If equilibrium constant for `N_2(g)+O_2(g)

Options

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

Explanation

Given, equilibrium constant for the reaction
`N_2(g)+O_2(g) `K=([NO]^2)/([N_2][O_2])`
Let equilibrium constant for the reaction,
`1/2N_2(g)+1/2O_2(g) `K^'=([NO])/([N_2]^(1//2)[O_2]^(1//2))`
On squaring both sides `K^('2)=([NO]^2)/([N_2][O_2])`
on comparing equation (i) and (iii) we get
`K=K^('2)` or `K^'=sqrtK`