Introductory Chemistry: An Active Learning ApproachSecond Edition
www.brookscole.com/chemistry
Chapter 14Combined Gas Law Applications
Chapter 14–Assignment A: Gases Revisited
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. In Chapter 14,quantity will be allowed to vary.
The three big ideas given below are review items from Chapter 4. This assignment ispresented for the purpose of reviewing these items.
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 Laws (Review Section 4.6, if necessary):
†
P1V1
T1
=
†
P2V2
T2
Learning Procedures
Study Section 14.1.
Strategy Review Chapter 4, if necessary.
Answer No end-of-chapter questions are given in Chapter 14 for this assignment.You may wish to practice with questions from Chapter 4, if necessary.
Chapter 14–Assignment B: Molar Volume, Density, and Molar Mass
Three ratios, molar volume, density, and molar mass, are important for understandingrelationships among the four measurable properties of a gas. We examine these three ratiosin this assignment. Look for these important ideas:
1) The molar volume of a gas is the volume occupied by one mole of gas at a giventemperature and pressure.
2) One mole of any gas at standard temperature and pressure, 0°C and 1 atm, occupies22.4 liters.
3) Density, by definition, is mass per volume. Gas densities are usually measured ingrams per liter.
4) Molar mass, by definition, is the mass of one mole of a substance. Molar mass isconstant, no matter the temperature and pressure.
Learning Procedures
Study Sections 14.2–14.4. Focus on Goals 1–6 as you study.
Strategy The emphasis in this assignment is on solving numeric problems. Practice by solving lots of them.
Answer Questions, Exercises, and Problems 1–13. Check your answers with those at the end of the chapter.
Workbook If your instructor recommends the Active Learning Workbook, doQuestions, Exercises, and Problems 1–13.
Chapter 14–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 14–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 stoichiometry path can be expanded to include gases. The molar volume of a gas at STP, 22.4 L/mol, provides a conversion between gas volume and moles of that gas.
Study Guide for Introductory Chemistry: An Active Learning Approach
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 14–15. Check your answers with thoseat the end of the chapter.
Workbook If your instructor recommends the Active Learning Workbook, doQuestions, Exercises, and Problems 14–15.
Chapter 14–Assignment D: Gas Stoichiometry at non-STP ConditionsMolar Volume Method
FLEXTEXT OPTIONSections 14.6 and 14.7 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 14.6 is assigned, use this option for Assignment D anddisregard the next option (Combined Gas Equation Method). If Section 14.7 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 14.6. Focus on Goal 8 as you study.
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 14.2 on molar volume and/or Section 9.1 on stoichiometry.
Answer Questions, Exercises, and Problems 16–19. Check your answers with those at the end of the chapter.
Workbook If your instructor recommends the Active Learning Workbook, doQuestions, Exercises, and Problems 16–19.
Chapter 14–Assignment D: Gas Stoichiometry at non-STP ConditionsCombined Gas Equation Method
FLEXTEXT OPTIONSections 14.6 and 14.7 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 14.7 is assigned, use this option for Assignment D anddisregard the previous option (Molar Volume Method). If Section 14.6 is assigned,disregard this option and use the previous option for Assignment D.
In this section, we use the combined gas equation from Chapter 4 along with the molarvolume of a gas at STP from Assignment B and the stoichiometry pattern from Chapter 9.There are no new concepts here; this assignment just introduces a new combination of oldconcepts.
The ideas to review are:
1) The combined gas laws equation is
†
P1V1
T1
=
†
P2V2
T2
If you know the volume of a gas at a certain temperature and pressure, the volume ata new temperature and pressure is given by algebraically rearranging the combinedgas laws equation to
V2 =
†
P1V1T2
P2T1
2) The coefficients in a chemical equation express the mole relationships between thedifferent substances in the reaction. The coefficients may be used in a dimensionalanalysis conversion from moles of one substance to moles of another.
3) The molar volume of all ideal gases at standard temperature and pressure (STP) is22.4 L/mol.
Learning Procedures
Study Section 14.7. Focus on Goal 8 as you study.
Strategy This assignment combines the three ideas listed above. Review them, ifnecessary, before starting this assignment. You may find a brief review ofSection 4.6 particularly helpful if it has been some time since you studiedChapter 4.
Answer Questions, Exercises, and Problems 16–19. Check your answers with thoseat the end of the chapter.
Workbook If your instructor recommends the Active Learning Workbook, doQuestions, Exercises, and Problems 16–19.
Chapter 14–Assignment E: Volume–Volume Gas Stoichiometry
Chapter 14 concludes with a section on converting between volumes of gases reacting andproduced in a chemical reaction. The main idea in this section is:
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 14.8. 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 20–23. Check your answers with those at the end of the chapter.
Workbook If your instructor recommends the Active Learning Workbook, doQuestions, Exercises, and Problems 20–23.
Chapter 14–Assignment F: Summary and Review
The first important idea presented in Chapter 14 is that the molar volume of an ideal gas atSTP is 22.4 L/mol. Memorize this relationship. The molar volume of a gas at any othertemperature and pressure can be found by a modification of the combined gas equationfrom Chapter 4:
V2/mol = V1/mol ¥
†
P1
P2
¥
†
T2
T1
We next introduced the three important ratios that have physical significance for gases:density, molar mass, and molar volume. To use these ratios, you must know theirdefinitions:
D ≡ m/V MV ≡ V/mol MM ≡ mass/mol
Problem solving with these ratios is much easier if you include units!
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.
the Chapter in Review and the Key Terms and Concepts, and read the StudyHints and Pitfalls to Avoid.
Answer Concept-Linking Exercises 1–2. 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 27–30 ifassigned by your instructor.
Take the chapter summary test that follows. Check your answers with those at theend of this assignment.
Chapter 14 Sample Test
1) What is the molar volume of fluorine gas at –17°C and 1.03 atm?
2) 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?
3) What is the volume occupied by 10.0 g helium at a temperature at which its densityis 0.175 g/L?
Study Guide for Introductory Chemistry: An Active Learning Approach
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)
Answers to Chapter 14 Sample Test
1) Molar Volume Temperature PressureInitial Value (1) 22.4 L/mol 273 K 1.00 atmFinal Value (2) V2 L/mol –17 + 273 = 256 K 1.03 atm
EQUATION: V2/mol = V1/mol ¥
†
P1
P2
¥
†
T2
T1
= 22.4 L/mol ¥
†
1.00 atm1.03 atm
¥
†
256 K273 K
=
20.4 L/mol
Study Guide for Introductory Chemistry: An Active Learning Approach
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