For the reaction, `N_2(g)+O_2(g)hArr2No(g)` equilibrium constant is `K_1`. The equilibrium constant is `K_2` for the reaction. `2NO(g)+O_2(g)hArr2NO_2(g)`. What is K for the reaction, `NO_2(g)hArr1/2N_2(g)+O_2(g)`-

Options

A. `1/(2K_1K_2)`
B. `1/(4K_1K_2)`
C. `[1/(K_1K_2)]^(1//2)`
D. `1/(K_1K_2)`

Explanation

(i) For the reaction, `N_2(g)+O_2(g) `K_1=([NO]^2)/([N_2][O_2])`
(ii) For the reaction, `2NO(g)+O_2(g) `K_2=([NO_2]^2)/([NO]^2[O_2])`
(iii) For the reaction, `NO_2(g) `K_3=([N_2]^(1//2)[O_2])/([NO_2])=([N_2]^(1//2)[O_2]^(1//2))/([NO])xx([NO][O_2]^(1//2))/([NO_2])`
`=1/sqrt(K_1)xx1/sqrt(K_2)=1/(sqrtK_1xxK_2)`