# Chapter 6 Quantities in Chemical Reactions

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1 Chapter 6 Quantities in Chemical Reactions The Meaning of a Balanced Chemical Equation Mole-Mole Conversions Mass-Mass Conversions Limiting Reactants Percent Yield Energy Changes Copyright The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 6-1 What do the coefficients in a balanced chemical equation mean? Let s consider the combustion of propane: C 3 H 8 (g) + O 2 (g) CO 2 (g) + H 2 O(g) 6-2 What do the coefficients in a balanced chemical equation mean? Balanced, the equation is: C 3 H 8 (g) + 5 O 2 (g) 3 CO 2 (g) + 4 H 2 O(g) The numbers in front of the oxygen, carbon dioxide, and water are stoichiometric coefficients (we ll just refer to them as coefficients)

2 What do the coefficients in a balanced chemical equation mean? (Cont d) C 3 H 8 (g) + 5 O 2 (g) 3 CO 2 (g) + 4 H 2 O(g) Atoms/Molecules/Formula Units We could say that in this reaction, 1 molecule of propane reacts with 5 molecules of oxygen gas to produce 3 molecules of carbon dioxide and 4 molecules of water. 6-4 What do the coefficients in a balanced chemical equation mean? (Cont d) C 3 H 8 (g) + 5 O 2 (g) 3 CO 2 (g) + 4 H 2 O(g) Moles Because Avogadro s number is the same number no matter what microscale particle, we could say that in this reaction, 1 mole of propane reacts with 5 moles of oxygen gas to produce 3 moles of carbon dioxide and 4 moles of water. 6-5 Summary The Meaning of the Coefficients Table 6.1 Relationships between Reactants and Products C 3 H 8 (g) + 5 O 2 (g) 3 CO 2 (g) + 4 H 2 O(g) 1 molecule 5 molecules 3 molecules 4 molecules 2 molecules 10 molecules 6 molecules 8 molecules 100 molecules 500 molecules 300 molecules 400 molecules x molecules 5 x (6.022 x ) molecules 3 x (6.022 x ) molecules 4 x (6.022 x ) molecules 1 mole 5 moles 3 moles 4 moles 6-6 2

3 Mole-Mole Conversions In mole-mole conversions, we relate the moles of a reactant or product to other reactants or products using a mole ratio. Mole ratios: are obtained from the coefficients in the balanced chemical equation. help us determine the moles of one substance in a reaction when the number of moles of another substance in the same reaction is known. are used as conversion factors in dimensional analysis problems. Moles (Known substance) Mole Ratio Moles (Unknown substance) 6-7 Practice: Mole-Mole Conversions Benzene (C 6 H 6 ) burns in air according to the following equation: 2 C 6 H 6 (g) + 15 O 2 (g) 12 CO 2 (g) + 6 H 2 O(g) 1. What is the mole ratio of O 2 to C 6 H 6? 2. How many moles of O 2 are required to react with each mole C 6 H 6? 3. How many moles of O 2 are required to react with 0.38 mole of C 6 H 6? 6-8 Practice Solutions: Mole-Mole Conversions 2 C 6 H 6 (g) + 15 O 2 (g) 12 CO 2 (g) + 6 H 2 O(g) 1. What is the mole ratio of O 2 to C 6 H 6? Based on the coefficients in the balanced chemical equation, the mole ratio can be written two ways: 15 moles O 2 OR 2 moles C 6 H 6 2 moles C 6 H 6 15 moles O 2 2. How many moles of O 2 are required to react with each mole C 6 H 6? 7.5 moles of O 2 are required to react with each mole of C 6 H 6 3. How many moles of O 2 are required to react with 0.38 mole of C 6 H 6? 0.38 mol C 6 H 6 x 15 moles O 2 = 2.9 moles O 2 2 moles C 6 H

4 Mass-Mass Conversions Figure 6.5 Typically, chemical measuring devices do NOT measure in moles. We are often given grams as our beginning unit in problems that use a mole ratio. Therefore, we need to convert from grams to moles 1 st. The conversion factor we need to convert from grams to moles (or vice versa) is the molar mass (MM) Mass-Mass Conversions Given: 2 H 2 (g) + O 2 (g) 2 H 2 O(g) If 1.8 x 10 8 g of hydrogen is used in the liftoff during a shuttle launch, then: 1. What mass of oxygen gas is consumed? 2. What mass of water vapor is produced? 3. Does the mass of the water vapor equal the masses of the reactants? If so, then what law describes this observation? 6-11 Solutions Mass-Mass Conversions 2 H 2 (g) + O 2 (g) 2 H 2 O(g) 1. What mass of oxygen gas is consumed? Start with the number that was given in the problem 1.8 x 10 8 g of H 2 (g). Convert to moles via the MM(H 2 ), then use a mole ratio to relate H 2 to O 2. Finally, convert from moles of O 2 to grams of O 2 using the MM(O 2 ). 1.8 x 10 8 g H 2 x 1 mole H 2 x 1 mole O 2 x g O g H 2 2 moles H 2 1 mole O 2 = 1.4 x 10 9 g O 2 Mass H 2 (Given in Problem) MM(H ) Mole 2 Ratio MM(O ) 2 Moles H 2 Moles O 2 Mass O

5 Solutions Mass-Mass Conversions 2 H 2 (g) + O 2 (g) 2 H 2 O(g) 2. What mass of water vapor is produced? Start again with the number that was given in the problem 1.8 x 10 8 g of H 2 (g). Convert to moles via the MM(H 2 ), then use a mole ratio to relate H 2 to H 2 O this time. Finally, convert from moles of H 2 O to grams of H 2 O using the MM(H 2 O). 1.8 x 10 8 g H 2 x 1 mole H 2 x 2 mole H 2 O x g H 2 O 2.02 g H 2 2 moles H 2 1 mole H 2 O = 1.6 x 10 9 g H 2 O Mass H 2 (Given in Problem) MM(H ) Mole 2 Ratio Moles MM(H O) 2 Moles H 2 Mass H H 2 O 2 O 6-13 Solutions Mass-Mass Conversions Given: 2 H 2 (g) + O 2 (g) 2 H 2 O(g) (1.8 x 10 8 g H 2 ) + (1.4 x 10 9 g O 2 ) = (1.6 x 10 9 g H 2 O) Does the mass of the water vapor equal the masses of the reactants? Yes or close to it hydrogen and oxygen added together equals 1.58 x 10 9 g H 2 O. If so, then what law describes this observation? The Law of Conservation of Mass! 6-14 The Law of Conservation of Mass The Law of Conservation of Mass states that the masses of the reactants must equal the masses of the products. Mass Reactants = Mass Products

6 Practice: Mass-Mass Conversions When aluminum metal is exposed to oxygen gas, a coating of aluminum oxide forms on the surface of the aluminum. The balanced equation for the reaction of aluminum metal with oxygen gas is: 4 Al(s) + 3 O 2 (g) 2 Al 2 O 3 (s) Suppose a sheet of pure aluminum gains g of mass when exposed to air. Assume that this gain can be attributed to its reaction with oxygen. 1.What mass of O 2 reacted with the Al? 2.What mass of Al is reacted? 3.What mass of Al 2 O 3 is formed? 6-16 Practice Solutions: Mass-Mass Conversions 4 Al(s) + 3 O 2 (g) 2 Al 2 O 3 (s) Suppose a sheet of pure aluminum gains g of mass when exposed to air. Assume that this gain can be attributed to its reaction with oxygen. 1. What mass of O 2 reacted with the Al? g O 2 2. What mass of Al is reacted? g O 2 x 1 mole O 2 x 4 mol Al x g Al = g 32.0 g O 2 3 mole O 2 1 mol Al Al 3. What mass of Al 2 O 3 is formed? g O 2 x 1 mole O 2 x 2 mole Al 2 O 3 x g Al 2 O g O 2 3 mol O 2 1 mol Al 2 O 3 = g Al 2 O Limiting Reagents Take the equation: 2 Na(s) + Cl 2 (g) 2 NaCl(s) When reactants are not mixed in relative amounts as described by the balanced chemical equation, one reactant does not react completely. In this case, the two reactants are known as: Limiting reactant Reacts completely Limits the amount of the other reactant that can react Limits the amount of product that can be made Excess reactant DOES NOT react completely

7 Limiting Reagents Figure Understanding Limiting Reagents If section A of this picture tells how many of each part you need to make a solar car, then given the parts in section B, how many cars can you make? 6-20 Steps for Determining the Limiting Reactant 1. Calculate the amount of one reactant (B) needed to react with the other reactant (A). 2. Compare the calculated amount of B (amount needed) to the actual amount of B that is given. a. If calculated B = actual B, there is no limiting reactant. Both A and B will react completely. b. If calculated B > actual B, B is the limiting reactant. Only B will react completely. c. If calculated B < actual B, A is the limiting reactant. Only A will react completely

8 Practice Limiting Reactants (Molecular Scale) The molecular-level diagram shows a mixture of reactant molecules (three O 2 molecules and 8 H 2 molecules) for the following reaction: 2 H 2 (g) + O 2 (g) 2 H 2 O(g) a. Draw what the mixture should look like when the reaction is complete. b. What is the limiting reactant? c. Which reactant is left over? 6-22 Practice Solutions Limiting Reactants (Molecular Scale) The molecular-level diagram shows a mixture of reactant molecules (three O 2 molecules and 8 H 2 molecules) for the following reaction: 2 H 2 (g) + O 2 (g) 2 H 2 O(g) a. Draw what the mixture should look like when the reaction is complete Practice Solutions Limiting Reactants (Molecular Scale) 2 H 2 (g) + O 2 (g) 2 H 2 O(g) b. What is the limiting reactant? Using mole ratios from the balanced chemical equation: 3 molecules O 2 x 2 molecules H 2 O = 6 molecules H 2 O 1 molecule O 2 8 molecules H 2 x 2 molecules H 2 O = 8 molecules H 2 O 2 molecules H 2 The limiting reactant is O 2 because it can create 6 molecules of H 2 O while H 2 can create 8 molecules of H 2 O. b. Which reactant is left over? H 2 is left over at the end of the reaction

9 Practice Limiting Reactants (Mole Scale) The balanced equation for the reaction of phosphorus and oxygen gas to form diphosphorus pentoxide is: P 4 (s) + 5 O 2 (g) 2 P 2 O 5 (s) What is the limiting reactant when each of the following sets of quantities of reactants is mixed? a mol P 4 and 5.0 mol O 2 b mol P 4 and 1.0 mol O 2 c mol P 4 and 0.75 mol O Practice Solutions Limiting Reactants (Mole Scale) P 4 (s) + 5 O 2 (g) 2 P 2 O 5 (s) What is the limiting reactant when each of the following sets of quantities of reactants is mixed? a mol P 4 and 5.0 mol O mol P 4 x 2 mol P 2 O 5 = 1.0 mol P 2 O 5 1 mol P mol O 2 x 2 mol P 2 O 5 = 2.0 mol P 2 O 5 5 mol O 2 Therefore, phosphorus (P 4 ) is the limiting reactant Practice Solutions Limiting Reactants (Mole Scale) P 4 (s) + 5 O 2 (g) 2 P 2 O 5 (s) What is the limiting reactant when each of the following sets of quantities of reactants is mixed? b mol P 4 and 1.0 mol O mol P 4 x 2 mol P 2 O 5 = 0.40 mol P 2 O 5 1 mol P mol O 2 x 2 mol P 2 O 5 = 0.40 mol P 2 O 5 5 mol O 2 Therefore, neither reactant is the limiting reactant. Both are completely reacted

10 Practice Solutions Limiting Reactants (Mole Scale) P 4 (s) + 5 O 2 (g) 2 P 2 O 5 (s) What is the limiting reactant when each of the following sets of quantities of reactants is mixed? c mol P 4 and 0.75 mol O mol P 4 x 2 mol P 2 O 5 = 0.50 mol P 2 O 5 1 mol P mol O 2 x 2 mol P 2 O 5 = 0.30 mol P 2 O 5 5 mol O 2 Therefore, oxygen gas (O 2 ) is the limiting reactant Practice Limiting Reactants (Mole Scale from Masses) The balanced chemical equation for the reaction of aluminum metal and chlorine gas is: 2 Al(s) + 3 Cl 2 (g) 2 AlCl 3 (s) Assume 0.40 g Al is mixed with 0.60 g Cl 2. a. What is the limiting reactant? b. What is the maximum amount of AlCl 3, in grams, that can be produced? 6-29 Practice Solutions Limiting Reactants (Mole Scale from Masses) 2 Al(s) + 3 Cl 2 (g) 2 AlCl 3 (s) Assume 0.40 g Al is mixed with 0.60 g Cl 2. a. What is the limiting reactant? 0.40 g Al x 1 mol Al x 2 mol AlCl 3 x g AlCl g Al 2 mol Al 1 mol AlCl 3 = 2.0 g AlCl g Cl 2 x 1 mol Cl 2 x 2 mol AlCl 3 x g AlCl g Cl 2 3 mol Cl 2 1 mol AlCl 3 = 0.75 g AlCl 3 The limiting reactant is Cl 2 because the starting amount of Cl 2 produced a smaller amount of AlCl

11 Practice Solutions Limiting Reactants (Mole Scale from Masses) 2 Al(s) + 3 Cl 2 (g) 2 AlCl 3 (s) Assume 0.40 g Al is mixed with 0.60 g Cl 2. b. What is the maximum amount of AlCl 3, in grams, that can be produced? 0.75 g AlCl Percent Yield Percent yield Describes how much of a product is actually formed in comparison to how much should have been formed Theoretical yield The maximum amount of product that can be obtained from given amounts of reactants Actual yield The amount of product we measure in the laboratory Usually less than the theoretical yield percent = actual yield x 100% yield theoretical yield Figure Practice Percent Yield A student was synthesizing aspirin in the laboratory. Using the amount of limiting reactant, she calculated the amount of aspirin that should form as 8.95 g. When she weighed her aspirin product on the balance, its mass was 7.44 g. a. What is the actual yield of the aspirin? b. What is the theoretical yield of the aspirin? c. Calculate the percent yield for this synthesis

12 Practice Solutions Percent Yield Using the amount of limiting reactant, she calculated the amount of aspiring that should form as 8.95 g. When she weighed her aspirin product on the balance, its mass was 7.44 g. a. What is the actual yield of the aspirin? 7.44 g aspirin b. What is the theoretical yield of the aspirin? 8.95 g aspirin c. Calculate the percent yield for this synthesis. % yield = actual yield x 100% = 7.44 g aspirin x 100% theoretical yield 8.95 g aspirin = 83.1% 6-34 The Law of Conservation of Energy Energy can be converted or transferred, but it cannot be created or destroyed. Figure Conversion Efficiencies Efficiency is the amount of useful work that is achieved from an energy conversion. No conversion is totally efficient. The efficiency of a conversion is the percentage that ends up in the form that we want. Figure

13 Exothermic and Endothermic Reactions Exothermic reaction A reaction that releases energy into the surroundings Endothermic reaction A reaction that absorbs energy from its surroundings 6-37 Heat Energy that is transferred between two objects because of a difference in their temperatures. Units are calories and Joules: 1 cal = J 6-38 Specific Heat The amount of heat that must be added to 1 g of a substance to raise its temperature by 1 C. Units are Joules per gram per degree Celsius [J/(g C)] Is specific to the substance. See Table 6.2 for some common specific heats. q = mc T where q is heat, m is mass, C is specific heat, and T is the change in temperature

14 Practice Specific Heat The specific heat of aluminum is J/(g C). If 156 g of aluminum at 75.0 C is cooled to 25.5 C, how much heat is transferred? What is the sign of q, and what is its significance? 6-40 Practice Solutions Specific Heat The specific heat of aluminum is J/(g C). If 156 g of aluminum at 75.0 C is cooled to 25.5 C, how much heat is transferred? What is the sign of q, and what is its significance? q = mc T T = T f T i = 25.5 C 75.0 C = C q = 156 g * J/(g C) * C q = x 10 3 J The sign of q is negative and its significance is that this reaction is exothermic and therefore releases 6.91 x 10 3 J into its surroundings Energy of the System and the Surroundings q system + q surroundings = 0 A system can be an object such as a piece of pipe, or a process, such as a physical or chemical change. The surroundings are everything around the system

15 Is the measurement of heat transfer when there is no net heat loss The insulated container that allows for no heat loss is called a calorimeter. In calorimetry, q system + q surroundings = 0 Calorimetry Figure Practice Calorimetry A sample of a metal alloy is heated and then placed in g of water held in a calorimeter at 22.5 C. The final temperature of the water is 29.0 C. Assume heat exchange only occurs between the water and the alloy. a. Was the initial temperature of the alloy greater than or less than the initial temperature of the water? b. What is the heat change of the alloy? 6-44 Practice Solutions Calorimetry a. Was the initial temperature of the alloy greater than or less than the initial temperature of the water? Since the temperature of the water increases, the initial temperature of the alloy must be greater than the initial temperature of the water. b. What is the heat change of the alloy? q alloy + q water = 0 q alloy = - q water q water = m water C water T water T water = T f T i = 29.0 C 22.5 C = 6.5 C q water = g x J/(g C) x 6.5 C = 3.4 x 10 3 J q alloy = - q water = x 10 3 J

16 Heat Changes in Chemical Reactions A bomb calorimeter is used to measure the heat transfer in a chemical reaction. Therefore, q reaction + q water = 0 q reaction + q calorimeter = 0 Figure Practice - Heat Changes in Chemical Reactions The balanced equation for the combination reaction of hydrogen gas and solid iodine is: H 2 (g) + I 2 (s) 2 HI(g) The heat change q for this reaction is kj per mole of I 2 that reacts. a. Is this reaction endothermic or exothermic? b. What is the energy change when 2.50 mol of I 2 reacts? 6-47 Practice Solutions - Heat Changes in Chemical Reactions H 2 (g) + I 2 (s) 2 HI(g) The heat change q for this reaction is kj per mole of I 2 that reacts. a. Is this reaction endothermic or exothermic? Endothermic (indicated by the positive charge on q) b. What is the energy change when 2.50 mol of I 2 reacts? 2.50 mol I 2 x kj = +133 kj 1 mol I

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