CBSE Class 11-science Answered

PCl₅ (g) ⇌ PCl₃ (g) + Cl₂ (g)

Initial             3                 0                 0

At equi:   3(1 – x )          3x               3x

(where x is degree of dissociation)

Total moles  = 3 (1 − x) + 3x + 3x = 3(1 + x)

1 mole of nitrogen is present, so actual total number of moles at equilibrium  

= 3 (1 + x) + 1
We know that, according to Ideal gas equation,
PV=nRT
Given, 

P = 2.05 atm, V = 100 litres, R = 0.082 atm × L/(mol×K)
T = (273 + 227) = 500 K
So, n = 0.082 × 5002.05 × 100 ​= 5
or 3(1 + x) + 1 = 5
3x = 1 or x = 0.333
Degree of dissociation is 0.333
At equilibrium, 

pPCl₅ = [3(1 – x) / (3x+4) ] ⨯ 2.05 atm

pPCl₃ = pCl₂ = [3x / (3x +4) ] ⨯ 2.05 atm

Kp = pPCl₃ ⨯ pPCl₂ / pPCl₅

= {[3x / (3x +4) ] ⨯ 2.05 atm}² /  [3(1 – x) / (3x+4) ] ⨯ 2.05 atm