Chapter 12: Gases and their Properties
Chapter 12 Problem Set
Pages 575-581
15, 19, 25, 31, 33, 39, 41, 45, 49, 53, 59, 61, 67
What are some reasons for studying gases? Page 539
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12.1 THE PROPERTIES OF GASES
What is pressure?
Atmospheric pressure can be measured with a mercury barometer.
Pressure exerted by a column of mercury is proportional to the height of the column times the density
of mercury.
What is a standard atmosphere? Different units. List all. Pascal is the only pressure unit directly
defined in terms of force per unit area. 1 Pa = 1 newton/meter2
EXAMPLE 12.1 Page 541 Pressure Unit Conversions
Convert a pressure of 575 mm Hg into atmospheres and kilopascals
12.2 GAS LAWS: THE EXPERIMENTAL BASIS
The Compressibility of Gases: Boyle’s Law
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The volume of a fixed amount of gas at a given temperature is inversely proportional to the pressure
of the gas is a statement of Boyle’s Law.
Stated mathematically
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PV
Since PV = CB @ const T
CB is determined by the # of moles
A convenient (useful) form of Boyle’s law is P1V1 = P2V2
EXERCISE 12.2 Page 545 Boyle’s Law
A sample of carbon dioxide has a pressure of 55 mm Hg in a volume of 125 mL. The sample is
compressed so that the new pressure of the gas is 78 mm Hg. What is the new volume of the gas? (T
does not change)
The Effect of Temperature on Gas Volume: Charles’s Law
Absolute zero in Celsius degrees is -273.15°C which is equal toO K.
Charles’s law: If a given quantity of gas is held at constant pressure, its volume is directly
proportional to Kelvin temp.
VT
V = CC  T
or
V
CC = T
Stated mathematically T 1  T 2
V1
V2
EXERCISE12.3 Page 547 Charles’s Law
A balloon is inflated with helium to a volume of 45 L at room temp (25°C). If the balloon is cooled to
–10°C, what is the new volume of the balloon? Assume that press does not change.
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Combining Boyle’s and Charles’ Laws: The General Gas Law
The mathematical equation is:
P1V 1
T1
 PT2V2 2
EXERCISE 12.4 Page 548 The General (Combined) Gas Law
You have a 22 L cylinder of helium at a press of 150 atmospheres and at 31 °C. How many balloons
can you fill, each with a volume of 5.0 L, on a day when the atmospheric press is 775 mm Hg and the
temperature is 22 °C?
The Laws of Gay-Lussac and Avogadro
What is Gay-Lussac’s law of combining volumes?
What is Avogadro’s hypothesis?
Equal volumes of gases under the same conditions of temperature and pressure have…
What is Avogadro’s law?
V  n or
V  CA
n = # of moles
EXERCISE 12.5 Page 550 Avogadro’s Law
Methane burns in oxygen to give carbon dioxide and water. If 22.4 L of gaseous methane is burned,
what volume of oxygen is required for complete combustion? What volumes of each product are
produced? Assume all gases have same temperature and pressure.
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12.3 THE IDEAL GAS LAW
The four interrelated quantities that can be used to describe a gas law are P, V, T, & n
Boyle’s law, Charles’ law, and Avogadro’s law can be combined into one equation
Boyle’s Law
Charles’s Law
Avogadro’s Law
PV
VT
Vn
Const T, n
Const P, n
Const T, P
1
nT
If all 3 are combined, the result is V  P
The gas constant R can be calculated from experimental values in P, V, n, and T.
One mole of gas occupies a volume of 22.414 L at 1.000 atm and 273.15 K (or 0o C).
PV = nRT
EXERCISE 12.6 Page 551 The Ideal Gas Law
The balloon used by Charles in his historic flight in 1783 was filled with about 1300 mol of H2. If the
temp of the gas was 23 °C, and the press was 750 mm Hg, what was the volume of the balloon?
Density of gases
m RT
Another form of the Ideal gas equation is PV  M
where m = mass and M = molar mass
m
PM
Since d  V , can rearrange above equation d  RT
EXERCISE 12.7 Page 553 Gas Density Calculation
Calculate the density of dry air at 15.0 °C and 1.00 atm if its molar mass (average) is 28.96 g/mol
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EXERCISE 12.8 Page 555 Molar Mass from P, V, and T Data
A 0.105-g sample of a gaseous compound has a pressure of 561 mm Hg in a volume of 125 mL at
23.00C. What is its molar mass?
12.4 GAS LAWS AND CHEMICAL REACTIONS
The gas laws can be combined with stoichiometric equations. I don’t really care for the outline on pg
555. But if you do that’s great. You will note that previous knowledge of limiting reactants is also
required.
EXAMPLE 12.9 Page 556 Gas Laws and Stoichiometry
Let us say that you are asked to design an air bag for a car. You know that the bag should be filled with
gas with a pressure higher than atmospheric pressure, say 829 mm Hg, at a temperature of 22.00C. The
bag has a volume of 45.5 L. What quantity of sodium azide, NaN3, should be used to generate the
required quantity of gas?
2 NaN3(s)  2 Na(s) + 3 N2(g)
EXAMPLE 12.10 Page 556 Gas Laws and Stoichiometry
Suppose we wish to prepare some deuterium gas, D2, for use in an experiment. One way to do this is to
react heavy water, D2O, with an active metal such as lithium. If we place 0.125 g of Li metal in 15.0
mL of D2O (d=1.11 g/mL), what quantity of D2 (in moles) can be prepared? If dry D2 is captured in a
1450 mL flask at 22.00C, what is the pressure of the gas in mm Hg? (Deuterium has a molar mass of
2.0147 g/mol)
2 Li(s) + 2 D2O(l)  2 LiOD(aq) + D2(g)
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EXERCISE 12.9 Page 558 Gas Laws and Stoichiometry
Gaseous ammonia is synthesized by the reaction
N2(g) + 3 H2(g)  2 NH3(g)
Assume that you take 355 L of H2 gas at 25.00C and 542 mm Hg and combine it with excess N2 gas.
What quantity of NH3 gas, in moles, is produced? If this amount of NH3 gas is stored in a 125-L tank
at 25.0C, what is the pressure of the gas?
EXERCISE 12.10 Page 558 Gas Laws and Stoichiometry
Oxygen reacts with aqueous hydrazine to produce water and gaseous nitrogen according to the
balanced equation
N2H4(aq) + O2(g)  2 H2O ( ) + N2(g)
If a solution contains 180 g of N2H4, what is the maximum volume of O2 that will react with the
hydrazine if the oxygen is measured at a pressure of 750 mm Hg and a temperature of 21.00C?
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12.5 GAS MIXTURES AND PARTIAL PRESSURES
What is John Dalton’s law of partial pressures?
Ptotal = P1 + P2 + P3 …
For a mixture of gases, we sometimes use a quantity called the mole fraction, X, which is defined as
the # moles of a particular subs in a mixture divided by the total # moles of all moles of all subs.
nA
XA = ntotal
An application of Dalton’s law occurs with laboratory exp that involves collecting a gas by displacing
water from a container. To find the press of the dry gas, the pressure of the water vapor must be
subtracted from the total pressure. A table of water vapor pressures at various temps is found in
Appendix G
EXAMPLE 12.11 Page 560 Partial Pressure of Gases
Halothane has the C2HBrClF3. It is a nonflammable, nonexplosive, and nonirritating gas that is a
commonly used as an inhalation anesthetic (Fig. 12.13). Suppose you mix 15.0 g of halothane vapor
with 23.5 g of oxygen gas. If the total pressure of the mixture is 855 mm Hg, what is the partial
pressure of each gas?
EXERCISE 12.12 Page 562 Partial Pressures of Gases
In an experiment similar to that in Figure 12.14, 352 mL of gaseous nitrogen is collected in a flask
over water at a temperature of 24 °C. The total press of the gases in the flask is 742 mm Hg. What
mass of N2 is collected? (See Appendix G for water vapor pressures)
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12.6 THE KINETIC-MOLECULAR THEORY OF GASES
The kinetic-molecular theory is a description of the behavior of gases at the molecular level.
The main features of the kinetic-molecular theory for gases are:
1. Gases consist of molecules whose separation is much greater than the size of the molecules
themselves.
2. The molecules of a gas are in continual, random, and rapid motion.
3. The average kinetic energy of gas molecules is proportional to the gas temperature. All molecules,
regardless of their mass, have the same average kinetic energy at the same temperature.
4. Gas molecules collide with each other and with the walls of their container, but they do so without
loss of energy.
Kinetic-Molecular Theory and the Gas Laws
The gas laws, which come from experiment, can be explained by the kinetic-molecular theory.
From a graph of the number of molecules versus their speed, two important observations can be made.
1. Some molecules have high speeds (high KE) and others have low speeds (lowKE).
2. As the temperature is increased, the most common speed goes up, and the number of molecules
traveling very fast goes up a great deal. There is an increase in average speed.
A mathematical equation, which relates the speed of a molecule to their mass and temperature, is…
u2 
and
3 RT
M
u2
where u2 = mean2
is root mean squared or rms speed
P is pressure in units of pascals (Kg/m·s2)
V is volume in units of m3
R is gas constant in SI units. 8.314510 J/K·mol
EXERCISE 12.13 Page 568 Molecular Speeds
Calculate the rms speeds of helium atoms and N2 molecules at 25 °C.
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12.7 DIFFUSION AND EFFUSION
What is diffusion?
What is effusion?
Graham’s law of effusion is
Rate1
Rate 2

molar mass 2
molar mass 1
EXERCISE 12.14 Page 570 Graham’s Law
A sample of pure methane, CH4, is found to effuse through a porous barrier in 1.50 min. Under the
same conditions, an equal number of molecules of an unknown gas effuses through the barrier in 4.73
min. What is the molar mass of the unknown gas?
12.8 SOME APPLICATIONS OF THE GAS LAW AND KINETIC-MOLECULAR THEORY
Rubber balloons and why they leak
Deep Sea Diving
12.9 NONIDEAL BEHAVIOR: REAL GASES
Deviations occur at high pressures and low temperature
What is the van der Waals equation?
An equation to correct for errors in non ideal gases
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