Dr. Saidane
Chem. 200
Lecture Notes
Chapter 10
Gases

A gas is a fluid state of matter that fills the container it occupies and can be easily
compressed.

There are 11 elements that are gas under normal conditions. They all lie toward the
upper right of the periodic table. Because gases expand quickly to fill their container,
they do not interact strongly.

Gases are highly compressible which suggests that there is a lot of empty space
between the molecules.

Gases fill rapidly their container, which suggests that the molecules are moving very
rapidly.
MOLECULAR CHARACTER OF GASES
The Ideal Gas
The properties of a gas indicate that molecular volumes and molecular forces
(interactions) are small. When they are negligibly small, each molecule is completely
independent of every other molecule, and the gas is said to be ideal.
An ideal gas is defined as: A gas which both the volume of molecules and the forces
between the molecules are so small that they have no effect on the behavior of the gas.
Pressure
The pressure of a gas arises from the collisions that its molecules make with the walls of
the container. The storm of collisions exerts an almost steady force on the walls.
The pressure of a gas is the force of collision a gas exerts divided by the area subjected to
the force. P = F/S.
The units for reporting pressure are Torr and atmospheres (1 atm = 760 Torr). The SI
unit is Pascal (1 Pa = 1 kg/m.s2).
A barometer is used to measure the pressure of the atmosphere. At sea level, the pressure
of the atmosphere is close to 1 atm.
THE GAS LAWS
The properties of gases were studied and resulted in several gas laws.
Boyle’s Law
Boyle observed that when he compressed a fixed amount of gas at constant
temperature, the pressure of the gas increased. When the volume of a gas is decreased,
there are more molecules in a given volume, so there are collisions with the walls.
Because the impact on the walls increases, so does the pressure. The implication of this
result is that for a fixed amount of gas at constant temperature, pressure is inversely
proportional to volume. P  1 / V or P = constant / V.
Charles’s Law
Charles and Gay-Lussac found that the volume of a gas in a container fitted with a
movable wall (to keep the pressure constant) increases as its temperature is raised. When
the temperature of a gas is increased and it is free to change its volume at constant
pressure (as depicted by the constant weight acting on the piston), the volume increases.
The implication of this result is that, for a fixed amount of gas under constant pressure,
the volume varies linearly with the temperature. V T or V = constant x T.
A similar expression summarizes the results of measuring the variation of
pressure of a sample of gas in a container of fixed volume. The pressure of a fixed
amount of gas in a vessel of constant volume is proportional to the absolute temperature.
It is found that the pressure varies linearly with temperature and that the data extrapolate
to zero pressure at –273C. P  T or P = Constant x T.
Avogadro’s Principle
The volume occupied by a sample of gas at constant pressure and temperature is
proportional to the number of moles of molecules present.
V  n or V = Constant x n.
The Ideal Gas Law
The observations made by Boyle, Charles, Gay-Lussac, and Avogadro have been
combined into one simple relation between the pressure (P), volume (V), temperature (T),
and the number of moles (n) of a gas. This relation is called the ideal gas law:
PV = n RT, where R is a constant called the gas constant.
A gas that obeys this law under all conditions is called an ideal gas.
Molar Volume
The molar volume of an ideal gas at 1 atm and 25C is about 24 L/mol
The molar volume (at the specified temperature and pressure) is used to convert the
amount of reactant or product in a chemical reaction into a volume of gas.
Gas Density
The densities of gases increase with increasing pressure and decreasing temperature, and
are proportional to the molar mass.
Mixtures of Gases
John Dalton showed how to calculate the pressure of a mixture of gases. He called the
partial pressure of each gas, the pressure the gas would exert if it occupied the container
alone. Dalton the described the behavior of gaseous mixtures by his law of partial
pressures: The total pressure of a mixture of gases is the sum of the partial pressures of
its components.
Ex: A mixture containing the gases A, B, and C, the total Pressure PT =PA + PB + PC.
MOLECULAR MOTION
The kinetic Model of an Ideal Gas
The kinetic model of an ideal gas is based on four assumptions:
1. A gas consists of a collection of molecules in continuous random motion.
2. Gas molecules are infinitely small.
3. Gas particles move in straight lines until they collide.
4. The molecules do not influence one another except during collisions.
The collisions change the speed and direction of the molecules, which gives an average
speed of gas molecules. The average speed, v, of the molecules in a gas sample is directly
proportional to the square root of the temperature and inversely proportional to the square
root of the molar mass. v  (temperature/molar mass)1/2.
The temperature of a gas is a measure of the average speed of its molecules: The
higher the temperature, the faster the molecules travel on average.
The Maxwell Distribution of Speeds
The molecules of all gases have a wide range of speeds. The fraction of gas molecules
moving at each speed at any instant is called the distribution of molecular speeds. The
ranges of molecular speeds are represented by the Maxwell distribution curves. The
range of speeds varies with the molar mass and the temperature: The greater the molar
mass, the narrower the spread of speeds, and the higher the temperature, the broader the
spread of speeds.
Diffusion and Effusion
The gradual dispersal of one substance through another substance is called diffusion.
The escape of one substance through a small hole into a vacuum is called effusion.
In diffusion, the molecules of one substance spread into the region occupied by molecules
of another in a series of random steps, undergoing collisions as they move.
In effusion, the molecules of one substance escape through a small hole in a barrier.
In both cases the rate increases with increasing temperature and decreases with increasing
molar mass.
Thomas Graham did a series of experiments on the rate of effusion and diffusion of gases
and found that the rate of effusion or diffusion is inversely proportional to the square root
of its molar mass. Heavy molecules diffuse or effuse more slowly than light molecules.
This observation is known as Graham’s Law:
Rate of effusion  (1/molar mass)1/2.
The time it takes the molecules of a gas to effuse through an opening or diffuse through
one another is directly proportional to the square root of their molar mass.
teffusion  (molar mass)1/2.
For mixture of molecules A and B we can write:
teffusion (A) / teffusion (B) = (molar mass of A / molar mass of B)1/2
Difference of molar masses can be used to separate gases by diffusion.
REAL GASES
Real gases, the gases that make up the atmosphere and that we use in laboratories, behave
like ideal gases, provided their pressures are low (below 2 atm) and the ideal gas law for
the real gases is the most accurate for pressures close to 0 atm. We say that the ideal gas
law is a limiting law. Deviations from ideal gas behavior arise because molecules have
definite volumes (not infinitely small) and attract and repel one another.
Many scientists have suggested ways of changing the ideal gas law so that it takes into
account the effect of the intermolecular forces and the volume occupied by gas
molecules. Johannes van der Waals proposed the best-improved equation:
( P + an2/V2) (V-nb) = nRT
This expression is called the van der Waals equation, in which the constant a represents
the effect of attractions between molecules, and the constant b represents the effect of
repulsions (also considered as the measure of the volume taken up by the gas molecules).
Skills you should have mastered
Conceptual
1. Explain the origin of pressure in molecular terms.
2. Describe the relation of molecular speed to temperature.
3. Explain the ideal gas law in terms of the kinetic model of gases.
4. List and explain the assumptions of the kinetic theory of gases.
5. Describe the effect of molar mass and temperature on the distribution of
molecular speeds.
6. Explain how real gases differ from ideal gases.
Problem-solving
1.
Use the ideal gas law to calculate P, V, T and n for given conditions or after a
change in conditions.
2.
Calculate the mass of reactant needed to react with a specified volume of gas.
3.
Calculate the molar volume of a gas from its mass.
4.
Calculate the volume of a gas involved in a reaction.
5.
Determine molar mass from gas density and vise versa.
6.
Calculate partial pressures of gases and the total pressure of a gas mixture.
7.
Use Graham’s law to account for relative rates of effusion.