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

Answer

D

Explanation

`N_(2)(g)+O_(2)(g) hArr 2NO(g)`
`K_(c)=([NO]^(2))/([N_(2)][O_(2)]\)=4xx10^(-4)`
For the reaction,
`NO(g)hArr (1)/(2)N_(2)(g)+(1)/(2)O_(2)(g)`
`K_(c)^(')=([N_(2)]^(2)[O_(2)]^((1)/(2)))/([NO])=(1)/(sqrt(K_(c)))`
`=(1)/(sqrt(4xx10^(-4))) =(1)/(2xx10^(-2))=(100)/(2)=50`