Chapter 13 · Chapter 13 ... Check your answers with those at the end of the chapter. ... Chapter...
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Copyright © 2004 Brooks/Cole, a division of Thomson Learning, Inc. No part of this work may be reproduced without the written permission of the publisher. 80 Free Study 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 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 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 n. Learning Procedures Study Sections 13.1–13.2. Focus on Goal 1 as you study. Strategy Review Chapter 4, if necessary. The Volume-Amount Law is similar to the other gas laws. Answer Questions, Exercises, and Problems 1. Check your answers with those at the end of the chapter.
Transcript of Chapter 13 · Chapter 13 ... Check your answers with those at the end of the chapter. ... Chapter...
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80
Free Study Guide forCracolice • Peters
Introductory Chemistry: An Active Learning ApproachSecond Edition
www.brookscole.com/chemistry
Chapter 13The 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 knowabout the mole, and in Chapter 13, quantity is added as an additional measurable gasproperty.
The first three big ideas given below are review items from Chapter 4. If you need to reviewthese 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, thevolume of a fixed quantity of a gas is directly proportional to the absolutetemperature, V µ T. (Review Section 4.4, if necessary.)
2) The Volume–Pressure (Boyle's) Law states that at constant temperature, thevolume 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 theCombined Gas Law (Review Section 4.6, if necessary):
†
P1V1
T1
=
†
P2V2
T2
4) The Volume–Amount (Avogadro's) Law states that equal volumes of two gasesat the same temperature and pressure contain the same number of molecules, V µ n.
Learning Procedures
Study Sections 13.1–13.2. Focus on Goal 1 as you study.
Strategy Review Chapter 4, if necessary. The Volume-Amount Law is similar to the other gas laws.
Answer Questions, Exercises, and Problems 1. Check your answers with those at the end of the chapter.
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Workbook If your instructor recommends the Active Learning Workbook, doQuestions, 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 gasmake it possible to combine them in a single equation. This is known as the ideal gasequation, and it may be used for any gas that behaves in accord with the model of an idealgas.
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 and62.4 L • torr/mol • K.
3) Given all the values in the ideal gas equation except one, the remaining value may becalculated.
4) The density of a gas is directly proportional to its molar mass. Either molar mass ordensity 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 ofany ideal gas at STP is 22.4 L/mol. This quantity is useful in calculations involvingmoles, mass, volume, density, and molar mass of a gas measured at STP.
Learning Procedures
Study Sections 13.3–13.5. Focus on Goals 2–6 as you study.
Strategy PV = nRT is the key equation. Since mass (g) divided by molar mass
(g/mol) is equal to moles, an equivalent expression is PV =
†
mMM
RT. To find density, defined as mass per unit volume, solve this equation for mass
over volume: D ≡
†
mV
=
†
(MM)PRT
. Molar volume is volume per mole, so
solve the ideal gas equation for that: MV ≡
†
Vn
=
†
RTP
. As long as you can remember the ideal gas equation and if you are comfortable with algebra, this assignment should be no problem.
Answer Questions, Exercises, and Problems 2–14. Check your answers with those at the end of the chapter.
Workbook If your instructor recommends the Active Learning Workbook, doQuestions, Exercises, and Problems 2–14.
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Chapter 13–Assignment C: Gas Stoichiometry at Standard Temperature andPressure (STP)
FLEXTEXT OPTIONChapter 9–Assignment B has the same title as this Assignment and the same Goal. If yourinstructor did not assign Assignment 9–B with Chapter 9, Assignment 13–C should bestudied now. If Assignment 9–B was included in your study of Chapter 9, you may omitthis assignment, although you might find a brief review helpful. Your ability to satisfy Goal7 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.
Learning Procedures
Study Section 13.6. Focus on Goal 7 as you study.
Strategy 22.4 L per mole is a dimensional analysis conversion factor that can be usedto convert between the volume of a gas at STP and the number of particles ofthat gas, counted in moles. 22.4 L/mol can be used only for ideal gases atSTP. If your stoichiometry skills are rusty, review Section 9.1.
Answer Questions, Exercises, and Problems 15–16. Check your answers with thoseat the end of the chapter.
Workbook If your instructor recommends the Active Learning Workbook, doQuestions, Exercises, and Problems 15–16.
Chapter 13–Assignment D: Gas Stoichiometry at non-STP ConditionsMolar Volume Method
FLEXTEXT OPTIONSections 13.7 and 13.8 offer alternative ways to solve gas stoichiometry problems at giventemperatures and pressures. Assignment D is also presented in alternative ways, each keyedto one of the sections. If Section 13.7 is assigned, use this option for Assignment D anddisregard 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 themolar volume of the gas and then following the stoichiometry path.
Learning Procedures
Study Section 13.7. Focus on Goal 8 as you study.
Chapter 13 The Ideal Gas Law and Its Applications
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Strategy 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.
Answer Questions, Exercises, and Problems 17–20. Check your answers with those at the end of the chapter.
Workbook If your instructor recommends the Active Learning Workbook, doQuestions, Exercises, and Problems 17–20.
Chapter 13–Assignment D: Gas Stoichiometry at non-STP ConditionsIdeal Gas Equation Method
FLEXTEXT OPTIONSections 13.7 and 13.8 offer alternative ways to solve gas stoichiometry problems at giventemperatures and pressures. Assignment D is also presented in alternative ways, each keyedto one of the sections. If Section 13.8 is assigned, use this option for Assignment D anddisregard 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 theideal gas equation and then following the stoichiometry path or by following thestoichiometry path and then applying the ideal gas equation.
Learning Procedures
Study Section 13.8. Focus on Goal 8 as you study.
Strategy 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.
Answer Questions, Exercises, and Problems 17–20. Check your answers with those at the end of the chapter.
Workbook If your instructor recommends the Active Learning Workbook, doQuestions, 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 andproduced in a chemical reaction. The main idea in this section is:
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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 convertbetween volumes, as long as the volumes are at the same temperature and pressure.
Learning Procedures
Study Section 13.9. Focus on Goal 9 as you study.
Strategy Two skills are combined in this assignment: using the equation
†
P1V1
T1
=
†
P2V2
T2
and the stoichiometry path. If you have mastered each of
these skills, you simply combine them to solve volume-volume gas stoichiometry problems.
Answer Questions, Exercises, and Problems 21–23. Check your answers with those at the end of the chapter.
Workbook If your instructor recommends the Active Learning Workbook, doQuestions, 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 unitcancellation does not give the wanted quantity, the solution is incorrect. Write the completeunits on the gas constant, R, too. If you follow this procedure, you will then be certain thatyou 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, thenget out your calculator and solve the problem.
Gas density and molar volume problems are just like determining a single variable from theideal gas equation, except that you are solving for a ratio of variables. Don't treat these ratio-of-variables problems any differently than single-variable problems.
As you solve stoichiometry problems involving gases, be sure to recognize that the pattern isidentical to that used in mass stoichiometry. The stoichiometry pattern is applied in bothcases. The only difference is the quantity unit being converted to moles, or vice versa. In onecase it is grams, and in the other, it is gas volume at specified temperature and pressure.
Learning Procedures
Review your lecture and textbook notes.
the Chapter in Review and the Key Terms and Concepts, and read the StudyHints and Pitfalls to Avoid.
Chapter 13 The Ideal Gas Law and Its Applications
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Answer Concept-Linking Exercises 1–4. Check your answers with those at the endof the chapter.
Questions, Exercises, and Problems 24–27. Include Questions 28–29 ifassigned by your instructor. Check your answers with those at the end of thechapter.
Workbook If your instructor recommends the Active Learning Workbook, doQuestions, Exercises, and Problems 24–26. Include Questions 27–28 ifassigned by your instructor.
Take the chapter summary test that follows. Check your answers with those at theend of this assignment.
Chapter 13 Sample Test
1) One of two identical containers holds oxygen, and the other container holdschlorine. Both gases exert a pressure of 1.19 atm at 21°C. Which statement isincorrect?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 thetemperature of the gas (°C)?
3) What is the density (g/L) of ammonia at STP?
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4) Find the molar mass of a gas if 0.460 L, measured at 819 torr and 22°C, has a massof 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 byreaction with potassium superoxide:
4 KO2(s) + 2 CO2(g) Æ 2 K2CO3(s) + 3 O2(g)
Calculate the mass of potassium superoxide needed to remove an STP volume of10.0 L of carbon dioxide.
Chapter 13 The Ideal Gas Law and Its Applications
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87
8) Calculate the mass (in grams) of zinc that must react to produce 148 mL ofhydrogen gas at 767 torr and 24°C by the reaction
Zn(s) + 2 HCl(aq) Æ H2(g) + ZnCl2(aq)
9) What volume of oxygen, measured at 0.891 atm and 18°C is needed to burncompletely 4.18 L of butane measured at 1.34 atm and 38°C? The gas-phasereaction is
2 C4H1 0(g) + 13 O2(g) Æ 8 CO2(g) + 10 H2O(g)
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Answers to Chapter 13 Sample Test
1) b
2) GIVEN: 0.028 mol; 0.377 L; 293 torr WANTED: T (°C)
EQUATION: T =
†
PVnR
= 293 torr ¥ 0.377 L ¥
†
10.028 mol
¥
†
mol ⋅ K62.4 L ⋅ torr
= 63 K63 – 273 = –2.10 ¥ 102 °C
3) GIVEN: 273 K; 1 atm; 17.03 g/mol WANTED: density (g/L)
EQUATION: D ≡
†
mV
=
†
(MM)PRT
=
†
17.03 gmol
¥ 1 atm ¥
†
mol ⋅ K0.0821 L ⋅ atm
¥
†
1273 K
=0.760 g/L
4) GIVEN: 0.460 L; 819 torr; 22°C (295 K); 0.369 g WANTED: MM
EQUATION: MM =
†
mRTPV
= 0.369 g ¥
†
62.4 L ⋅ torrmol ⋅ K
¥ 295 K ¥
†
1819 torr
¥
†
10.460 L
= 18.0 g/mol
5) GIVEN: –17°C (256 K); 1.03 atm WANTED: molar volume (L/mol)
EQUATION: MV ≡
†
Vn
=
†
RTP
=
†
0.0821 L ⋅ atmmol ⋅ K
¥ 256 K ¥
†
11.03 atm
= 20.4 L/mol
6) GIVEN: MV = 23.2 L/mol; 1.25 L WANTED: mol
PER/PATH: L
†
23.3 L/molæ Æ æ æ æ æ mol
1.25 L ¥
†
1 mol23.2 L
= 0.0539 mol
7) GIVEN: 10.0 L CO2 at STP WANTED: mass KO2 (assume g)
PER/PATH: L CO2
†
22.4 L CO2/mol CO2æ Æ æ æ æ æ æ æ æ æ mol CO2
†
4 mol KO2/2 mol CO2æ Æ æ æ æ æ æ æ æ æ æ mol KO2
†
71.1 g KO2/mol KO2æ Æ æ æ æ æ æ æ æ æ g KO2
10.0 L CO2 ¥
†
1 mol CO2
22.4 L CO2
¥
†
4 mol KO2
2 mol CO2
¥
†
71.1 g KO2
mol KO2
= 63.5 g KO2
Chapter 13 The Ideal Gas Law and Its Applications
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89
8) Molar volume method
GIVEN: 767 torr; 24°C (297 K) WANTED: MV (L/mol)
EQUATION: MV ≡
†
Vn
=
†
RTP
=
†
62.4 L ⋅ torrmol ⋅ K
¥ 297 K ¥
†
1767 torr
= 24.2 L/mol
GIVEN: 148 mL H2 WANTED: g Zn
PER/PATH: mL H2
†
1000 mL H2/L H2æ Æ æ æ æ æ æ æ æ L H2
†
24.2 L H2/mol H2æ Æ æ æ æ æ æ æ æ mol H2
†
1 mol Zn/1 mol H2æ Æ æ æ æ æ æ æ æ mol Zn
†
65.39 g Zn/mol Znæ Æ æ æ æ æ æ æ æ g Zn
148 mL H2 ¥
†
1 L H2
1000 mL H2
¥
†
1 mol H2
24.2 L H2
¥
†
1 mol Zn1 mol H2
¥
†
65.39 g Znmol Zn
= 0.400 g Zn
Ideal gas equation method
GIVEN: 148 mL; 767 torr; 24°C (297 K) WANTED: mol H2
EQUATION: n =
†
PVRT
= 767 torr ¥ 148 mL ¥
†
mol ⋅ K62.4 L ⋅ torr
¥
†
1297 K
¥
†
1 L1000 mL
=0.00613 mol H2
GIVEN: 0.00613 mol H2 WANTED: g Zn
PER/PATH: mol H2
†
1 mol Zn/1 mol H2æ Æ æ æ æ æ æ æ æ mol Zn
†
65.39 g Zn/mol Znæ Æ æ æ æ æ æ æ æ g Zn
0.00613 mol H2 ¥
†
1 mol Zn1 mol H2
¥
†
65.39 g Znmol Zn
= 0.401 g Zn
9) Volume Temperature PressureInitial Value (1) 4.18 L 38 + 273 = 311 K 1.34 atmFinal Value (2) V2 18 + 273 = 291 K 0.891 atm
V2 = V1 ¥
†
P1
P2
¥
†
T2
T1
= 4.18 L ¥
†
1.34 atm0.891 atm
¥
†
291 K311 K
= 5.88 L
GIVEN: 5.88 L C4H1 0 WANTED: volume O2 (assume L)
PER/PATH: L C4H1 0
†
13 L O2/2 L C4H10æ Æ æ æ æ æ æ æ æ L O2
5.88 L C4H1 0 ¥
†
13 L O2
2 L C4H10
= 38.2 L O2
