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
Solution 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.
Solution 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`]
