Chapter 13 The Ideal Gas Law and Its Applications

Free Guide for Cracolice Peters Introductory Chemistry: An Active Learning Approach Second Edition www.brookscole.com/chemistry Chapter 13 The Ideal Gas Law and Its Applications Chapter 13 Assignment A: Gases Revisited and the Volume Amount Law In Section 4.3, you learned that there are four measurable properties of a gas: pressure, volume, temperature, and quantity. In Chapter 4, quantity was constant. You now know about the mole, and in Chapter 13, quantity is added as an additional measurable gas property. The first three big ideas given below are review items from Chapter 4. If you need to review these items, do so before going on. The Chapter 13 big ideas start with Item 4. 1) The Volume Temperature (Charles') Law states that at constant pressure, the volume of a fixed quantity of a gas is directly proportional to the absolute temperature, V µ T. (Review Section 4.4, if necessary.) 2) The Volume Pressure (Boyle's) Law states that at constant temperature, the volume of a fixed quantity of a gas is inversely proportional to its pressure, V µ 1/P. (Review Section 4.5, if necessary). 3) The Volume Temperature and Volume Pressure Laws can be coupled as the Combined Gas Law (Review Section 4.6, if necessary): P 1 V 1 T 1 = P 2 V 2 T 2 4) The Volume Amount (Avogadro's) Law states that equal volumes of two gases at the same temperature and pressure contain the same number of molecules, V µ n. Sections 13.1 13.2. Focus on Goal 1 as you study. Review Chapter 4, if necessary. The Volume-Amount Law is similar to the other gas laws. Questions, Exercises, and Problems 1. Check your answers with those at the end of the chapter. 80

Chapter 13 The Ideal Gas Law and Its Applications If your instructor recommends the Active Learning, do Questions, Exercises, and Problems 1. Chapter 13 Assignment B: The Ideal Gas Law and its Applications The proportional relationships among pressure, volume, quantity, and temperature of a gas make it possible to combine them in a single equation. This is known as the ideal gas equation, and it may be used for any gas that behaves in accord with the model of an ideal gas. There are five Goals for this assignment that all come together in the ideal gas equation. Look for this single recurring theme through the following ideas: 1) The ideal gas equation is PV = nrt. 2) Two values of the universal gas constant, R, are 0.0821 L atm/mol K and 62.4 L torr/mol K. 3) Given all the values in the ideal gas equation except one, the remaining value may be calculated. 4) The density of a gas is directly proportional to its molar mass. Either molar mass or density can be calculated from the other using the ideal gas equation. 5) Molar volume is the volume occupied by one mole of a gas. The molar volume of any ideal gas at STP is 22.4 L/mol. This quantity is useful in calculations involving moles, mass, volume, density, and molar mass of a gas measured at STP. Sections 13.3 13.5. Focus on Goals 2 6 as you study. PV = nrt is the key equation. Since mass (g) divided by molar mass m (g/mol) is equal to moles, an equivalent expression is PV = RT. To MM find density, defined as mass per unit volume, solve this equation for mass over volume: D m V = (MM)P. Molar volume is volume per mole, so RT solve the ideal gas equation for that: MV V n = RT. As long as you can P remember the ideal gas equation and if you are comfortable with algebra, this assignment should be no problem. Questions, Exercises, and Problems 2 14. Check your answers with those at the end of the chapter. If your instructor recommends the Active Learning, do Questions, Exercises, and Problems 2 14. 81

Guide for Introductory Chemistry: An Active Learning Approach Chapter 13 Assignment C: Pressure (STP) Gas Stoichiometry at Standard Temperature and FLEXTEXT OPTION Chapter 9 Assignment B has the same title as this Assignment and the same Goal. If your instructor did not assign Assignment 9 B with Chapter 9, Assignment 13 C should be studied now. If Assignment 9 B was included in your study of Chapter 9, you may omit this assignment, although you might find a brief review helpful. Your ability to satisfy Goal 7 should help you decide if a review is necessary. The main new idea in this section is: 1) The molar volume of all ideal gases at standard temperature and pressure (STP) is 22.4 L/mol. Section 13.6. Focus on Goal 7 as you study. 22.4 L per mole is a dimensional analysis conversion factor that can be used to convert between the volume of a gas at STP and the number of particles of that gas, counted in moles. 22.4 L/mol can be used only for ideal gases at STP. If your stoichiometry skills are rusty, review Section 9.1. Questions, Exercises, and Problems 15 16. Check your answers with those at the end of the chapter. If your instructor recommends the Active Learning, do Questions, Exercises, and Problems 15 16. Chapter 13 Assignment D: Gas Stoichiometry at non-stp Conditions Molar Volume Method FLEXTEXT OPTION Sections 13.7 and 13.8 offer alternative ways to solve gas stoichiometry problems at given temperatures and pressures. Assignment D is also presented in alternative ways, each keyed to one of the sections. If Section 13.7 is assigned, use this option for Assignment D and disregard the next option (Ideal Gas Equation Method). If Section 13.8 is assigned, disregard this option and use the next option for Assignment D. The big idea in this section is: 1) A gas stoichiometry problem at non-stp conditions can be solved by finding the molar volume of the gas and then following the stoichiometry path. Section 13.7. Focus on Goal 8 as you study. 82

Chapter 13 The Ideal Gas Law and Its Applications You combine two skills in this assignment: finding the molar volume of a gas and stoichiometry. If you have learned each of these skills, you simply combine them in this section. If you have trouble, review Section 13.5 on molar volume and/or Section 9.1 on stoichiometry. Questions, Exercises, and Problems 17 20. Check your answers with those at the end of the chapter. If your instructor recommends the Active Learning, do Questions, Exercises, and Problems 17 20. Chapter 13 Assignment D: Gas Stoichiometry at non-stp Conditions Ideal Gas Equation Method FLEXTEXT OPTION Sections 13.7 and 13.8 offer alternative ways to solve gas stoichiometry problems at given temperatures and pressures. Assignment D is also presented in alternative ways, each keyed to one of the sections. If Section 13.8 is assigned, use this option for Assignment D and disregard the previous option (Molar Volume Method). If Section 13.7 is assigned, disregard this option and use the previous option for Assignment D. The big idea in this section is: 1) A gas stoichiometry problem at non-stp conditions can be solved by applying the ideal gas equation and then following the stoichiometry path or by following the stoichiometry path and then applying the ideal gas equation. Section 13.8. Focus on Goal 8 as you study. You combine two skills in this assignment: using the ideal gas equation and stoichiometry. If you have learned each of these skills, you simply combine them in this section. If you have trouble, review Assignment B on the Ideal Gas Law and its applications and/or Section 9.1 on stoichiometry. Questions, Exercises, and Problems 17 20. Check your answers with those at the end of the chapter. If your instructor recommends the Active Learning, do Questions, Exercises, and Problems 17 20. Chapter 13 Assignment E: Volume Volume Gas Stoichiometry Chapter 13 concludes with a section on converting between volumes of gases reacting and produced in a chemical reaction. The main idea in this section is: 83

Guide for Introductory Chemistry: An Active Learning Approach 1) The ratio of volumes of gases in a reaction is the same as the ratio of moles, provided that the gas volumes are measured at the same temperature and pressure. Thus the coefficients in a balanced chemical equation can be used to convert between volumes, as long as the volumes are at the same temperature and pressure. Section 13.9. Focus on Goal 9 as you study. Two skills are combined in this assignment: using the equation P 1 V 1 = P V 2 2 and the stoichiometry path. If you have mastered each of T 1 T 2 these skills, you simply combine them to solve volume-volume gas stoichiometry problems. Questions, Exercises, and Problems 21 23. Check your answers with those at the end of the chapter. If your instructor recommends the Active Learning, do Questions, Exercises, and Problems 21 23. Chapter 13 Assignment F: Summary and Review When using the ideal gas equation, solve the equation algebraically for the wanted quantity, and then substitute the given values, including units. Don't solve the problem yet. If the unit cancellation does not give the wanted quantity, the solution is incorrect. Write the complete units on the gas constant, R, too. If you follow this procedure, you will then be certain that you are using the correct value for R and that you converted temperature from C to K. Once you've solved the ideal gas equation for the wanted quantity and canceled units, then get out your calculator and solve the problem. Gas density and molar volume problems are just like determining a single variable from the ideal gas equation, except that you are solving for a ratio of variables. Don't treat these ratioof-variables problems any differently than single-variable problems. As you solve stoichiometry problems involving gases, be sure to recognize that the pattern is identical to that used in mass stoichiometry. The stoichiometry pattern is applied in both cases. The only difference is the quantity unit being converted to moles, or vice versa. In one case it is grams, and in the other, it is gas volume at specified temperature and pressure. Review your lecture and textbook notes. the Chapter in Review and the Key Terms and Concepts, and read the Hints and Pitfalls to Avoid. 84

Chapter 13 The Ideal Gas Law and Its Applications Concept-Linking Exercises 1 4. Check your answers with those at the end of the chapter. Questions, Exercises, and Problems 24 27. Include Questions 28 29 if assigned by your instructor. Check your answers with those at the end of the chapter. Take If your instructor recommends the Active Learning, do Questions, Exercises, and Problems 24 26. Include Questions 27 28 if assigned by your instructor. the chapter summary test that follows. Check your answers with those at the end of this assignment. Chapter 13 Sample Test 1) One of two identical containers holds oxygen, and the other container holds chlorine. Both gases exert a pressure of 1.19 atm at 21 C. Which statement is incorrect? a) The number of molecules of oxygen is the same as the number of molecules of chlorine. b) The mass of oxygen is equal to the mass of chlorine. c) The number of moles of oxygen is equal to the number of moles of chlorine. d) The number of oxygen atoms is equal to the number of chlorine atoms. 2) There is 0.028 mol of an ideal gas in a 0.377 L container at 293 torr. What is the temperature of the gas ( C)? 3) What is the density (g/l) of ammonia at STP? 85

Guide for Introductory Chemistry: An Active Learning Approach 4) Find the molar mass of a gas if 0.460 L, measured at 819 torr and 22 C, has a mass of 0.369 gram. 5) What is the molar volume of fluorine gas at 17 C and 1.03 atm? 6) The molar volume of hydrogen bromide gas at 14 C and 772 torr is 23.2 L/mol. How many moles of gas are in a 1.25 L vessel at these conditions? 7) Carbon dioxide can be removed from a closed-container breathing apparatus by reaction with potassium superoxide: 4 KO 2 (s) + 2 CO 2 (g) Æ 2 K 2 CO 3 (s) + 3 O 2 (g) Calculate the mass of potassium superoxide needed to remove an STP volume of 10.0 L of carbon dioxide. 86

Chapter 13 The Ideal Gas Law and Its Applications 8) Calculate the mass (in grams) of zinc that must react to produce 148 ml of hydrogen gas at 767 torr and 24 C by the reaction Zn(s) + 2 HCl(aq) Æ H 2 (g) + ZnCl 2 (aq) 9) What volume of oxygen, measured at 0.891 atm and 18 C is needed to burn completely 4.18 L of butane measured at 1.34 atm and 38 C? The gas-phase reaction is 2 C 4 H 10 (g) + 13 O 2 (g) Æ 8 CO 2 (g) + 10 H 2 O(g) 87

Guide for Introductory Chemistry: An Active Learning Approach s to Chapter 13 Sample Test 1) b 2) GIVEN: 0.028 mol; 0.377 L; 293 torr WANTED: T ( C) EQUATION: T = PV nr = 293 torr 0.377 L 1 0.028 mol mol K 62.4 L torr = 63 K 63 273 = 2.10 10 2 C 3) GIVEN: 273 K; 1 atm; 17.03 g/mol WANTED: density (g/l) EQUATION: D m V = (MM)P RT = 17.03 g mol 1 atm mol K 0.0821 L atm 1 273 K = 0.760 g/l 4) GIVEN: 0.460 L; 819 torr; 22 C (295 K); 0.369 g WANTED: MM EQUATION: MM = mrt PV 62.4 L torr = 0.369 g mol K 295 K 1 819 torr 1 0.460 L = 18.0 g/mol 5) GIVEN: 17 C (256 K); 1.03 atm WANTED: molar volume (L/mol) EQUATION: MV V n = RT P 0.0821 L atm = mol K 256 K 6) GIVEN: MV = 23.2 L/mol; 1.25 L WANTED: mol PER/PATH: L 1.25 L 1 mol 23.2 L 23.3 L/mol æ æ æ æ æ Æ mol = 0.0539 mol 7) GIVEN: 10.0 L CO 2 at STP WANTED: mass KO 2 (assume g) 1 = 20.4 L/mol 1.03 atm PER/PATH: L CO 2 22.4 L CO 2 /mol CO æ æ æ æ æ æ æ æ 2Æ mol CO 2 4 mol KO 2 /2 mol CO æ æ æ æ æ æ æ æ æ 2Æ mol KO 2 71.1 g KO 2 /mol KO æ æ æ æ æ æ æ æ æ 2Æ g KO 2 10.0 L CO 2 1 mol CO 2 22.4 L CO 2 4 mol KO 2 2 mol CO 2 71.1 g KO 2 mol KO 2 = 63.5 g KO 2 88

Chapter 13 The Ideal Gas Law and Its Applications 8) Molar volume method GIVEN: 767 torr; 24 C (297 K) WANTED: MV (L/mol) EQUATION: MV V n = RT P GIVEN: 148 ml H 2 62.4 L torr = mol K 297 K 1 767 torr WANTED: g Zn = 24.2 L/mol PER/PATH: ml H 2 1000 ml H 2 /L H æ æ æ æ æ æ æ 2Æ L H 2 24.2 L H 2 /mol H æ æ æ æ æ æ æ 2Æ mol H 2 1 mol Zn/1 mol H æ æ æ æ æ æ æ æ 2 Æ mol Zn 65.39 g Zn/mol Zn æ æ æ æ æ æ æ æ Æ 148 ml H 2 Ideal gas equation method 1 L H 2 1000 ml H 2 1 mol H 2 24.2 L H 2 1 mol Zn 1 mol H 2 65.39 g Zn mol Zn g Zn = 0.400 g Zn GIVEN: 148 ml; 767 torr; 24 C (297 K) WANTED: mol H 2 EQUATION: n = PV RT = 767 torr 148 ml mol K 62.4 L torr 1 297 K 1 L 1000 ml = 0.00613 mol H 2 GIVEN: 0.00613 mol H 2 WANTED: g Zn PER/PATH: mol H 2 1 mol Zn/1 mol H æ æ æ æ æ æ æ æ 2 Æ mol Zn 65.39 g Zn/mol Zn æ æ æ æ æ æ æ æ Æ g Zn 0.00613 mol H 2 1 mol Zn 1 mol H 2 65.39 g Zn mol Zn = 0.401 g Zn 9) Volume Temperature Pressure Initial Value (1) 4.18 L 38 + 273 = 311 K 1.34 atm Final Value (2) V 2 18 + 273 = 291 K 0.891 atm V 2 = V 1 P 1 P 2 T 2 T 1 = 4.18 L 1.34 atm 0.891 atm 291 K 311 K = 5.88 L GIVEN: 5.88 L C 4 H 10 WANTED: volume O 2 (assume L) PER/PATH: L C 4 H 10 13 L O 2 /2 L C 4 H æ æ æ æ æ æ æ 10 Æ L O 2 5.88 L C 4 H 10 13 L O 2 2 L C 4 H 10 = 38.2 L O 2 89