Chapter 10. Gases
Media Resources
Figures and Tables in Transparency Pack: Section:
Figure 10.1 Calculating Atmospheric Pressure 10.2 Pressure
Figure 10.2 A Mercury Barometer 10.2 Pressure
Figure 10.3 A Mercury Manometer 10.2 Pressure
Activities: Section:
Manometer 10.2 Pressure
Gas Laws 10.3 Gas Laws
Density of Gases 10.5 Further Applications of the Ideal-Gas
Animations: Section:
P-V Relationships 10.3 The Gas Laws
Airbags 10.5 Further Applications of the Ideal-Gas
Equation
Kinetic Energy of a Gas 10.7 Kinetic-Molecular Theory of Gases
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Other Resources
Further Readings: Section:
Gases and Their Behavior 10.1 Characteristics of Gases
Carbon Dioxide Flooding: A Classroom Case Study 10.1 Characteristics of Gases
Derived from Surgical Practice
Live Demonstrations: Section:
Boiling at Reduced Pressure 10.2 Pressure
Boyle’s Law 10.3 The Gas Laws
Boyle’s Law and the Monster Marshmallow 10.3 The Gas Laws
Robert Boyle: The Founder of Modern Chemistry 10.3 The Gas Laws
Boyle’s Law and the Mass of a Textbook 10.3 The Gas Laws
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Chapter 10. Gases
Common Student Misconceptions
• Students need to be told to always use temperature in Kelvin in gas problems.
• Due to several systems of units, students often use ideal gas constants with units inconsistent with
values.
Teaching Tips
• Students should always use units in gas-law problems to keep track of required conversions.
Encourage them to use dimensional analysis to detect conversion errors.
Lecture Outline
10.1 Characteristics of Gases
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• All substances have three phases: solid, liquid and gas.
• Substances that are liquids or solids under ordinary conditions may also exist as gases.
• These are often referred to as vapors.
• As a result, each molecule of gas behaves largely as though other molecules were absent.
FORWARD REFERENCES
• Thermodynamics of phase changes will be discussed in Chapter 19.
• Such important gaseous reactions as the Haber process or equilibria involving nitrogen oxides
will be covered in Chapter 15.
10.2 Pressure
• Pressure is the force acting on an object per unit area:
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Atmospheric Pressure and the Barometer
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• The SI unit of force is the newton (N).
• 1 N = 1 kg-m/s2
• The SI unit of pressure is the pascal (Pa).
• 1 Pa = 1 N/m2
• A related unit is the bar, which is equal to 105 Pa.
• Another pressure unit is pounds per square inch (psi, lbs/in2).
• The pressure of enclosed gases is measured with a manometer.
FORWARD REFERENCES
• Osmotic pressure (in atm) will be calculated in Chapter 13 (section 13.5).
• Kp’s and thermodynamic equilibrium constants in Chapter 15 will use pressure (in atm).
• Pressure and Le Châtelier’s principle will be discussed in Chapter 15 (section 15.7).
10.3 The Gas Laws
• The equations that express the relationships among T (temperature), P (pressure), V (volume), and n
(number of moles of gas) are known as gas laws.
The Pressure-Volume Relationship: Boyle’s Law
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• Weather balloons are used as a practical application of the relationship between pressure and volume
of a gas.
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Figure 10.1 from Transparency Pack
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Figure 10.2 from Transparency Pack
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“Boiling at Reduced Pressure” from Live Demonstrations
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“Manometer” Activity from Instructor’s Resource CD/DVD
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• According to Boyle’s law, when the volume of the lungs increases, the pressure decreases;
therefore, the pressure inside the lungs is less than atmospheric pressure.
• Atmospheric pressure then forces air into the lungs until the pressure once again equals
atmospheric pressure.
• As we breathe out, the diaphragm moves up and the ribs contract. Therefore, the volume of the
lungs decreases.
• By Boyle’s law, the pressure increases and air is forced out.
The Temperature-Volume Relationship: Charles’s Law
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• We know that hot-air balloons expand when they are heated.
• Charles’s law: The volume of a fixed quantity of gas at constant pressure is directly proportional to
The Quantity-Volume Relationship: Avogadro’s Law
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• Gay-Lussac’s law of combining volumes: At a given temperature and pressure the volumes of gases
that react with one another are ratios of small whole numbers.
FORWARD REFERENCES
• Vapor pressure vs. temperature will be discussed in Chapter 13 (section 13.5).
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“Effect of Pressure on the Size of a Balloon” from Live Demonstrations
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“Charles’ Law of Gases” from Live Demonstrations
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• Increasing entropy of gases with temperature as well as entropy of gases vs. other states of
matter will be discussed in Chapter 19 (section 19.3).
10.4 The Ideal-Gas Equation
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• Summarizing the gas laws:
• Boyle: V 1/P (constant n, T)
• Charles: V T (constant n, P)
• Avogadro: V n (constant P, T)
• Combined: V nT/P
Relating the Ideal-Gas Equation and the Gas Laws
• If PV = nRT and n and T are constant, then PV is constant and we have Boyle’s law.
• Other laws can be generated similarly.
• In general, if we have a gas under two sets of conditions, then
FORWARD REFERENCES
• The ideal gas constant will be used in Chapter 14 in the Arrhenius equation (section 14.5).
• The ideal gas constant will be used in Chapter 15 in conversions between Kc and Kp (section
10.5 Further Applications of the Ideal-Gas Equation
Gas Densities and Molar Mass
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• Density has units of mass over volume.
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“Gay–Lussac: Chemist Extraordinary” from Further Readings
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• Rearranging the ideal-gas equation with M as molar mass we get
Volumes of Gases in Chemical Reactions
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• The ideal-gas equation relates P, V, and T to number of moles of gas.
• The n can then be used in stoichiometric calculations.
FORWARD REFERENCES
• Solubility of gases vs. temperature (Henry’s law) will be covered in Chapter 13 (section
13.3).
10.6 Gas Mixtures and Partial Pressures
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• Since gas molecules are so far apart, we can assume they behave independently.
• Dalton observed:
• The total pressure of a mixture of gases equals the sum of the pressures that each would exert if
present alone.
Partial Pressures and Mole Fractions
• Let n1 be the number of moles of gas 1 exerting a partial pressure P1, then
P1 =
Pt
• Where
is the mole fraction (n1/nt).
• Note that a mole fraction is a dimensionless number.
Collecting Gases over Water
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• It is common to synthesize gases and collect them by displacing a volume of water.
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FORWARD REFERENCES
• Vapor pressure, volatility, and temperature relationships will be introduced in Chapter 11
(section 11.5) and further applied to Raoult’s Law in Chapter 13 (section 13.5).
• Air – a mixture of gases – will be discussed in Chapter 18 (section 18.1) and 22 (section
22.7).
10.7 Kinetic-Molecular Theory of Gases
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• The kinetic molecular theory of gases was developed to explain gas behavior.
• It is a theory of moving molecules.
• Summary:
• 1. Gases consist of a large number of molecules in constant random motion.
• 2. The combined volume of all the molecules is negligible compared with the volume of the
container.
Distributions of Molecular Speed
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• As kinetic energy increases, the velocity of the gas molecules increases.
• Root-mean-square (rms) speed, urms, is the speed of a gas molecule having average kinetic
energy.
• Average kinetic energy, , is related to rms speed:
= ½ mu2
• where m = mass of the molecule.
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1
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2
1
M
M
r
r=
Application of Kinetic-Molecular Theory to the Gas-Laws
• We can understand empirical observations of gas properties within the framework of the kinetic–
molecular theory.
• Effect of an increase in volume (at constant temperature):
• As volume increases at constant temperature, the average kinetic of the gas remains constant.
• Therefore, u is constant.
• Therefore, pressure increases.
FORWARD REFERENCES
• The collision model in Chapter 14 (section 14.5) will be based on the kinetic-molecular
theory.
10.8 Molecular Effusion and Diffusion
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• The average kinetic energy of a gas is related to its mass:
= ½ mu2
• Consider two gases at the same temperature: the lighter gas has a higher rms speed than the heavier
Graham’s Law of Effusion
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• The rate of effusion can be quantified.
• Consider two gases with molar masses M1 and M2, with effusion rates, r1 and r2, respectively:
• The relative rate of effusion is given by Graham’s law:
• Only those molecules that hit the small hole will escape through it.
• Therefore, the higher the rms speed, the more likely that a gas molecule will hit the hole.
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Diffusion and Mean Free Path
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• Diffusion is faster for light gas molecules.
• Diffusion is significantly slower than the rms speed.
• Diffusion is slowed by collisions of gas molecules with one another.
FORWARD REFERENCES
• Similar molar mass related issues (e.g., passing of particles of solute through semipermeable
membranes) for solutions will be discussed in Chapter 13 (section 13.5).
10.9 Real Gases: Deviations from Ideal Behavior
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• From the ideal gas equation:
• As the pressure on a gas increases, the molecules are forced closer together.
• As the molecules get closer together, the free space in which the molecules can move gets
smaller.
• The smaller the container, the more of the total space the gas molecules occupy.
• Therefore, the higher the pressure, the less the gas resembles an ideal gas.
• As the gas molecules get closer together, the intermolecular distances decrease.
• The smaller the distance between gas molecules, the more likely that attractive forces will
develop between the molecules.
n
RT
PV =
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The van der Waals Equation
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• We add two terms to the ideal gas equation to correct for
• The volume of molecules:
• To understand the effect of intermolecular forces on pressure, consider a molecule that is about to
strike the wall of the container.
• The striking molecule is attracted by neighboring molecules.
• Therefore, the impact on the wall is lessened.
FORWARD REFERENCES
• The name of van der Waals will come up again in Chapter 11 for van der Waals forces.
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“Nonideal Gas Behavior” Activity from Instructor’s Resource CD/DVD
( )
nbV−
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Further Readings:
1. Joseph S. Schmuckler, “Gases and Their Behavior,” J. Chem. Educ., Vol. 57, 1980, 885. A collection
of gas law references from past editions of the Journal of Chemical Education
5. Andreas Madlung, “The Chemistry Behind the Air Bag,” J. Chem. Educ., Vol. 73, 1996, 347–348.
6. William L. Bell, “Chemistry of Air Bags,” J. Chem. Educ., Vol. 67, 1990, 61.
Live Demonstrations:
1. Lee R. Summerlin, Christie L. Borgford and Julie B. Ealy, “Boiling at Reduced Pressure,” Chemical
Demonstrations, A Sourcebook for Teachers, Volume 2 (Washington: American Chemical Society, 1988),
pp 24-25. The volume of a gas-filled balloon is changed by immersion in an ice bath or a warm water
bath in this demonstration of Charles’s Law.
2. Rick Broniec, “Boyle’s Law and the Monster Marshmallow,” J. Chem. Educ., Vol. 59, 1982, 974. A
quick demonstration of Boyle’s law.
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8. John T. Petty, “Charles’ Law of Gases: A Simple Experimental Demonstration,” J. Chem. Educ, Vol.
72, 1995, 257. A short demonstration of Charles’s Law.
11. Lee R. Summerlin and James L. Ealy, Jr., “Determining the Molecular Weight of a Gas,” Chemical
Demonstrations, A Sourcebook for Teachers, Volume 1, 2nd edition (Washington: American Chemical
Society, 1988), pp. 19–20. The molar mass of butane is determined from its mass and the volume of
water it displaces.
12. Lee R. Summerlin and James L. Ealy, Jr., “Diffusion of Gases,” Chemical Demonstrations, A
Sourcebook for Teachers, Volume 1, 2nd edition (Washington: American Chemical Society, 1988), pp.
14–15. Graham’s Law is checked by timing color changes in pH paper caused by HCl(g) or NH3(g).