Section 3.7 Temperature Presentation Slides to Accompany Cracolice/Peters Introductory Chemistry: An Active Learning Approach, Third Edition Copyright © 2007 Brooks/Cole, a part of the Thomson Corporation.

Goal 14 Given a temperature in either Celsius or Fahrenheit degrees, convert it to the other scale. Presentation Slides to Accompany Cracolice/Peters Introductory Chemistry: An Active Learning Approach, Third Edition Copyright © 2007 Brooks/Cole, a part of the Thomson Corporation.

Goal 15 Given a temperature in Celsius degrees or kelvins, convert it to the other scale. Presentation Slides to Accompany Cracolice/Peters Introductory Chemistry: An Active Learning Approach, Third Edition Copyright © 2007 Brooks/Cole, a part of the Thomson Corporation.

Presentation Slides to Accompany Cracolice/Peters Introductory Chemistry: An Active Learning Approach, Second Edition Copyright © 2004 Brooks/Cole, a division of Thomson Learning, Inc.

Fahrenheit Temperature Scale Water freezes at 32°F and boils at 212°F Celsius Temperature Scale Water freezes at 0°C and boils at 100°C T°F – 32 = 1.8 T°C Presentation Slides to Accompany Cracolice/Peters Introductory Chemistry: An Active Learning Approach, Third Edition Copyright © 2007 Brooks/Cole, a part of the Thomson Corporation.

Kelvin (Absolute) Temperature Scale The degree is the same size as a Celsius degree, but the lowest temperature possible is set at zero TK = T°C + 273 Presentation Slides to Accompany Cracolice/Peters Introductory Chemistry: An Active Learning Approach, Third Edition Copyright © 2007 Brooks/Cole, a part of the Thomson Corporation.

Convert 65°F to its equivalent in degrees Celsius and kelvins. GIVEN: 65°F WANTED: °C EQUATION: T°F – 32 = 1.8 T°C T°C = T°F – 32 1.8 = 65 – 32 1.8 = 18°C TK = T°C + 273 = 18 + 273 = 291 K Presentation Slides to Accompany Cracolice/Peters Introductory Chemistry: An Active Learning Approach, Third Edition Copyright © 2007 Brooks/Cole, a part of the Thomson Corporation.

Section 3.8 Proportionality and Density Presentation Slides to Accompany Cracolice/Peters Introductory Chemistry: An Active Learning Approach, Third Edition Copyright © 2007 Brooks/Cole, a part of the Thomson Corporation.

Goal 16 Write a mathematical expression indicating that one quantity is directly proportional to another quantity. Presentation Slides to Accompany Cracolice/Peters Introductory Chemistry: An Active Learning Approach, Third Edition Copyright © 2007 Brooks/Cole, a part of the Thomson Corporation.

Goal 17 Use a proportionality constant to convert a proportionality to an equation. Presentation Slides to Accompany Cracolice/Peters Introductory Chemistry: An Active Learning Approach, Third Edition Copyright © 2007 Brooks/Cole, a part of the Thomson Corporation.

Goal 18 Given the values of two quantities that are directly proportional to each other, calculate the proportionality constant, including its units. Presentation Slides to Accompany Cracolice/Peters Introductory Chemistry: An Active Learning Approach, Third Edition Copyright © 2007 Brooks/Cole, a part of the Thomson Corporation.

Goal 19 Write the defining equation for a proportionality constant and identify units in which it might be expressed. Presentation Slides to Accompany Cracolice/Peters Introductory Chemistry: An Active Learning Approach, Third Edition Copyright © 2007 Brooks/Cole, a part of the Thomson Corporation.

Goal 20 Given two of the following for a sample of a pure substance, calculate the third: mass, volume, and density. Presentation Slides to Accompany Cracolice/Peters Introductory Chemistry: An Active Learning Approach, Third Edition Copyright © 2007 Brooks/Cole, a part of the Thomson Corporation.

A direct proportionality exists between two quantities when they increase or decrease at the same rate. If a graph of two related measurements is a straight line that passes through the origin, the measured quantities are directly proportional to each other. a  b a is proportional to b Presentation Slides to Accompany Cracolice/Peters Introductory Chemistry: An Active Learning Approach, Third Edition Copyright © 2007 Brooks/Cole, a part of the Thomson Corporation.

Direct proportionalities between measured quantities can be described by PER expressions. Direct proportionalities between measured quantities yield two conversion factors between the quantities. Given either quantity in a direct proportionality and the conversion factor between the quantities, the other quantity can be calculated by dimensional analysis. Presentation Slides to Accompany Cracolice/Peters Introductory Chemistry: An Active Learning Approach, Third Edition Copyright © 2007 Brooks/Cole, a part of the Thomson Corporation.

The mass and volume of any pure substance at a given temperature are directly proportional: mass  volume mass is proportional to volume A proportionality is changed into an equation by inserting a multiplier called a proportionality constant. Let D be the proportionality constant: mass = D x volume Presentation Slides to Accompany Cracolice/Peters Introductory Chemistry: An Active Learning Approach, Third Edition Copyright © 2007 Brooks/Cole, a part of the Thomson Corporation.

Solving for the proportionality constant yields the defining equation for a physical property of a pure substance called density: The symbol identifies a definition Density mass volume In words, density is the mass per unit volume of a substance In symbols, D m V Presentation Slides to Accompany Cracolice/Peters Introductory Chemistry: An Active Learning Approach, Third Edition Copyright © 2007 Brooks/Cole, a part of the Thomson Corporation.

The definition of density establishes its common units Density mass volume The common laboratory units for mass and volume are grams and cubic centimeters or milliliters, respectively, so density is typically expressed in g/cm3 or g/mL Presentation Slides to Accompany Cracolice/Peters Introductory Chemistry: An Active Learning Approach, Third Edition Copyright © 2007 Brooks/Cole, a part of the Thomson Corporation.

Presentation Slides to Accompany Cracolice/Peters Introductory Chemistry: An Active Learning Approach, Third Edition Copyright © 2007 Brooks/Cole, a part of the Thomson Corporation.

Ice floats on liquid water; ice is less dense than liquid water Presentation Slides to Accompany Cracolice/Peters Introductory Chemistry: An Active Learning Approach, Second Edition Copyright © 2004 Brooks/Cole, a division of Thomson Learning, Inc.

What is the volume of 15 g of silver? GIVEN: 15 g silver WANTED: volume (assume cm3) PATH: g cm3 > PER: 10.5 g/cm3 15 g x 1 cm3 10.5 g = 1.4 cm3 Presentation Slides to Accompany Cracolice/Peters Introductory Chemistry: An Active Learning Approach, Third Edition Copyright © 2007 Brooks/Cole, a part of the Thomson Corporation.

Section 3.9 A Strategy for Solving Problems Presentation Slides to Accompany Cracolice/Peters Introductory Chemistry: An Active Learning Approach, Third Edition Copyright © 2007 Brooks/Cole, a part of the Thomson Corporation.

Presentation Slides to Accompany Cracolice/Peters Introductory Chemistry: An Active Learning Approach, Third Edition Copyright © 2007 Brooks/Cole, a part of the Thomson Corporation.

Section 3.10 Thoughtful and Reflective Practice Presentation Slides to Accompany Cracolice/Peters Introductory Chemistry: An Active Learning Approach, Third Edition Copyright © 2007 Brooks/Cole, a part of the Thomson Corporation.

The only way to learn how to solve problems is to solve them for yourself. However, we can provide you with some general guidelines for solving chemistry problems. Presentation Slides to Accompany Cracolice/Peters Introductory Chemistry: An Active Learning Approach, Third Edition Copyright © 2007 Brooks/Cole, a part of the Thomson Corporation.

conversion factor for each expression, the If GIVEN and WANTED quantities can be linked by one or more PER expressions and you know the conversion factor for each expression, the problem can be solved by dimensional analysis. If GIVEN and WANTED quantities appear in an algebraic equation in which the WANTED quantity is the only unknown, the problem can be solved by algebra. Presentation Slides to Accompany Cracolice/Peters Introductory Chemistry: An Active Learning Approach, Third Edition Copyright © 2007 Brooks/Cole, a part of the Thomson Corporation.