## About General Gas Equation

General Gas Equation is also termed as Ideal Gas Equation

To give a relation between the volume, pressure and number of moles of n gas, Boyle’s law, Charle’s law and Avogadro’s law are used.

According to Boyle’s law | V ∞ 1 / P

According to Charle’s law | V ∞ T

According to Avogadro’s law | V ∞ n

By combining these laws we get

V ∞ 1 / P x T x n

OR

V = R x 1 / P x T x P

OR

P V = n R T

This equation is known as general gas equation n is also known as equation of state because when we specify the four variables = pressure, temperature, volume and number of moles we define the state for a gas.

In this equation “R” is a constant known as gas constant.

### Value of R

- When Pressure is Expressed in Atmosphere and Volume in Litres or dm3

According to general gas equation

P V = n R T

OR

R = PV / nT

For 1 mole of a gas at S.T.P we know that

V = 22.4 dm3 or litres

T = 273 K (standard temperature)

P = 1 atm (standard pressure)

So,

R = PV / nT

= 1 atm x 22.4 dm3 / 1 mole x 273 K

= 0.0821 dm3 K-1 mol0-1 - When Pressure is Expressed in Newtons Per Square Metre and Volume in Cubic Metres

For 1 mole of a gas at S.T.P

V = 0.0224 m3 ………. ( 1 dm3 = 10-3 m3)

n = 1 mole

T = 273 K

P = 101200 Nm-2

So,

R = PV / nT

= 101300 Nm-2 x 0.0224 m3 / 1 mole x 273 K

= 8.3143 Nm K-1 mole-1

= 8.3143 J K-1 mol-1

### Derivation of Gas Equation

According to general gas equation

P V = n R T

For 1 mole of a gas n = 1

P V = R T

OR

P V / T = R

Consider for a known mass of a gas the volume of the gas is V1 at a temperature T1 and pressure P1. Therefore for this gas we can write as

P1 V1 / T1 = R

If this gas is heated to a temperature T2 due to which the pressure is changed to P2 and volume is changed to V2. For this condition we may write as

P2 V2 / T2 = R

P1 V1 / T1 = P2 V2 / T2 = R

P1 V1 / T1 = P2 V2 / T2

This equation is known as gas equation