# Chapter 22: Ideal Gases

Properties of Gas

Pressure: When a gas particle collides with the walls of its container it causes pressure. Pressure is measured in pascals, Pa. (1 Pa = 1 Nm-2)

Temperature: It is the measure of internal energy of the gas and it is equal to the average K.E. of its particles. It is measured in Kelvin, K.

Volume: It is the space occupied by the particle that makes up the gas. It is measured in meters cubed, m3.

Mass:  It is considered the amount of gas. It is measured in mole.

One mole of a material is the amount of that substance which contains the same number of particles as there are in 0,012 kg of carbon-12.

One mole of any substance contains Na particles.

Na = 6.02 × 1023 mol-1

Boyle’s Law

The pressure exerted by a fixed mass of gas is inversely proportional to its volume, provided the temperature of gas remains constant.

P α 1/v        for constant T

So, P1V1 = P2V2

Charles’s Law

The volume occupied by gas at constant pressure is directly proportional to its thermodynamic temperature.

V1/T1 = V2/T2ussac’s L

Pressure Law

P1/T1 = P2/T2

Ideal Gas

We know from the three gas laws that pV/T = constant

Ideal gases all behave in the same way so we can keep R as constant,

PV/T = R

If the volume and temperature of a gas are kept constant then the pressure depends on R and the number of particles in the container. We must take account to this by bring number of moles, n:

pV/T = nR

PV = nRT

Which is the ideal gas equation for n moles.

Using the Avogadro’s equation for n;

pV = nRT

pV = N/NART

pV =N (R/NA) T

Boltzmann Constant

It provides evidence for the fast, random movement of molecules in gas. The Boltzmann constant is represented by k and is given as;

R/NA=k

Kinetic Theory of Gases

It is the theory which links these microscopic properties of particles to the macroscopic properties of a gas. The assumptions of the kinetic theory of an ideal gas are:

Time of collision negligible compared to time between collisions.

No intermolecular forces except during collision.

Consider a collision in which a single molecule with mass m is moving with speed c parallel to one side of the box. Collision in side ABCD is elastically rebounded, so momentum from single collision is:

Change in momentum = -mc – (+mc)

= -mc – mc     = 2mc

Between the consecutive collisions with side ABCD, molecule travels distance 2l at speed c.

Time = 2l/c

Force =2mc/(2l/c)    =mc2/l

Pressure is given by,

Pressure = mc2/l3

For large number N of molecule,

P = Nm <c2>/l3

P = 1/3 Nm <c2>/l3

P = 1/3 Nm/V <c2>

PV = 1/3 Nm <c2>

Since the average K.E. of molecule is;

Ek = ½ m <c2> = 3/2 kT