A vessel of volume , `V = 5.0` litre contains `1.4 g` of nitrogen at a temperature `T = 1800 K`. Find the pressure of the gas if `30%` of its molecules are dissociated into atoms at this temperature.

Explanation

Given, `V = 5 litre, m = 1.4 g, T = 1800 K`
The vessel contains molecular nitrogen and atomic nitrogen.
Moles of molecular nitrogen
`n_(1) = (m(1 - 0.3))/(M_(0)) = (0.7 m)/(M_(0))`
Moles of atomic nitrogen
`n_(2) = (0.3 m)/(M_(0)//2) = (0.6 m)/(M_(0))`
`M_(0)` : molecular mass nitrogen
`P = (n_(1) + n_(2)) = ((0.7 m + 0.06)/(M_(0))) (R T)/(V)`
`= (1.3 m R T)/(M_(0) V) = (1.3 xx 1.4 xx 8.3 xx 1800)/(28 xx 10^(-3) xx 5 xx 10^(-3))`
`= 1.94 xx 10^(5) N//m^(2)`
OR
`underset(1-x)overset(1)(N) hArr underset(2x)overset(0)(2 N) overset(=1)(=1)+x`
`PV = n R T = (1 + x)(m)/(M_(0)) R T`
`P = ((1 + 0.3) m R T)/(V) = 1.94 xx 10^(5) N//m^(2)`