Question

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

Answer 1

 

The ideal gas equation relating pressure (P), volume (V), and absolute temperature (T) is given as:

PV = nRT

Where,

R is the universal gas constant = 8.314 J mol^–1 K^–1

n = Number of moles = 1

T = Standard temperature = 273 K

P = Standard pressure = 1 atm = 1.013 × 10⁵ Nm^–2

`:.V= (nRT)/T`

`= (1xx8.314xx273)/(1.013xx10^5)`

`= 0.0224 m^3`

= 22.4 litres

Hence, the molar volume of a gas at STP is 22.4 litres.

Answer 2

For one mole of an ideal gas, we have

`PV = RT => V = "RT"/P`

Putting  `R = 8.31 J mol^(-1) K^(-1)`, T = 273 K and `P = 1 " atmosphere" = 1.013 xx 10^5 Nm^(-2)`

`:. V = (8.31 xx 273)/(1.013xx 10^5) = 0.0224 m^3`

`= 0.0224 xx 10^6 cm^3 = 22400 ml`       [`1 cm^3 = 1ml`]