Gases
Chapter 12 pp. 470-508
General properties & kinetic theory
• Gases are made up of particles that have
(relatively) large amounts of energy.
• A gas has no definite shape or volume
and will spread out to fill as much space
as possible.
• A gas will exert a pressure on the walls of
any container it is held in.
• As a result gases are easily compressed.
Pressure
• A pressure is exerted when the gas
particles collide with the walls of the
container. Pressure can be measured in a
number of units.
1 atm = 760 mmHg = 760 torr = 101325 Pa = 101325 N/m2
Example #1
Use the factor labeling method to perform
the following conversions
1. 1,657 mmHg to N/m2
2. 832 torr to atmospheres
3. 17.8 kPa to atmospheres
4. 120,000 Pa to mmHg
Kinetic theory
• The kinetic theory can be summarized by the five
postulates below:
1. Gases are composed of tiny atoms or molecules
(particles) whose size is negligible compared to
the average distance between them. This means
that the volume of the individual particles in a gas
can be assumed to be negligible (close to zero).
2. The particles move randomly in straight lines in
all directions and at various speeds.
The Rest of the Post…
3. The forces of attraction or repulsion between two
particles in a gas are very weak or negligible
(close to zero), except when they collide.
4. When particles collide with one another, the
collisions are elastic (no kinetic energy is lost).
The collisions with the walls of the container
create the gas pressure.
5. The average kinetic energy of a molecule is
proportional to the Kelvin temperature and all
calculations should be carried out with
temperatures converted to K.
Pressure and Volume relationships:
Boyles Law
• Boyles Law states that, at constant
temperature, pressure is inversely
proportional to volume. This means that as
the pressure increases the volume
decreases and visa-versa.
• P1V1 = P2V2
Example #2
1. If a 1.25 L sample of a gas at 56 torr is
pressurized to 250 torr at a constant
temperature what is the new volume?
2. The pressure on a 415 mL sample of gas
is decreased form 823 mmHg to 791
mmHg. What will the new volume of
the gas be?
Volume and Temperature
relationships: Charles’s Law
• Charles’s Law states that, at constant
pressure, volume is directly proportional to
temperature. This means the volume of a
gas increases with increasing temperature
and visa-versa.
• V1T2 = V2T1
Example #3
1. A 12.0L sample of air is collected at
296K and then cooled by 15K. The
pressure is held constant at 1.2 atm.
Calculate the new volume of the air.
2. A gas has a volume of 0.672L at 35oC
and 1 atm pressure. What is the
temperature of a room where this gas has
a volume of 0.535L at 1 atm?
Volume and Moles relationships:
Avogadro’s Law
• Avogadro’s Law states that, at constant
temperature and pressure, volume is
directly proportional to the number of
moles of gas present. This means the
volume of a gas increases with increasing
number of moles and visa-versa.
• V1n2 = V2n1
Example #4
• 1. A 13.3 L sample of 0.5 moles of
oxygen gas is at a pressure of 1 atm and
25ºC. If all of the oxygen is converted to
ozone (O3) what will be the volume of
ozone produced?
• 2. If 2.11g of Helium gas occupies a
volume of 12.0L at 28ºC, what volume
will 6.50g occupy under the same
conditions?
The Ideal Gas Law
• The combination of Boyle’s, Charles’s &
Avogadro’s Laws leads to the formulation
of the Ideal Gas Law.
• Most gases obey this law at temperatures
above 0ºC and at pressures of 1 atm or
lower.
• PV = nRT
• R = 0.08206 L·atm / mol·K
Different forms of Ideal GL
• n = mass / MW so…
– PV = (m/MW)RT
• Density = mass / V so…
– D = P·MW / RT
The General Gas equation
• P1V1n2T2 = P2V2n1T1
• If the number of moles of gas are
constant in a problem, then we have the
combined gas law…
• P1V1T2 = P2V2T1
Example #5
1. Assuming that the gas behaves ideally,
how many moles of hydrogen gas are in a
sample of H2 that has a volume of 8.16L
at a temperature of 0ºC and a pressure of
1.2 atm?
2. A sample of aluminum chloride weighing
0.1g was vaporized at 350ºC and 1 atm
pressure to produce 19.2cm3 of vapor.
Calculate a value for the MW of
aluminum chloride.
Deviations from ideal behavior
•
•
•
At high pressures and low temperatures gas
particles come close enough together to
make the kinetic theory assumptions below
become invalid:
Gases are composed of tiny particles whose
size is negligible compared to the average
distance between them, and
The forces of attraction or repulsion between
two particles in a gas are very weak or
negligible (close to zero)
Non-Ideality (cont)
• At this point gases are said to behave
non-ideally or like real gases. This has
two consequences.
Non-Ideality (cont)
•
Under these real conditions the actual
volume occupied by the gas is smaller
than one would expect when assuming
the size of particles is negligible. Since
in a small volume the size of the
particles is not negligible, the observed
volume is larger than it really is. This
necessitates the need to correct the
volume by subtracting a factor.
Non-Ideality (cont)
• Under these real conditions the actual pressure
of a gas is higher than one would expect when
assuming there was no attractive forces
between the molecules. Because the particles
are attracted to one another they collide with
the walls with less velocity and the observed
pressure is less than it really is. This
necessitates the need to correct the pressure by
adding a factor.
Van der Waal’s Equation
Real Gases
for
(P + a(n/V)2)·(V-nb) = nRT
a and b are constants, where a corrects for
intermolecular forces and b corrects for
molecular volume
Example #6
• You want to store 165g of CO2 gas in a 12.5L
tank at room temperature (25ºC). Calculate
the pressure the gas would have using (a) the
ideal gas law and (b) the van der Waals
equation. (For CO2, a = 3.59 atm·L2/mol2 and
b = 0.0427 L/mol)
Molar Volume
• We have seen how Avogadro's law states
that equal volumes of all gases at constant
temp and pressure will contain equal
numbers of moles.
• The volume of one mole of any gas is
called its molar volume and can be
calculated using the ideal gas equation.
PVm = nRT
Molar Volume (cont)
• By applying the data, pressure (P) = 1atm,
temp (T) = 273K, the gas constant (R) =
0.08206 L·atm·mol-1 K-1, number of moles (n) =
1 mol, the molar volume (Vm) can be found.
• A simple calculation finds its value to be 22.4L.
• That is to say, for one mole of any ideal gas, at
standard temp and pressure (s.t.p), the volume
it occupies will be 22.4 L.
Example #7
• Calculate the mass of ammonium chloride required
to produce 22L of ammonia (at s.t.p) in the reaction
below.
2NH4Cl(s) + Ca(OH)2(s)  2NH3(g) + CaCl2(s) + 2H2O(g)
Example #8
• What mass of potassium chlorate must be
heated to give 3.25L of oxygen at s.t.p?
• 2KClO3(s)  2KCl(s) + 3O2(g)
Example #9
• Barium carbonate decomposes according to
the equation below. Calculate the volume of
carbon dioxide produced at s.t.p when 9.85g of
barium carbonate is completely decomposed.
• BaCO3(s)  BaO(s) + CO2(g)
Example #10
• What volume of oxygen (at s.t.p.) is required
to burn exactly 1.5L of methane (CH4)
• CH4(g) + 2O2(g)  CO2(g) + 2H2O(g)
Distribution of Molecular Speeds
• When considering the kinetic theory
postulate #2 introduces the idea that all of
the gas particles move at different speeds
• and postulate #5 that the speed (velocity),
and therefore the kinetic energy, is
dependent upon the temperature.
Root Mean Square of the
energy of the particles
Greatest number
of particles are
moving with this
energy
A typical plot showing the variation in particle speeds
is shown below for hydrogen gas at 273K..
Root Mean Square
• The root-mean-square-speed is the
square root of the averages of the squares
of the speeds of all the particles in a gas
sample at a particular temperature.
μrms = (3RT / MW)1/2
Where R = universal gas constant =
8.3145 kg·m2/s2 mol·K, T = temperature in Kelvin,
MW = molar mass of the gas in kg/mol.
Example #11
• Determine the μrms of hydrogen gas at 25ºC.
Determine the μrms of nitrogen gas at 25ºC.
• Determine the μrms of argon gas at 25ºC.
• Determine the μrms of the gases in questions 1,
2 and 3 at a temperature of 50ºC.
• What can be said quantitatively about the μrms
of a gas in relation to its molar mass and its
temperature?
Grahams Law of Effusion and
Diffusion
• Effusion is the process in which a gas escapes
from one chamber of a vessel to another by
passing through a very small opening.
• Grahams Law of effusion states that the rate of
effusion is inversely proportional to the square
root of the density of the gas at constant
temperature.
Grahams Law of Effusion and
Diffusion
• Diffusion is the process by which a
homogeneous mixture is formed by the
random motion and mixing of two different
gases.
• Grahams Law of diffusion states that the rate
at which gases will diffuse is inversely
proportional to the square roots of their
respective densities and molecular masses.
Dalton’s Law of Partial Pressures
• Dalton’s Law states that in a mixture of gases
the total pressure exerted by the mixture is
equal to the sum of the individual partial
pressures of each gas.
• PT = P1 + P2 + P3 + …+ Pn