**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, m^{3}.

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

**Avogadro and the 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 N_{a} particles.

N_{a} = 6.02 × 10^{23} 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, P_{1}V_{1} = P_{2}V_{2}

**Charles’s Law**

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

V_{1}/T_{1} = V_{2}/T_{2ussac’s L}

**Pressure Law**

P_{1}/T_{1 }= P_{2}/T_{2}

**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/N_{A}RT

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) * * =mc ^{2}/l*

Pressure is given by,

*Pressure = mc ^{2}/l^{3}*

For large number N of molecule,

*P = Nm <c ^{2}>/l^{3}*

*P = 1/3 Nm <c ^{2}>/l^{3}*

*P = 1/3 Nm/V <c ^{2}>*

*PV = 1/3 Nm <c ^{2}>*

*Since the average K.E. of molecule is;*

*E _{k} = ½ m <c^{2}> = 3/2 kT*