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10.2 Mole-Mass and MoleVolume Relationships > Chapter 10 Chemical Quantities 10.1 The Mole: A Measurement of Matter 10.2 Mole-Mass and MoleVolume Relationships 10.3 Percent Composition and Chemical Formulas 1 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. . 10.2 Mole-Mass and MoleVolume Relationships > CHEMISTRY & YOU How can you calculate the pieces of a substance in a given mass or volume? 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. 2 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. . 10.2 Mole-Mass and MoleVolume Relationships > 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? 3 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. . 10.2 Mole-Mass and MoleVolume Relationships > 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. 4 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. . 10.2 Mole-Mass and MoleVolume Relationships > 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 these relationships. molar mass 1 mol 5 or 1 mol molar mass Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. . 10.2 Mole-Mass and MoleVolume Relationships > The Mole-Mass Relationship In some situations the term molar mass may be unclear. • What is the molar mass of nitrogen? 6 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. . 10.2 Mole-Mass and MoleVolume Relationships > The Mole-Mass Relationship In some situations the term molar mass may be unclear. • What is the molar mass of nitrogen? – If you assume elemental nitrogen (N), then the answer is 14.0 g/mol. – If you assume molecular nitrogen (N2), then the molar mass is 28.0 g/mol (2 × 14.0 g/mol). 7 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. . 10.2 Mole-Mass and MoleVolume Relationships > The Mole-Mass Relationship In some situations the term molar mass may be unclear. • What is the molar mass of nitrogen? – If you assume elemental nitrogen (N), then the answer is 14.0 g/mol. – If you assume molecular nitrogen (N2), then the molar mass is 28.0 g/mol (2 × 14.0 g/mol). • You can avoid confusion by using the formula of the substance you want. ( N or N2 ) 8 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. . 10.2 Mole-Mass and MoleVolume Relationships > Sample Problem 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 (Aℓ2O3). This tough, resistant coating prevents any further corrosion. What is the mass, in grams, of 12.51 mol of aluminum oxide? 9 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. . 10.2 Mole-Mass and MoleVolume Relationships > Sample Problem 1 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 = 12.51 mol Aℓ2O3 UNKNOWN mass = ? g Aℓ2O3 10 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. . 10.2 Mole-Mass and MoleVolume Relationships > Sample Problem 2 Calculate Solve for the unknown. First determine the mass of 1 mol of Aℓ2O3. 2 mol Aℓ × 27.0 g Aℓ 1 1 mol Aℓ 3 mol O 1 11 = 54.0 g Aℓ Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. . 10.2 Mole-Mass and MoleVolume Relationships > Sample Problem 2 Calculate Solve for the unknown. First determine the mass of 1 mol of Aℓ2O3. 2 mol Aℓ × 27.0 g Aℓ 1 1 mol Aℓ 3 mol O × 16.0 g O 1 1 mol O 12 = = Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. . 10.2 Mole-Mass and MoleVolume Relationships > Sample Problem 2 Calculate Solve for the unknown. First determine the mass of 1 mol of Aℓ2O3. 2 mol Aℓ × 27.0 g Aℓ 1 1 mol Aℓ 3 mol O × 16.0 g O 1 1 mol O = 54.0 g Aℓ = 48.0 g O 1 mol Aℓ2O3 = 54.0 g Aℓ + 48.0 g O 13 = 102.0 g of Aℓ2O3 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. . 10.2 Mole-Mass and MoleVolume Relationships > Sample Problem 2 Calculate Solve for the unknown. Identify the conversion factor needed. 102.0 g Aℓ2O3 1 mol Aℓ2O3 or 1 mol Aℓ2O3 102.0 g Aℓ2O3 14 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. . 10.2 Mole-Mass and MoleVolume Relationships > Sample Problem 2 Calculate Solve for the unknown. Multiply the given number of moles by the conversion factor. 12.51 mol Aℓ2O3 × 102.0 g Aℓ2O3 1 1 mol Aℓ2O3 = 1276.02 g of Aℓ2O3 = 1276 g of Aℓ2O3 15 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. . Sample Problem 3 Evaluate Does the result make sense? • The number of moles of Aℓ2O3 is approximately 12, and each has a mass of approximately 100 g. • The answer should be close to 1200 g. • The answer has been rounded to the correct number of significant figures. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. . 10.2 Mole-Mass and MoleVolume Relationships > Sample Problem Converting Mass to Moles When iron is exposed to air, it corrodes to form a redbrown rust. Rust is iron(III) oxide (Fe2O3). How many moles of iron(III) oxide are contained in 33.3 g of pure Fe2O3? 17 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. . 10.2 Mole-Mass and MoleVolume Relationships > Sample Problem 1 Analyze List the known and the unknown. The number of moles of the compound is calculated from the known mass of the compound. The conversion is mass → moles. KNOWN mass = 33.3 g Fe2O3 UNKNOWN number of moles = ? mol Fe2O3 18 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. . 10.2 Mole-Mass and MoleVolume Relationships > Sample Problem 2 Calculate Solve for the unknown. First determine the mass of 1 mol of Fe2O3. 2 mol Fe × 1 3 mol O × 1 19 56 g Fe = 1 mol Fe 16.0 g O = 1 mol O Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. . 10.2 Mole-Mass and MoleVolume Relationships > Sample Problem 2 Calculate Solve for the unknown. First determine the mass of 1 mol of Fe2O3. 20 2 mol Fe × 1 56 g Fe = 1 mol Fe 3 mol O × 1 16.0 g O = 1 mol O Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. . 10.2 Mole-Mass and MoleVolume Relationships > Sample Problem 2 Calculate Solve for the unknown. First determine the mass of 1 mol of Fe2O3. 21 2 mol Fe × 1 56 g Fe = 112 g Fe 1 mol Fe 3 mol O × 1 16.0 g O = 48.0 g O 1 mol O Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. . 10.2 Mole-Mass and MoleVolume Relationships > Sample Problem 2 Calculate Solve for the unknown. First determine the mass of 1 mol of Fe2O3. 2 mol Fe × 1 56 g Fe = 112 g Fe 1 mol Fe 3 mol O × 1 16.0 g O = 48.0 g O 1 mol O 1 mol Fe2O3 = 112 g Fe + 48.0 g O 22 = 160 g Fe2O3 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. . 10.2 Mole-Mass and MoleVolume Relationships > Sample Problem 2 Calculate Solve for the unknown. Identify the conversion factor relating grams of Fe2O3 to moles of Fe2O3. 1 mol Fe2O3 160 g Fe2O3 Note that the known unit (g) is in the denominator and the unknown unit (mol) is in the numerator. 23 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. . 10.2 Mole-Mass and MoleVolume Relationships > Sample Problem 2 Calculate Solve for the unknown. Multiply the given mass by the conversion factor. 33.3 g Fe2O3 × 1 1 mol Fe2O3 160 g Fe2O3 = 0.208125 mol of Fe2O3 = 0.208 mol of Fe2O3 24 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. . Sample Problem 3 Evaluate Does the result make sense? The given mass (about 33 g) is slightly less than the mass of one-quarter mole of Fe2O3 (about 40 g), so the answer should be slightly less than one-quarter (0.25) mol. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. . You know how many grams of a substance you have and want to find out how many moles this is. What other information do you need to know, and where can you find it? Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. . You know how many grams of a substance you have and want to find out how many moles this is. What other information do you need to know, and where can you find it? You also need to know the molar mass, which you can calculate using the chemical formula based on the atomic mass listed in the periodic table of elements. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. . 10.2 Mole-Mass and MoleVolume Relationships > 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. 28 moth crystals glucose water Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. . 10.2 Mole-Mass and MoleVolume Relationships > The Mole-Volume Relationship The Mole-Volume Relationship How does the relationship between the volume of a gas at STP and the number of moles of that gas compare to solids and liquids? STP stands for STANDARD TEMPERATURE and PRESSURE 29 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. . 10.2 Mole-Mass and MoleVolume Relationships > The Mole-Volume Relationship The Mole-Volume Relationship Unlike liquids and solids, the volumes of moles of gases, are much more predictable measured under the same physical conditions. 30 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. . 10.2 Mole-Mass and MoleVolume Relationships > The Mole-Volume Relationship Avogadro’s Hypothesis Avogadro’s hypothesis states that equal volumes of gases at STP contain equal numbers of particles. * Whether the particles are big or small, there are large amounts of empty space between individual particles of gas. 31 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. . The Mole-Volume Relationship Avogadro’s Hypothesis Same amount of space and same amount of particles. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. . 10.2 Mole-Mass and MoleVolume Relationships > The Mole-Volume Relationship Avogadro’s Hypothesis The volume of a gas varies with a change in temperature and/or a change in pressure. 33 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. . 10.2 Mole-Mass and MoleVolume Relationships > The Mole-Volume Relationship Avogadro’s Hypothesis The volume of a gas varies with a change in temperature and/or a change in pressure. • Due to variations in temperature and pressure, the volume of a gas is usually measured at STP. 34 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. . 10.2 Mole-Mass and MoleVolume Relationships > The Mole-Volume Relationship Avogadro’s Hypothesis The volume of a gas varies with a change in temperature and/or a change in pressure. • Due to variations in temperature and pressure, the volume of a gas is usually measured at STP. • Standard temperature and pressure (STP) means a temperature of 0°C and a pressure of 101.3 kPa, or 1 atmosphere (atm). 35 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. . 10.2 Mole-Mass and MoleVolume Relationships > The Mole-Volume Relationship Avogadro’s Hypothesis At STP, 1 mol or 6.02 × 1023 representative particles, of any gas occupies a volume of 22.4 L. • The quantity, 22.4 L, is called the molar volume of a gas. 36 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. . 10.2 Mole-Mass and MoleVolume Relationships > 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 22.4 L = 1 mol at STP. 22.4 L and 1 mol 37 1 mol 22.4 L Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. . 10.2 Mole-Mass and MoleVolume Relationships > Sample Problem Calculating Gas Quantities at STP Carbon dioxide (CO2) is a gas produced by burning coal. It is the leading pollutant that adds to the “Greenhouse Effect”. Determine the volume, in liters, of 0.71 mol of CO2 gas at STP. 38 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. . 10.2 Mole-Mass and MoleVolume Relationships > Sample Problem 1 Analyze List the knowns and the unknown. Since CO2 is a gas, the volume at STP can be calculated from the known number of moles. KNOWNS number of moles = 0.71 mol CO2 1 mol CO2 = 22.4 L CO2 at STP UNKNOWN volume = ? L CO2 39 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. . Sample Problem 2 Calculate Solve for the unknown. First identify the conversion factor relating moles of CO2 to volume of CO2 at STP. 22.4 L CO2 1 mol CO2 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. . 10.2 Mole-Mass and MoleVolume Relationships > Sample Problem 2 Calculate Solve for the unknown. Multiply the given number of moles by the conversion factor. 0.71 mol CO2 × 22.4 L CO2 1 mol CO2 1 = 15.904 L CO2 = 16 L CO2 41 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. . Sample Problem 3 Evaluate Does the result make sense? • One mole of any gas at STP has a volume of 22.4 L, so 0.71 mol should have a volume slightly less than threequarters of a mole of the gas or 16.8 L. • The answer should have two significant figures. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. . 10.2 Mole-Mass and MoleVolume Relationships > The Mole-Volume Relationship Calculating Molar Mass and Density A gas-filled 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. 43 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. . 10.2 Mole-Mass and MoleVolume Relationships > The Mole-Volume Relationship Calculating Molar Mass and Density • At STP, the density of a gas and the molar volume (22.4 L/mol) can be used to calculate the molar mass of the gas. 44 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. . 10.2 Mole-Mass and MoleVolume Relationships > The Mole-Volume Relationship Calculating Molar Mass and Density • At STP, the density of a gas and the molar volume (22.4 L/mol) can be used to calculate the molar mass of the gas. • Similarly, the molar mass of a gas and the molar volume can be used to calculate the density of a gas at STP. 45 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. . 10.2 Mole-Mass and MoleVolume Relationships > Sample Problem Calculating the Molar Mass of a Gas at STP The density of an unknown Noble gas is found to be 5.862 g/L at STP. What is the molar mass of this gas? What is the identity of this Noble gas? 46 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. . 10.2 Mole-Mass and MoleVolume Relationships > Sample Problem 1 Analyze List the knowns and the unknown. The molar mass of a gas is calculated from the known density of the gas and the molar volume at STP. KNOWNS density = 5.862 g/L 1 mol of gas at STP = 22.4 L UNKNOWN molar mass = ? g/mol Noble gas = ? 47 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. . Sample Problem 2 Calculate Solve for the unknown. First identify the conversion factor needed to convert density to molar mass. 22.4 L 1 mol Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. . 10.2 Mole-Mass and MoleVolume Relationships > Sample Problem 2 Calculate Solve for the unknown. Multiply the given density by the conversion factor. 5.862 g 1L × 22.4 L 1 mol = 131.3088 g/mol = 131.3 g/mol Noble gas = Xenon 49 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. . Sample Problem 3 Evaluate Does the result make sense? • The density of the gas is relatively high so one would expect the molar mass to be relatively high. • The answer should have four significant figures. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. . 10.2 Mole-Mass and MoleVolume Relationships > Sample Problem Calculating the Molar Mass of a Gas at STP What is the density of fluorine gas at STP? 51 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. . 10.2 Mole-Mass and MoleVolume Relationships > Sample Problem 1 Analyze List the knowns and the unknown. The density of a gas is calculated from the known molar mass of the gas and the molar volume at STP. KNOWNS molar mass of F = 19 g/mol 1 mol of gas at STP = 22.4 L UNKNOWN density of F2 = ? g/L 52 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. . 10.2 Mole-Mass and MoleVolume Relationships > Sample Problem 2 Calculate Solve for the unknown. First calculate the molar mass of F2. 2 mol F 1 x 19 g 1 mol F = 38 g 1 mol F2 = 38 g F 53 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. . 10.2 Mole-Mass and MoleVolume Relationships > Sample Problem 2 Calculate Solve for the unknown. Now identify the conversion factor needed to convert density to molar mass. 1 mol 22.4 L 54 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. . 10.2 Mole-Mass and MoleVolume Relationships > Sample Problem 2 Calculate Solve for the unknown. Multiply the given density by the conversion factor. 38 g 1 mol × 1 mol 22.4 L = 1.6964285 g/L = 1.7 g/L 55 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. . 10.2 Mole-Mass and MoleVolume Relationships > The Mole-Volume Relationship The mole is at the center of chemical calculations. • To convert from one unit to another, you must use the mole as an intermediate step. 56 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. . Why does one mole of any gas always occupy the same volume (22.4 L) at standard temperature and pressure? Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. . Why does one mole of any gas always occupy the same volume (22.4 L) at standard temperature and pressure? Gas molecules vary in size, just like molecules of solids and liquids, but the particles in a gas are so far apart that the change in volume (size) of the molecules doesn’t change the volume the gas occupies at STP. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. . 10.2 Mole-Mass and MoleVolume Relationships > 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. 59 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. . 10.2 Mole-Mass and MoleVolume Relationships > END OF 10.2 60 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. .