K1, K2 and K3 are the equilibrium constants of the following reactions (I), (II) and (III) respectively:
(I) N2 + 2O2 ⇌ 2NO2
(II) 2NO2 ⇌ N2 + 2O2
(III) NO2 ⇌ 1/2N2 + O2
The correct relation from the following is
(a) K1 = \(\frac{1}{K_2}\) = \(\frac{1}{K_3}\)
(b) K1 = \(\frac{1}{K_2}\) = \(\frac{1}{(K_3)^2}\)
(c) K1 = \(\sqrt{K_2}\) = K3
(d) K1 = \(\frac{1}{K_2}\) = K3
Correct answer: (b) K1 = \(\frac{1}{K_2}\) = \(\frac{1}{(K_3)^2}\)
Explanation:
(I) N2 + 2O2 + K1 ⇌ 2NO2
K1 = \(\frac{[NO_2]^2}{[N_2][O_2]^2}\) .....(i)
(II) 2NO2 + K2 ⇌ N2 + 2O2
K2 = \(\frac{[N_2][O_2]^2}{[NO_2]^2}\) ......(ii)
(III) NO2 ⇌ 1/2N2 + O2
K3 = \(\frac{[N_2]^{\frac{1}{2}}}{[NO_2]^2}\)
∴ (K3)2 = \(\frac{[N_2][O_2]^2}{[NO_2]^2}\) .....(iii)
∴ from equation (i), (ii) and (iii)
K1 = \(\frac{1}{K_2}\) = \(\frac{1}{(K_3)^2}\)