GASES
Unit #8
AP Chemistry
I.
Characteristics of Gases
A. Gas Characteristics:
1. Fills its container
a. no definite shape
b. no definite vol.
2. Easily mixes w/ other gases
3. Exerts pressure on its surroundings
II.
Gas Pressure
A. Pressure – force exerted by a gas on a surface
B. Standard Atmospheric Pressure and the Barometer – force resulting from the
mass of the air being pulled toward the center of the earth by gravity; the
force resulting from the weight of the air.
Sample Exercise – 10.1 a) convert 0.357 atm to torr b) convert 6.6 x 10-2 torr to atm. c) convert 147.2
Kpa to torr.
C. Manometers – basic instrument for measuring pressure of gas in a container
III.
The Gas Laws
A. Boyle’s Law – the volume of a given sample of gas @ constant temperature
varies inversely w/ the pressure
PV = k
Where k is a constant
• P vs. V plot gives a hyperbola
• V vs. 1/P plot gives straight line slope = k
• Holds best @ low pressures (more “ideal”) see fig. 5.6 p. 194
B. Charles’s Law – the vol. of a give sample of gas @ constant pressure is
directly proportional to the temp. in Kelvins
V = bT
Where T is the temp. in Kelvins and b is the proportionality
constant
• Volumes of all gases extrapolate to zero @ same temp.
-273ºC = 0 K = absolute zero
• K = ºC + 273
Sample Exercise 5.4: Charles’s Law (p. 196)
A sample of gas at 15ºC and 1 atm has a volume of 2.58 L. What volume will
this gas occupy at 38ºC and 1 atm?
(p. 233 #32)
C. Avogadro’s Law – equal volumes of gases at the same temp. and press.
contain the same # of particles
V = an
Where a is a proportionality constant and n = the # of moles
for a gas at constant temp. and press. the volume is
directly proportional to the # of moles of gas
Sample Exercise 5.5: Avogadro’s Law (p. 197)
Suppose we have a 12.2-L sample containing 0.50 mol oxygen gas (O2) at a
pressure of 1 atm and a temperature of 25ºC. If all this O2 were converted to
ozone (O3) at the same temperature and pressure, what would be the
volume of the ozone?
(p. 233 #33, 34)
IV.
The Ideal Gas Equation
A. The Ideal Gas Equation:
PV = nRT
Where R is the universal gas constant and has a value of
0.08206 Latm/Kmol
B. Standard Temperature and Pressure (STP) –
Temperature = 0ºC or 273 K
Pressure = 1 atm or 101.3 kPa or 760 mmHg or 760 torr
* Molar volume = 22.42 L @ STP
Sample Exercise 5.6: Ideal Gas Law I (p. 199)
A sample of hydrogen gas (H2) has a volume of 8.56 L at a temperature of
0ºC and a pressure of 1.5 atm. Calculate the moles of H2 molecules present
in this gas sample.
(p. 233 #35, 37, 39)
Sample Exercise 5.7: Ideal Gas Law II (p. 199)
Suppose we have a sample of ammonia gas with a volume of 7.0 mL at a
pressure of 1.68 atm. The gas is compressed to a volume of 2.7 mL at a
constant temperature. Use the ideal gas law to calculate the final pressure.
(p. 233 #41)
Sample Exercise 5.8: Ideal Gas Law III (p. 200)
A sample of methane gas that has a volume of 3.8 L at 5ºC is heated to 86ºC
at a constant pressure. Calculate its new volume.
(p. 233 #43, 44)
Sample Exercise 5.9: Ideal Gas Law IV (p. 201)
A sample of diborane gas (B2H6), a substance that bursts into flame when
exposed to air, has a pressure of 345 torr at a temperature of -15ºC and a
volume of 3.48 L. If conditions are changed so that the temperature is 36ºC
and the pressure is 468 torr, what will be the volume of the sample?
(p. 234 #45)
Sample Exercise 5.10: Ideal Gas Law V (p. 202)
A sample containing 0.35 mol argon gas at a temperature of 13ºC and a
pressure of 568 torr is heated to 56ºC and a pressure of 897 torr. Calculate
the change in volume that occurs.
(p. 234 #47)
V.
Molar Mass and Gas Density
A. The Equation Derived:
n = grams of gas
molar mass
=
mass _
molar mass
=
m
_
molar mass
Substitute into the ideal gas equation:
P=
nRT
V
=
(m/molar mass) RT
V
mRT __
= V(molar mass)
According to the equation for density: d = m
V
Therefore,
Molar mass =
, so P =
dRT _
molar mass
dRT
P
Sample Exercise 5.14: Gas Density/Molar Mass
The density of a gas was measured at 1.50 atm and 27ºC and found to be
1.95 g/L. Calculate the molar mass of the gas.
(p. 235 #59, 61)
VI.
Gas Mixtures and Partial Pressure
A. Partial Pressure – the pressure that a particular gas would exert if it was
alone in the container
B. Dalton’s Law of Partial Pressure – for a mixture of gases in a container, the
total pressure exerted is the sum of the pressures that each gas would exert
if it was alone.
PTOTAL = P1 + P2 + P3 + …
Sample Exercise 5.15: Dalton’s Law I
Mixtures of helium and oxygen can be used in scuba diving tanks to help
prevent “the bends.” For a particular dive, 46 L He at 25ºC and 1.0 atm
and 12 L O2 at 25ºC and 1.0 atm were pumped into a tank with a volume
of 5.0 L. Calculate the partial pressure of each gas and the total pressure
in the tank at 25ºC.
(p. 235 #63, 65)
C. Mole Fraction – the ratio of the number of moles of a given component in a
mixture to the total number of moles in the mixture.
χ1 =
n1 _
nTOTAL
=
n1
_
n1 + n2 + n3 + . . .
From the ideal gas equation we know that the number of moles of a gas is
directly proportional to the pressure of the gas, since
n1 = P1
V_
RT
, n2 = P2
V_
RT
Therefore,
χ1 =
n1 _
nTOTAL
=
P1 _
PTOTAL
Sample Exercise 5.16: Dalton’s Law II
The partial pressure of oxygen was observed to be 156 torr in air with a
total atmospheric pressure of 743 torr. Calculate the mole fraction of O2
present.
(p. 235 #67)
Sample Exercise 5.17: Dalton’s Law III
The mole fraction of nitrogen in the air is 0.7808. Calculate the partial
pressure of N2 in air when the atmospheric pressure is 760 torr.
(p. 235 #68)
VII.
Gas Stoichiometry
A. Collecting Gas over Water – a mixture of gases results whenever a gas is
collected by displacement of water (water vapor is present in addition to the
gas being collected)
• Water molecules escape from surface and collect in space above
• When rate of escape = rate of return, pressure from H2O vapor
remains constant vapor pressure of H2O
Sample Exercise 5.18: Gas Collection over Water
A sample of solid potassium chlorate (KClO3) was heated in a test tube
(see fig. 5.13) and decomposed by the following reaction:
2KClO3(s) 2KCl(s) + 3O2(g)
The oxygen produced was collected by displacement of water at 22ºC at a
total pressure of 754 torr. The volume of the gas collected was 0.650 L,
and the vapor pressure of water at 22ºC is 21 torr. Calculate the partial
pressure of O2 in the gas collected and the mass of KClO3 in the sample
that was decomposed.
(p. 235 #69, 71)
VIII. Kinetic Molecular Theory
A. The Model – attempts to explain the properties of an “ideal gas” by
describing the particles:
1. The particles are so small compared w/ the distances between them
that the volume of the individual particles can be assumed to be
negligible (zero). See Figure 5.14
2. The particles are in constant motion. The collisions of the particles w/
the walls of the container are the cause of the pressure exerted by the
gas.
3. The particles are assumed to exert no force on each other; they are
assumed neither to attract nor repel one another.
4. The average kinetic energy of a collection of gas particles is assumed to
be directly proportional to the Kelvin temperature of the gas.
B. Root- mean Square Velocity (see p. 216-217 for derivation):
C. KMT application to the Gas Laws –
• P & V (Boyle’s Law)
P = (nRT) 1/V
(constant)
• P & T (Lussac’s Law)
P = (nR/V) T
(constant)
• V & T (Charles’s Law)
V = (nR/P) T
(constant)
• V & n (Avogadro’s Law)
V = (RT/P) n
(constant)
• Mixture of gases (Dalton’s Law)
KMT assumes that all gas particles
are independent of each other
IX.
Molecular Effusion and Diffusion
A. Effusion – the passage of a gas through a tiny orifice into an evacuated
chamber
B. Gram’s Law of Effusion – the relative rates of effusion of two gases at the
same temperature and pressure are given by the inverse ratio of the square
roots of the masses of the gas particles:
Rate of effusion for gas 1
Rate of effusion for gas 2
=
√M2
√M1
C. Diffusion – (see p. 221-222)
Sample Exercise 5.20: Effusion Rates
Calculate the ratio of the effusion rates of hydrogen gas (H2) and uranium
hexafluoride (UF6), a gas used in the enrichment process to produce fuel for
nuclear reactors (see Fig. 5.23).
X.
Deviations from Ideal Behavior
A. The Van der Waals Equation –
B. Sample Exercise 10-15 If 1.000 mol of an ideal gas were confined to 22.4 L at 0.0°C, it
would exert a pressure of 1.000 atm. Use the Van der Waals equation and the constants
in Table 10.3 to estimate the pressure exerted by 1.000 mol of Cl2 (g) in 22.4 L at 0.0°C