March 22, 2014
Kinetic Molecular Theory
• A model to explain the physical properties of ideal
gases
1. Gas particles are much smaller than the
distances between them.
2. Gas particles do not attract or repel
each other.
3. Gas particles are in constant, random
motion. Collisions are elastic
4. The average kinetic energy of the gas
molecules is directly proportional to the
temperature of the gas (K)
March 22, 2014
Kinetic Energy and Temperature
• Temperature = measure of average kinetic energy
of the particles in a sample of matter
• Kinetic energy and temperature are directly
proportional.
KEavg=1/2mv2
KEavg=3/2RT
The higher the temperature, the faster the
molecules are moving.
March 22, 2014
Maxwell-Boltzman Distribution
March 22, 2014
Maxwell-Boltzman Distribution
At the same temperature, all gasses have the
same average kinetic energy.
March 22, 2014
Maxwell-Boltzman Distribution
March 22, 2014
Diffusion and Effusion
Diffusion = random
movement of particles from
area of higher concentration
to area of lower
concentration
March 22, 2014
Example 1:
If two bottles of the same gasses where gas 1 has a
molar mass of 32g/mol and gas 2 has a molar mass
of 20 g/mol, which gas will have a greater rate of
diffusion?
March 22, 2014
Gas Laws: Relates volume, pressure, temperature,
and amount of gas
variable
1.
2.
3.
4.
Temperature
Pressure
Volume
Amount
symbol
T
P
V
n
K= ºC + 273
units
kelvin
atm, psi, mmHg
liters
moles
March 22, 2014
What is pressure?
P= force
area
force exerted by gas
molecule in a collision
surface area
force is determined by:
➀ how fast molecule is traveling
➁ mass of molecule
➂ number of collisions
March 22, 2014
Units and conversions for pressure
1atm =
=
=
=
=
760 mmHg
760 torr
29.9 in. Hg
101.3 kPa
14.7 psi
March 22, 2014
Barometer measures atmospheric pressure
March 22, 2014
Manometer measures pressure of confined gas
height difference indicates pressure of gas
relative to atmospheric pressure.
Example 2: What is the pressure of the confined gas if the
height of the mercury is 155 mm and the atmospheric
pressure is 775mmHg?
March 22, 2014
Volume
1 mol of a gas at STP (standard temperature and
pressure) has a volume of 22.4 L.
STP: 273K and 1 atm
Example 3: What is the volume of a gas if you
have 4g of oxygen gas at STP?
March 22, 2014
Gas Laws!
1. Boyle's Law
2. Charles's Law
3. Gay-Lussac's Law
5. Ideal Gas Law
4. Combined Gas
Law
March 22, 2014
1. Boyle's Law
• Relates pressure and volume of gas when
temperature and amount (n) is constant
March 22, 2014
volume (L)
Boyle's Law
pressure (atm)
March 22, 2014
March 22, 2014
Example 4: The volume of a gas at 99.0 kPa is
300.0mL. If the pressure is increased to 188 kPa,
what will be the new volume?
March 22, 2014
Example 5: A sample of neon gas occupies 0.220L at
0.860 atm. What will be its volume at 29.2 kPa?
March 22, 2014
2. Charles's Law
• Relates temperature and volume of gas when
pressure and amount (n) is constant
Volu
prop
pres
March 22, 2014
Example 6: A gas sample at 40.0º C occupies a
volume of 2.32 L. If the temperature is raised to
75.0ºC, what will the volume be, assuming pressure
remains constant?
March 22, 2014
Example 7: A gas at 89º C occupies a volume of
0.67L. At what celsius temperature will the volume
increase to 1.12L (constant pressure and amount).
March 22, 2014
3. Gay-Lussac's Law
• Relates pressure and temperature of gas when
volume and amount (n) is constant
March 22, 2014
Example 8: the pressure of a gas in a tank is
3.20atm at 22.0ºC. If the temperature rises to
60.0ºC, what will be the gas pressure in the tank?
March 22, 2014
Example 9: A gas in a sealed container has a
pressure of 125 kPa at a temperature of 30.0ºC. If
the pressure in the container is increased to 201
kPa, what is the new temperature?
March 22, 2014
Combined Gas Law
• Can combine Boyle's, Charles's, and Gay-Lussac's
law into one law: relates T, P, V of a fixed amount
of gas.
*If you know this law, you can derive any of
the other three laws.
March 22, 2014
Example 10:
A helium-filled balloon at sea level has a volume of
2.1 L at 0.998 atm and 36ºC. If it is released and
rises to an elevation at which the pressure is 0.900
atm and the temperature is 28ºC, what will be the
new volume of the balloon?
March 22, 2014
Example 11:
At 0.00ºC and 1.00 atm pressure, a sample of gas
occupies 30.0mL. If the temperature is increased to
30.0ºC and the entire gas sample is transferred to a
20.0mL container, what will be the gas pressure
inside the container?
March 22, 2014
Ideal Gas Law
• Combines all four variables: P, T, V, and n
PV=nRT
R = gas constant
Value depends on units of pressure:
March 22, 2014
Example 12: What is the volume of 1 mole of gas at
STP?
March 22, 2014
Example 13:
Calculate the number of moles of gas contained in a
3.0L vessel at 3.00x102 K with a pressure of 1.50
atm.
March 22, 2014
March 22, 2014
Example 14:
Determine the celsius temperature of 2.49 moles of
gas contained in a 1.00 L vessel at a temperature of
143 kPa.
March 22, 2014
Example 15:
Calculate the number of molecules of air in a breath
of air whose volume is 2.5 L at a body temperature
of 37ºC and a pressure of 100kPa.
March 22, 2014
Gas Laws and Stoichiometry! Hooray
• remember...PV=nRT (n is moles of gas)
• 1 mol of any gas at STP has a volume of 22.4L
March 22, 2014
Example 16: What is the volume of water vapor that
can be produced from 25.0g of oxygen gas at a
temperature of 35ºC and a pressure of 1.3atm?
2H2 + O2 ⟶"2H2O
March 22, 2014
Dalton's Law of Partial Pressures
The pressure of a gas mixture is the sum of the
partial pressures of the gases present.
The partial pressure is the pressure that the gas
would exert if it were alone in a container.
*Do
wha
use
March 22, 2014
Dalton's Law of Partial Pressures
Ptotal = P1 + P2 + P3....
March 22, 2014
Example 17: A mixture of neon and argon gases
exerts a total pressure of 2.39 atm. The partial
pressure of the neon alone is 1.84 atm, what is the
partial pressure of the argon?
March 22, 2014
In a lab, when a gas is collected over water, the
partial pressure of water vapor must be taken into
account.
Ptotal = PH2O vapor + Pgas
March 22, 2014
March 22, 2014
Example"20:"A"450"mL"sample"of"hydrogen"is"collect"over"
water"at"12"C."""The"pressure"of"the"hydrogen"and"water"
vapor"mixture"is"78.5"kPa.""What"is"the"partial"pressure"of"the"
dry"hydrogen"gas?"
March 22, 2014
Example 21: A sample of oxygen gas is saturated
with water vapor at 27ºC. The total pressure of the
mixture is 772 torr and the vapor pressure of water
is 26.7 torr at 27ºC. What is the partial pressure of
the oxygen gas?
March 22, 2014
Example 23: A 500. mL sample of O2 gas at 24ºC
was prepared by the following equation:
2H2O2 (aq)
2H2O(g) + O2(g)
The oxygen prepared was collected by displacement
of water. The total pressure of gas collected was
755mmHg.
1. What is the partial pressure of O2? (The vapor
pressure of water at 24ºC is 23mmHg)
2. How many moles of O2 were prepared?