Chem. 1411 Chapter 5
Gases
Properties of Gases
 Gases are compressible and possess low density
 They assume the shape and volume of their container
 Their intermolecular distance is large and has negligible intermolecular forces of attraction.
Pressure of Gas
The pressure exerted by the gas is due to the collision of its molecules on the walls of the container.
Pressure = Force / Area
(P = F /A)
The SI unit of pressure is Pascal (Pa)
1 Pa = 1N/m2
Atmospheric pressure
This is the pressure exerted by the gas molecules of the air in the atmosphere
1 atm = 760 mm of Hg = 760 torr =101325 Pa
Atmospheric pressure is measured using the instrument ‘Barometer’
A ‘Manometer’ is used to measure the pressure of gases other than atmosphere.
In a closed tube manometer, P gas = Ph
In an open tube manometer P gas = P atm + Ph
The Gas Laws
1. Boyle’s Law (Relationship between Pressure and Volume of gas)
This law states that the pressure (P) of a given mass of gas multiplied by its volume (V) is a constant
at a constant temperature.
PV = constant
or
P1V1 = P2V2 (at a constant temperature)
2. Charles’s Law (Relationship between Temperature and Volume)
This law states that the volume (V) of a given mass of gas is directly proportional to its temperature
(T) in Kelvin scale, at a constant Pressure (P). (As the Temperature increases Volume of the gas
increases at constant P)
V = (constant) x T
V
= Constant
or
V1 = V2
(at constant P)
T
T1
T2
3. Gay Lussac’s Law (Relationship between Pressure and Temperature)
This law states that the pressure (P) of a gas is directly proportional to its temperature (T) in Kelvin
scale at a constant volume (V). (As the Temperature increases, the pressure of the gas increases at
constant V)
P = (constant) x T
P
=
T
Constant
or P1 = P2
T1
T2
(at constant V)
4. Avogadro’s Law (Relationship between Volume and number of moles or molecules)
This law states that equal volumes (V) of all gases at the similar conditions of temperature (T) and
pressure (P) contain equal number of molecules (N).
VN
or V  n
(Where ‘n’ is the number of moles of the gas)
V = (constant) x n
V1 = V2 = constant
n1
n2
The combined gas Law
By combining Boyle’s Law and Gay Lussac’s Law, we get
PV = constant
T
P1V1 = P2V2
This is the combined gas law.
T1
T2
The Ideal Gas Equation
By combining the Boyle’s law, Charles law and Avogadro’s law, we get the Ideal Gas Equation
(PV) /(nT) = constant
PV = nRT
or n = PV/RT
(R = universal gas constant)
Value of R
R = PV/nT
R = (1 atm) x (22.4 L)
(1 mol) x (273 K)
= 0.0821 L atm mol-1 K-1
(At STP, T = 273K and P = 760mm of Hg or 1 atm. The volume of 1 mole of a gas at STP is 22.4 L)
Gas Laws and Molecular mass (M)
g
PV
n=
=
M
RT
g RT
M=
d RT
M=
V
P
P
Dalton’s Law of Partial Pressures
Total pressure of a mixture of gases is equal to the sum of the individual pressures of all the gases in
the mixture. The individual pressures are called partial pressure.
Ptotal = PA + PB
Partial pressure of Gas A (PA ) = nART / V
If the total pressure of the mixture were given, then the partial pressure of gas A would be,
PA = Pmix x mole fraction of A
Mole fraction of a component in the mixture = Number of moles of that component
Total Number of moles
Kinetic molecular Theory of Gases
Assumptions
1. A gas is composed of very minute particles called molecules.
2. The molecules are in a state of constant motion in random directions. During their movement
they collide with each other and also with the walls of the container.
3. The molecules are perfectly elastic and the collisions do not result in any loss of energy.
4. There are no intermolecular forces of attraction between molecules.
5. The volume occupied by a molecule is negligible when compared with the total volume of the
gas.
6. The average kinetic energy of the molecules is directly proportional to the temperature of the
gas in Kelvin.
According to Kinetic theory of gases,
PV = 1 / 3 mNu2
m = mass of a single molecule, N = total # of molecules, u2 = mean square velocity
3PV
Root mean square Velocity (rms velocity) u =
For 1 mole of the gas
3PV
=
mN0
3RT
=
M
M
N0 = Avogadro’s number
M = Molar mass of gas
Diffusion
The gradual mixing of molecules of one gas with the molecules of another by virtue of their kinetic
properties is called diffusion.
Effusion
The process by which a gas under pressure escapes from one compartment to another through a
small hole is called effusion.
Graham’s law of Diffusion
The law states that under same conditions of temperature and pressure the rate of diffusion of a gas
is inversely proportional to the square root of its molecular mass.
1
r 
r1
or
M
M2
=
r2
M1
Deviation form ideal Behavior
In actual practice it has been found that real gases deviate from ideal behavior. The deviation from
ideal behavior is more prominent at conditions of low temperature and high pressure.
At these conditions it is not wise to assume that the two postulates (postulates # 4 and 5) of kinetic
theory of gases are good.
Hence, J.D.van der Waal corrected the ideal gas equation as,
(P + a n2 /V2) (V – nb) = nRT
a = proportionality constant
nb = represents the volume occupied by ‘n’ moles of gas