Gases
Gas

Takes the size and shape of it’s container

Easily compressed

Mixes completely with any other gas
Pressure – amount of force exerted by gas molecules hitting the walls of their container. A force per unit area
1 atm = 760 mm Hg = 760 torr = 101.3 kPa = 14.7 psi (pounds per square inch)
Ideal Gas – Follows Boyle’s law exactly
Kinetic Molecular Theory (KMT)– a simple model that attempts to explain the properties of an ideal gas
Assumptions
1. The volume of the individual gas particles can be assumed to be zero.
2. The particles are in constant motion and their hitting the walls of their container cause pressure.
3. The particles exert no forces on each other.
4. The average kinetic energy of the gas particles is directly proportional to their temperature in Kelvin.
Boyle’s Law – At constant temperature, pressure and volume of a gas are inversely related
P1V1 = P2V2
Where,
P1 = Pressure at one state
P2 = Pressure at another state
V1 = Volume at one state
V2 = Volume at another state
(KMT) – since a decrease in volume means that the gas particles will hit the wall more often, then there
is an increase in the pressure
Charles’s Law – If amount and pressure of a gas are constant, the volume of a gas is directly proportional to
temperature.
V1
T1
V2
T2
(KMT) – When a gas is heated to a higher temperature, the speeds of its molecules increase and thus they hit the
walls more often and with more force. Therefore, the only way to keep the pressure constant is to increase the
volume of the container.
Guy-Lussac’s Law – If amount and volume of gas are constant, pressure is directly proportional to
temperature.
P1
T1
P2
T2
(KMT) – when the temperature of a gas increases, the speeds of its particles incres, the particles hitting the wall
with greater force and greater frequency. Since the volume remains the same, the pressure will increase.
Avogadro’s Law – Equal volumes of gases at the same temperature and pressure contain the same number of
particles. For a gas at constant temperature and pressure, the volume is directly proportional to the number of
moles of gas.
V1 = V2
n1
n2
(KMT) – an increase in the number of gas particles at the same temperature would cause the pressure to
increase if the volume were held constant. If you wanted to maintain constant pressure, then the volume would
have to increase.
Ideal Gas Law – an equation of state for a gas. If you know 3 of these properties you can completely define
the state of the gas. Unless you are given information to the contrary, you should assume ideal gas behavior
when solving problems involving gases.
PV = nRT
Where, P = pressure, V = volume, n = moles, R = Universal Gas Constant, T = Temperature in Kelvin
R = 0.08206 L atm/ K mol or R = 8.314 J/K mol.
Gas Stoichiometry
Standard Temperature and Pressure (STP) – the conditions of 1 atm and 0oC.
Using the ideal gas law with 1 mole of a gas at 0oC and 1 atm or STP, you will find the volume of the one mole
of gas to be 22.4 L Molar volume of an ideal gas at STP is 22.4L
1 mole = 22.4 L (for any gas at STP)
If the conditions of a problem are different from STP, the ideal gas law must be used to compute the volume.
Example
A sample of methane (CH4) gas having a volume of 2.80 L at 25 oC and 1.65 atm was mixed with a
sample of oxygen gas having a volume of 35.0 L at 31 oC and 1.25 atm. The mixture was then ignited to form
carbon dioxide and water. Calculate the volume of CO2 formed at a pressure of 2.50 atm and a temperature of
125 oC.
Note:
Moles = grams of a gas/ molar mass = m/MM
Substituting into the ideal gas equation,
P = nRT = mRT
V
V (MM)
Notice that Density = m/V, Therefore,
P = DRT
MM
or
MM = DRT
P
Datlon’s Law of Partial Pressure – for studies of mixtures of gases
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 were alone.
Ptot = P1 + P2 + P3 + …
Mole Fraction - the ratio of the number of moles of a given component in a mixture to the total number of
moles in a mixture.
1
By substitution the mole fraction also equals,
Which can be rearranged to give:
= n1
ntotal
1
P1 =
= P1
Ptotal
1
Ptotal
Gas collection over water – must make adjustments for the vapor pressure of water also contained in the gas
produced.
Example
A sample of solid potassium chlorate (KClO3) was heated in a test tube and decomposed by the
following reaction:
2KClO3(s)  2 KCl(s) + 3 O2(g)
The oxygen produced was collected by displacement of water at 22 oC at a total pressure of 754 torr. The
volume of gas collected was 0.650 L, and the vapor pressure of water at 22 oC is 21 torr. Calculate the partial
pressure of O2 in the gas collected and the mass of KClO3 in the sample that was decomposed.
Temperature
 Temperature – all gas volumes extrapolate to zero at the same temperature, -273 oC, or absolute Zero, 0
K. Gases cannot have a negative volume that’s why it’s called absolute temperature – the lowest
temperature that can be attained.
 The exact relationship between temperature and average kinetic energy can shown as

(KE)avg = 3/2 RT
The Kelvin Temperature is an index of the random motions of the particles of a gas. (It is also the index
of the random motion of solids and liquids, too)
Root Mean Square Velocity
The average velocity of the gas particles is a special kind of average
Urms = 3RT
MM(in kg)
Effusion and Diffusion
 Effusion – the passage of a gas through a tiny orifice into an evacuated chamber. The rate of effusion
measure the speed at which the gas is transferred into the chamber.
 Graham’s law of effusion states that the relative rates of effusion of two gases at the same temjperaure
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

MM2
MM1
Diffusion – describes the mixing of different gases.
Real Gases – no gas exactly follows the ideal gas law. However, at very low pressures and/or high
temperatures most gases come very close.
 Real gases do have volumes and real gases do have attractions for each other.
 (KMT)
o At low pressures, gas particles are far apart and their volumes appear to be negligible. However,
at higher pressures the particles are pushed closer together and the amount of space they take up
in a smaller container becomes noticeable.
o At high temperature, gas particles move so fast they don’t have time to interact with each other.
However, if you lower the temperature the particles move slower and have a better chance of
being attracted to each other.
 Van der waals equation – puts corrections into the ideal gas equation to account for these two effects
(particles have volume and interact with each other)
[Pobs + a(n/V)2] + [V – nb] = nRT
(Where Pobs = observed pressure, V = volume of container, n = moles, R = Gas Constant, T = Temp. in Kelvin
and a and b are experimental values for correction – listed on table 5.3 pg 224)