Equilibirum constants `K_(1)` and `K_(2)` for the following equilibria
`NO(g) + (1)/(2)O_(2)hArrNO_(2)(g)` and `2NO_(2)(g)hArr`
`2NO(g) + O_(2)(g)` are related as

Options

A. `K_(2)=1//K_(1)`
B. `K_(2)=K_(1)//2`
C. `K_(2)=1//K_(1)^(2)`
D. `K_(2)=K_(1)^(2)`

Answer

C

Explanation

Second equilibrium equation can be genrated from the first one in two stages:
Stage 1: Reverse the equilibrium equation
`NO_(2)(g)hArr NO(g)+(1)/(2)O_(2)(g)`
`:. K_(eq)= (1)/(K_(1))`
Stage 2: Multiply the reversed equilibrium equation by 2.
`2NO_(2)(g)hArr 2NO(g)+O_(2)(g)`
`:. K_(eq)= ((1)/(K_(1)))^(2)`
This implies
`K_(2)= (1)/(K_(1)^(2))`