Derive ideal gas equation PV = nRT.

1. The relation between three variables of a gas i.e., pressure, volume and absolute temperature is called as ideal gas equation.

From Boyle’s law,

V ∝ \(\frac{T}{P}\), at constant temperature ….(1)

From Charles’ law,

V ∝ T, at constant pressure … .(2)

2. Combining equations (1) and (2) 

we get,

∴ V ∝ \(\frac{T}{P}\)

∴ \(\frac{PV}{T}\) = constant

3. For one mole of a gas,

\(\frac{PV}{T}\) = R or PV = RT … (3)

where R is the constant of proportionality.

4. Equation (3) is called ideal gas equation. The value of constant R is same for all gases. Therefore, R is called as universal gas constant. R = 8.31 JK^-1mol^-1.

5. For ‘n’ moles of gas, i.e. if the gas contains ‘n’ moles, equation (3) can be written as,

PV = nRT