The equilibrium constant for the reaction
`N_(2)(g)+O_(2)(g) hArr 2NO(g)`
at temperature T is `4xx10^(-4)`.
The value of `K_(c)` for the reaction
`NO(g) hArr 1/2 N_(2)(g)+1/2 O_(2)(g)`
at the same temperature is

Options

A. `0.02`
B. `50`
C. `4xx10^(-4)`
D. `2.5xx10^(-2)`

Explanation

`N_(2)+O_(2)hArr2NO`
`K_(c_(1))=([NO]^(2))/([N_(2)][O_(2)])=4xx10^(-4)`
`NOhArr1//2N_(2)+1//2O_(2)`
`K_(c_(2))=([N_(2)]^(1//2)[O_(2)]^(1//2))/([NO])`
`K_(c_(2))=sqrt((1)/(K_(c_(1))))=sqrt((1)/(4xx10^(-4)))=50`