10.2 Mole-Mass and Mole- Volume Relationships. Chapter 10 Chemical Quantities. Volume Relationships The Mole: A Measurement of Matter

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1 Chapter 10 Chemical Quantities 101 The Mole: A Measurement of Matter 102 Mole-Mass and Mole- 103 Percent Composition and Chemical Formulas 1

2 istry/chemical-reactions/molar-mass/ 2

3 CHEMISTRY & YOU How can you calculate the moles of a substance in a given mass or volume? 3 Guess how many pennies are in the container In a similar way, chemists use the relationships between the mole and quantities such as mass, volume, and number of particles to solve problems in chemistry

4 The Mole-Mass Relationship The Mole-Mass Relationship How do you convert the mass of a substance to the number of moles of the substance? 4

5 The Mole-Mass Relationship Use the molar mass of an element or compound to convert between the mass of a substance and the moles of the substance 5

6 The Mole-Mass Relationship Use the molar mass of an element or compound to convert between the mass of a substance and the moles of the substance The conversion factors for these calculations are based on the relationship molar mass = 1 mol molar mass 1 mol and 1 mol molar mass 6

7 Sample Problem 105 Converting Moles to Mass Items made out of aluminum, such as aircraft parts and cookware, are resistant to corrosion because the aluminum reacts with oxygen in the air to form a coating of aluminum oxide (Al 2 O 3 ) This tough, resistant coating prevents any further corrosion What is the mass, in grams, of 945 mol of aluminum oxide? 7

8 Sample Problem Analyze List the known and the unknown The mass of the compound is calculated from the known number of moles of the compound The desired conversion is moles mass KNOWN number of moles = 945 mol Al 2 O 3 UNKNOWN mass =? g Al 2 O 3 8

9 Sample Problem Calculate Solve for the unknown First determine the mass of 1 mol of Al 2 O g Al 2 mol Al 1 mol Al = 540 g Al 160 g O 3 mol O 1 mol O = 480 g O 1 mol Al 2 O 3 = 540 g Al g O = 1020 g Al 2 O 3 9

10 Sample Problem Calculate Solve for the unknown Identify the conversion factor relating moles of Al 2 O 3 to grams of Al 2 O g Al 2 O 3 Use the relationship 1 mol Al 2 O 3 1 mol Al 2 O 3 = 1020 g Al 2 O 3 10

11 Sample Problem Calculate Solve for the unknown Multiply the given number of moles by the conversion factor 945 mol Al 2 O g Al 2O 3 1 mol Al 2 O 3 = 964 g Al 2 O 3 11

12 Sample Problem 106 Converting Mass to Moles When iron is exposed to air, it corrodes to form a redbrown rust Rust is iron(iii) oxide (Fe 2 O 3 ) How many moles of iron(iii) oxide are contained in 922 g of pure Fe 2 O 3? 12

13 The Mole-Volume Relationship The Mole-Volume Relationship How do you convert the volume of a gas at STP to the number of moles of the gas? 13

14 The Mole-Volume Relationship Notice that the volumes of one mole of different solid and liquid substances are not the same The volumes of one mole of glucose (blood sugar) and one mole of parachlorobenzene (moth crystals) are much larger than the volume of one mole of liquid water 14

15 The Mole-Volume Relationship Unlike liquids and solids, the volumes of moles of gases, measured under the same physical conditions, are much more predictable 15

16 The Mole-Volume Relationship Avogadro s Hypothesis Avogadro s hypothesis states that equal volumes of gases at the same temperature and pressure contain equal numbers of particles 16

17 The Mole-Volume Relationship Avogadro s Hypothesis The particles that make up different gases are not the same size However, particles in all gases are so far apart that a collection of relatively large particles does not require much more space than the same number of relatively small particles 17

18 The Mole-Volume Relationship Avogadro s Hypothesis Whether the particles are large or small, large expanses of space exist between individual particles of gas 18

19 The Mole-Volume Relationship Avogadro s Hypothesis The volume of a gas varies with a change in temperature or a change in pressure 19

20 The Mole-Volume Relationship Avogadro s Hypothesis The volume of a gas varies with a change in temperature or a change in pressure Due to these variations with temperature and pressure, the volume of a gas is usually measured at standard temperature and pressure 20

21 The Mole-Volume Relationship 21 Avogadro s Hypothesis The volume of a gas varies with a change in temperature or a change in pressure Due to these variations with temperature and pressure, the volume of a gas is usually measured at standard temperature and pressure Standard temperature and pressure (STP) means a temperature of 0 C and a pressure of 1013 kpa, or 1 atmosphere (atm)

22 The Mole-Volume Relationship Avogadro s Hypothesis At STP, 1 mol, or representative particles, of any gas occupies a volume of 224 L The quantity, 224 L, is called the molar volume of a gas 22

23 The Mole-Volume Relationship Calculating the Volume and Moles of a Gas at STP The molar volume is used to convert between the number of moles of gas and the volume of the gas at STP The conversion factors for these calculations are based on the relationship 224 L = 1 mol at STP 224 L 1 mol and 1 mol 224 L 23

24 The Mole-Volume Relationship Calculating the Volume and Moles of a Gas at STP You can use these conversion factors to convert a known number of moles of gas to the volume of the gas at STP Similarly, you can convert a known volume of gas at STP to the number of moles of the gas 224 L 1 mol and 1 mol 224 L 24

25 Sample Problem 107 Calculating Gas Quantities at STP Sulfur dioxide (SO 2 ) is a gas produced by burning coal It is an air pollutant and one of the causes of acid rain Determine the volume, in liters, of 060 mol SO 2 gas at STP 25

26 Sample Problem Analyze List the knowns and the unknown Since SO 2 is a gas, the volume at STP can be calculated from the known number of moles KNOWNS number of moles = 060 mol SO 2 1 mol SO 2 = 224 L SO 2 at STP UNKNOWN volume =? L SO 2 26

27 Sample Problem Calculate Solve for the unknown First identify the conversion factor relating moles of SO 2 to volume of SO 2 at STP 224 L SO 2 1 mol SO 2 The following relationship applies for gases at STP: 224 L = 1 mol 27

28 Sample Problem Calculate Solve for the unknown Multiply the given number of moles by the conversion factor 060 mol SO L SO 2 1 mol SO 2 = 13 L SO 2 28

29 Sample Problem Evaluate Does the result make sense? One mole of any gas at STP has a volume of 224 L, so 060 mol should have a volume slightly larger than onehalf of a mole or 112 L The answer should have two significant figures 29

30 CHEMISTRY & YOU How can you calculate the moles of a substance in a given mass? How can you calculate the moles of a gas in a given volume at STP? 30

31 CHEMISTRY & YOU How can you calculate the moles of a substance in a given mass? How can you calculate the moles of a gas in a given volume at STP? You can calculate the moles of a substance in a given mass by using the relationship molar mass = 1 mol You can calculate the moles of gas in a given volume at STP by using the relationship 224 L = 1 mol at STP 31

32 The Mole-Volume Relationship Calculating Molar Mass and Density A gas-filled air balloon will either sink or float in the air depending on whether the density of the gas inside the balloon is greater or less than the density of the surrounding air Different gases have different densities Usually the density of a gas is measured in grams per liter (g/l) and at a specific temperature 32

33 The Mole-Volume Relationship Calculating Molar Mass and Density The density of a gas at STP and the molar volume at STP (224 L/mol) can be used to calculate the molar mass of the gas Similarly, the molar mass of a gas and the molar volume at STP can be used to calculate the density of a gas at STP 33

34 Sample Problem 108 Calculating the Molar Mass of a Gas at STP The density of a gaseous compound containing carbon and oxygen is found to be 1964 g/l at STP What is the molar mass of the compound? 34

35 Sample Problem Analyze List the knowns and the unknown The molar mass of the compound is calculated from the known density of the compound and the molar volume at STP KNOWNS density = 1964 g/l 1 mol of gas at STP = 224 L UNKNOWN molar mass =? g/mol 35

36 Sample Problem Calculate Solve for the unknown First identify the conversion factor needed to convert density to molar mass 224 L 1 mol Use the density and molar volume at STP to calculate the molar mass g molar mass = mol = g 224 L L 1 mol 36

37 Sample Problem Calculate Solve for the unknown Multiply the given density by the conversion factor 1964 g 1 L = 440 g/mol 224 L 1 mol 37

38 Sample Problem Evaluate Does the result make sense? The ratio of the calculated mass (440 g) to the volume (224 L) is about 2, which is close to the known density The answer should have three significant figures 38

39 The Mole-Volume Relationship The mole is at the center of your chemical calculations To convert from one unit to another, you must use the mole as an intermediate step 39

40 Why does one mole of any gas occupy the same volume (224 L) at standard temperature and pressure? 40

41 Why does one mole of any gas occupy the same volume (224 L) at standard temperature and pressure? Gas molecules do vary in size, just like molecules of solids and liquids, but the particles in a gas are always so far apart that the change in volume of the molecules doesn t change the volume the gas occupies at STP 41

42 Key Concepts Use the molar mass of an element or compound to convert between the mass of a substance and the moles of the substance The molar volume is used to convert between the number of moles of gas and the volume of the gas at STP 42

43 Glossary Terms Avogadro s hypothesis: equal volumes of gases at the same temperature and pressure contain equal numbers of particles standard temperature and pressure (STP): the conditions under which the volume of a gas is usually measured; standard temperature is 0 C, and standard pressure is 1013 kpa, or 1 atmosphere (atm) 43 molar volume: the volume occupied by 1 mole of a gas at standard temperature and pressure (STP); 224 L

44 BIG IDEA The Mole and Quantifying Matter The mole allows you to convert among the amount of representative particles in a substance, the mass of a substance, and the volume of a gas at STP 44