For the reaction `N_(2)(g)+O_(2)(g) hArr 2NO(g)`, the equilibrium constant is `K_(1)`. The equilibrium constant is `K_(2)` for the reaction
`2NO(g)+O_(2) hArr 2NO_(2)(g)`
What is `K` for the reaction
`NO_(2)(g) hArr 1/2 N_(2)(g)+O_(2)(g)`?

Options

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

Answer

A

Explanation

`N_(2)+O_(2) hArr 2NO.....K_(1)" "......(i)`
`2NO+O_(2) hArr 2NO_(2) .......K_(2)" "......(ii)`
`NO_(2)hArr 1//2 N_(2) +O_(2), K=sqrt((1)/(K_(1)K_(2)))`