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12.2 Chemical Calculations > Chapter 12 Stoichiometry 12.1 The Arithmetic of Equations 12.2 Chemical Calculations 12.3 Limiting Reagent and Percent Yield 1 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. 12.2 Chemical Calculations > CHEMISTRY & YOU How do manufacturers know how to make enough of their desired product? If chemical plants produce too much ammonia, then it might be wasted. But if too little is produced, then there might not be enough for all their customers. 2 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. 12.2 Chemical Calculations > Writing and Using Mole Ratios Writing and Using Mole Ratios How are mole ratios used in chemical calculations? 3 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. 12.2 Chemical Calculations > Writing and Using Mole Ratios A mole ratio is a conversion factor derived from the coefficients of a balanced chemical equation interpreted in terms of moles. 4 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. 12.2 Chemical Calculations > Types of Stoichiometry Problems to solve using the mole ratios of balanced chemical equations. 1. Mole-Mole Problems 2. Mole-Mass Problems 3. Mass-mass 4. Mass-volume 5. Volume-volume 5 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. 12.2 Chemical Calculations > Mole-Mole Problems Example: NH4NO3 ------> N2O + 2 H2O Find the number of moles of N2O and H2O produced from the decomposition of 2.25 mole of NH4NO3? 6 12.2 Chemical Calculations > Mole-Mole Problems The balanced chemical equation states that for every 1 mole of NH4NO3 that decomposes, 1 mole of N2O and 2 moles of water are produced. 7 12.2 Chemical Calculations > Mole-Mole Problems Use this mole ratio from the chemical equation to calculated the number of moles of N20 & H2O produced: 2.25 mol NH4NO3 1 mole N20 1mol NH4NO3 = 2.25 mole N20 2.25 mol NH4NO3 2 mole H20 1mol NH4NO3 = 4.5 mole H20 NH4NO3 ------> N2O + 2 H2O 8 12.2 Chemical Calculations > Mole-Mole Problems Magnesium burns in oxygen to produce magnesium oxide. How many moles of oxygen are needed to burn 0.52 moles of magnesium? Write a balanced equation for this reaction: 2 Mg + O2 2 MgO Solve: 0.52 mol Mg 1 mol 02 2 mol Mg = .26 mol O2 9 12.2 Chemical Calculations > Mole-Mole Problems The equation for the composition of water is: 2 H2 + O2 ---> 2 H2O How many moles of H2O are produced when 5.00 moles of oxygen are used? 5 moles O2 2 mole H2O 1 moles O2 = 10 moles H20 10 12.2 Chemical Calculations > Writing and Using Mole Ratios In chemical calculations, -mole ratios are used to convert between a given number of moles of a reactant or product to moles of a different reactant or product. These mole ratios are represented by the coefficients of a balanced chemical equation 11 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. 12.2 Chemical Calculations > Writing and Using Mole Ratios Mass-Mass Calculations In the laboratory, the amount of a substance is usually determined by measuring its mass in grams. • If a given sample is measured in grams, then the mass can be converted to moles by using the molar mass. • Then the mole ratio from the balanced equation can be used to calculate the number of moles of the unknown. • If it is the mass of the unknown that needs to be determined, the number of moles of the unknown can be multiplied by the molar mass. 12 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. 12.2 Chemical Calculations > I. Mass-Mass Problems Mass-Mass Calculations In a mass-mass problem you are given the mass of one substance and ask to find the mass of another substance involved in the same reaction. 13 12.2 Chemical Calculations > I. Mass-Mass Problems Mass-Mass Calculations All mass-mass problems can be solved by following these steps: 1. Write a balanced equation for the chemical reaction 2. 3. 4. 14 involved. Convert the given mass of the substance given (A) to moles of substance (A) using the molar mass of the substance(A) . Convert the moles of the substance given (A) to the moles of the substance (B) by using the mole ratio from the balanced chemical equation. Change moles of substance (B) to the mass of substance (B) using the molar mass of the substance. 12.2 Chemical Calculations > Summary of Mass-Mass Problem 1. 2. 3. 4. 15 Write a balanced equation for the chemical reaction involved. Convert the given mass of the substance given (A) to moles of substance (A) using the molar mass of the substance(A) . Convert the moles of the substance given (A) to the moles of the substance (B) by using the mole ratio from the balanced chemical equation. Change moles of substance (B) to the mass of substance (B) using the molar mass of the substance. 12.2 Chemical Calculations > Sample Problem 12.4 Calculating the Mass of a Product Calculate the number of grams of NH3 produced by the reaction of 5.40 g of hydrogen with an excess of nitrogen. The balanced equation is: N2(g) + 3H2(g) 2NH3(g) 16 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. 12.2 Chemical Calculations > Sample Problem 12.4 Calculate Solve for the unknown. Start with the given quantity, and convert from mass to moles. 1 mol H2 5.40 g H2 2.0 g H2 Given quantity 17 Change given unit to moles Don’t forget to cancel the units at each step. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. 12.2 Chemical Calculations > Sample Problem 12.4 Calculate Solve for the unknown. Then convert from moles of reactant to moles of product by using the correct mole ratio. 1 mol H2 2 mol NH3 5.40 g H2 2.0 g H 3 mol H 2 2 Given quantity 18 Change given unit to moles Mole ratio Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. 12.2 Chemical Calculations > Sample Problem 12.4 Calculate Solve for the unknown. Finish by converting from moles to grams. Use the molar mass of NH3. 1 mol H2 2 mol NH3 17.0 g NH3 5.40 g H2 2.0 g H 3 mol H 1 mol NH 2 2 3 Given quantity Change given unit to moles Mole ratio Change moles to grams = 31 g NH3 19 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. 12.2 Chemical Calculations > Phosphorus burns in air to produce a phosphorus oxide in the following reaction: 4P(s) + 5O2(g) P4O10(s) What mass of phosphorus will be needed to produce 3.25 mol of P4O10? 20 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. 12.2 Chemical Calculations > Phosphorus burns in air to produce a phosphorus oxide in the following reaction: 4P(s) + 5O2(g) P4O10(s) What mass of phosphorus will be needed to produce 3.25 mol of P4O10? 4 mol P 31.0 g P 3.25 mol P4O10 1 mol P O 1 mol P = 403 g P 4 10 21 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. 12.2 Chemical Calculations > Mass-Mass Calculations Example: 50 g of Ammonium dichromate, (NH4)2Cr2O7, decomposes when heated strongly to generate nitrogen gas, N2, gaseous water, H2O, and the green crystalline compound chromium(III) oxide, Cr2O3. How many grams of water are produced? 22 12.2 Chemical Calculations > Mass-Mass Calculations Write a balanced chemical equation for the reaction. (NH4)2Cr2O7 N2 + 4 H2O + Cr2O3 50 g (NH4)2Cr2O7 1 mol (NH4)2Cr2O7 4 mol H2O 18 g H20 252 g (NH4)2Cr2O7 1 mol (NH4)2Cr2O7 1 mol H20 = 14.28 g H20 23 II. Mass-Volume 12.2 Chemical Calculations > Problems Mass-Volume Calculations In Mass-volume problems you are given the mass of one substance in a chemical reaction asked to find the volume of another substance- in this case a gas. 24 II. Mass-Volume 12.2 Chemical Calculations > Problems Mass-Volume Calculations 1. Write the balanced equation. 2. Convert the given mass (A) into moles (A) using the molar mass of the substance 3. Convert the moles of the substance given (A) to the moles of the substance (B) by using the mole ratio from the balanced chemical equation. 4. Convert the number of moles (B) of the unknown quantity to volume (B) using the molar volume of a gas 25 12.2 Chemical Calculations > Summary of Mass-Volume Calculations 1. Write the balanced equation. 2. Convert the given mass (A) into moles (A) using the molar mass of the substance 3. Convert the moles of the substance given (A) to the moles of the substance (B) by using the mole ratio from the balanced chemical equation. 4. Convert the number of moles (B) of the unknown quantity to volume (B) using the molar volume of a gas 26 II. Mass-Volume 12.2 Chemical Calculations > Problems Mass-Volume Calculations Example: 10.0 g of Zn react with HCl acid to produce zinc chloride and hydrogen gas. How many liters of hydrogen gas will be produced? 1. Write the balanced equation: Zn + 2 HCl ZnCl2 + H2 27 II. Mass-Volume 12.2 Chemical Calculations > Problems Mass-Volume Calculations 1. Convert the given mass (A) into moles (A) using the molar mass of the substance Zn + 2 HCl ZnCl2 + H2 10 g Zn 1 mol Zn 65.4 g Zn 28 II. Mass-Volume 12.2 Chemical Calculations > Problems Mass-Volume Calculations Convert the moles of the substance given (A) to the moles of the substance (B) by using the mole ratio from the balanced chemical equation: Zn + 2 HCl ZnCl2 + H2 10 g Zn 1 mol Zn 65.4 g Zn 29 1 mol H2 1 mol Zn II. Mass-Volume 12.2 Chemical Calculations > Problems Mass-Volume Calculations Convert the number of moles (B) of the unknown quantity to volume (B) using the molar volume of a gas at STP (22.4 L) Zn + 2 HCl ZnCl2 + H2 10 g Zn 1 mol Zn 65.4 g Zn = 3.4 L H2 30 1 mol H2 22.4 L H2 1 mol Zn 1 mol H2 12.2 Chemical Calculations > Sample Problem 12.5 Calculating the Molecules of a Product How many molecules of oxygen are produced when 29.2 g of water is decomposed by electrolysis according to this balanced equation? 2H2O(l) 31 electricity 2H2(g) + O2(g) Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. 12.2 Chemical Calculations > Sample Problem 12.5 1 Analyze List the knowns and the unknown. The following calculations need to be performed: g H2O mol H2O mol O2 molecules O2 The appropriate mole ratio relating mol O2 to mol H2O from the balanced equation is: 1 mol O2 2 mol H2O 32 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. 12.2 Chemical Calculations > Sample Problem 12.5 Calculate Solve for the unknown. Start with the given quantity, and convert from mass to moles. 29.2 g H2O Given quantity 1 mol H2O 18.0 g H2O Change to moles Remember to also start your calculations with the given quantity, even if the given quantity is a product in the reaction. 33 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. 12.2 Chemical Calculations > Sample Problem 12.5 2 Calculate Solve for the unknown. Then, convert from moles of reactant to moles of product. 29.2 g H2O Given quantity 34 1 mol H2O 1 mol O2 18.0 g H2O 2 mol H2O Change to moles Mole ratio Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. 12.2 Chemical Calculations > Sample Problem 12.5 2 Calculate Solve for the unknown. Finish by converting from moles to molecules. 1 mol H2O 1 mol O2 6.02 1023 molecules O2 29.2 g H2O 18.0 g H2O 2 mol H2O 1 mol O2 Given quantity 35 Change to moles Mole ratio Change to molecules Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. 12.2 Chemical Calculations > Sample Problem 12.5 2 Calculate Solve for the unknown. Finish by converting from moles to molecules. 1 mol H2O 1 mol O2 6.02 1023 molecules O2 29.2 g H2O 18.0 g H2O 2 mol H2O 1 mol O2 Given quantity Change to moles Mole ratio Change to molecules = 4.88 1023 molecules O2 36 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. 12.2 Chemical Calculations > Sample Problem 12.5 3 Evaluate Does the result make sense? • The given mass of water should produce a little less than 1 mol of oxygen, or a little less than Avogadro’s number of molecules. • The answer should have three significant figures. 37 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. 12.2 Chemical Calculations > Sample Problem 12.6 Volume-Volume Stoichiometric Calculations Nitrogen monoxide and oxygen gas combine to form the brown gas nitrogen dioxide, which contributes to photochemical smog. How many liters of nitrogen dioxide are produced when 34 L of oxygen react with an excess of nitrogen monoxide? Assume conditions are at STP. 2NO(g) + O2(g) 2NO2(g) 38 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. 12.2 Chemical Calculations > Sample Problem 12.6 1 Analyze List the knowns and the unknown. For gaseous reactants and products at STP, 1 mol of a gas is equal to 22.4 L. KNOWNS volume of oxygen = 34 L O2 2 mol NO2/1 mol O2 (mole ratio from balanced equation) 1 mol O2 = 22.4 L O2 (at STP) 1 mol NO2 = 22.4 L NO2 (at STP) UNKNOWN volume of nitrogen dioxide = ? L NO2 39 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. 12.2 Chemical Calculations > Sample Problem 12.6 2 Calculate Solve for the unknown. Start with the given quantity, and convert from volume to moles by using the volume ratio. 34 L O2 Given quantity 1 mol O2 22.4 L O2 Change to moles Did you notice that the 22.4 L/mol factors canceled out? This will always be true in a volume-volume problem. 40 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. 12.2 Chemical Calculations > Sample Problem 12.6 2 Calculate Solve for the unknown. Then, convert from moles of reactant to moles of product by using the correct mole ratio. 34 L O2 Given quantity 41 1 mol O2 2 mol NO2 22.4 L O2 1 mol O2 Change to moles Mole ratio Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. 12.2 Chemical Calculations > Sample Problem 12.6 2 Calculate Solve for the unknown. Finish by converting from moles to liters. Use the volume ratio. 34 L O2 Given quantity 1 mol O2 2 mol NO2 22.4 L NO2 22.4 L O2 1 mol O2 1 mol NO2 Change to moles Mole ratio Change to liters = 68 L NO2 42 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. 12.2 Chemical Calculations > Sample Problem 12.6 3 Evaluate Does the result make sense? • Because 2 mol NO2 are produced for each 1 mol O2 that reacts, the volume of NO2 should be twice the given volume of O2. • The answer should have two significant figures. 43 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. 12.2 Chemical Calculations > Sample Problem 12.7 Finding the Volume of a Gas Needed for a Reaction Assuming STP, how many milliliters of oxygen are needed to produce 20.4 mL SO3 according to this balanced equation? 2SO2(g) + O2(g) 2SO3(g) 44 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. 12.2 Chemical Calculations > Sample Problem 12.7 1 Analyze List the knowns and the unknown. • For a reaction involving gaseous reactants or products, the coefficients also indicate relative amounts of each gas. • You can use the volume ratios in the same way you have used mole ratios. KNOWNS volume of sulfur trioxide = 20.4 mL 2 mL SO3/1 mL O2 (volume ratio from balanced equation) UNKNOWN volume of oxygen = ? mL O2 45 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. 12.2 Chemical Calculations > Sample Problem 12.7 2 Calculate Solve for the unknown. Multiply the given volume by the appropriate volume ratio. 20.4 mL SO3 1 mL O2 2 mL SO3 = 10.2 mL O2 The volume ratio can be written using milliliters as the units instead of liters. 46 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. 12.2 Chemical Calculations > Sample Problem 12.7 3 Evaluate Does the result make sense? • Because the volume ratio is 2 volumes SO3 to 1 volume O2, the volume of O2 should be half the volume of SO3. • The answer should have three significant figures. 47 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. 12.2 Chemical Calculations > Methane burns in air by the following reaction: CH4(g) + 2O2(g) CO2(g) + 2H2O(g) What volume of water vapor is produced at STP by burning 501 g of methane? 48 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. 12.2 Chemical Calculations > Methane burns in air by the following reaction: CH4(g) + 2O2(g) CO2(g) + 2H2O(g) What volume of water vapor is produced at STP by burning 501 g of methane? 501 g CH4 49 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. 12.2 Chemical Calculations > Methane burns in air by the following reaction: CH4(g) + 2O2(g) CO2(g) + 2H2O(g) What volume of water vapor is produced at STP by burning 501 g of methane? 501 g CH4 50 1 mol CH4 16.05 g CH4 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. 12.2 Chemical Calculations > Methane burns in air by the following reaction: CH4(g) + 2O2(g) CO2(g) + 2H2O(g) What volume of water vapor is produced at STP by burning 501 g of methane? 501 g CH4 51 1 mol CH4 2 mol H2O 16.05 g CH4 1 mol CH4 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. 12.2 Chemical Calculations > Methane burns in air by the following reaction: CH4(g) + 2O2(g) CO2(g) + 2H2O(g) What volume of water vapor is produced at STP by burning 501 g of methane? 501 g CH4 1 mol CH4 16.05 g CH4 2 mol H2O 1 mol CH4 22.4 L H2O 1 mol H2O = 1398.4 L 52 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. 12.2 Chemical Calculations > Key Concepts In chemical calculations, mole ratios are used to convert between moles of reactant and moles of product, between moles of reactants, or between moles of products. In a typical stoichiometric problem, the given quantity is first converted to moles. Then, the mole ratio from the balanced equation is used to calculate the moles of the wanted substance. Finally, the moles are converted to any other unit of measurement related to the unit mole. 53 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. 12.2 Chemical Calculations > Glossary Terms mole ratio: a conversion factor derived from the coefficients of a balanced chemical equation interpreted in terms of moles 54 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. 12.2 Chemical Calculations > BIG IDEA The Mole and Quantifying Matter Mole ratios from the balanced equation are used to calculate the amount of a reactant or product in a chemical reaction from a given amount of one of the reactants or products. 55 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. 12.2 Chemical Calculations > END OF 12.2 56 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.