Molar volume is the volume occupied by 1 mol of any (ideal) gas at standard temperature and pressure (STP : 1 atmospheric pressure, 0 °C). Show that it is 22.4 litres.

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Solution

Given, the number of moles of the ideal gas is 1 mole.

Let P be the pressure of an ideal gas, V be its volume, T be the temperature and n be the number of moles of the gas, then the ideal gas equation is,

PV=nRT(1)

Here, R is the universal gas constant, i.e. 8.314 J/ mol ⋅K.

Take the value of standard temperature T as 273 K, standard pressure P as 1 atm=1.013× 10 5 N/ m 2 and number of moles n=1.

The volume V from (1) is,

V= nRT P

Substitute the values in the above expression.

V= 1×8.314×273 1.013× 10 5 =0.0224 m 3 or 22.4 litres

Therefore, the value of molar volume occupied by 1 mol of the gas is 22.4 litres.

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