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/(2K_1K_2)`
B. `1/(4K_1K_2)`
C. `(1/(K_1K_2))^(1//2)`
D. `1/(K_1K_2)`

Answer

C

Explanation

`{:(" "N_2(g)+O_2(g) hArr 2NO(g) " " K_1),(2NO(g) + O_2(g) hArr 2NO_2(g) " " K_2),(N_2(g)+2O_2(g)hArr 2NO_2(g) " " K=K_1xxK_2) :}`
For `2NO_2(g) hArr N_2(g) +2O_2(g) K.=1/(K_1K_2)`
or `NO_(2)(g) hArr 1/2N_2(g) +O_2(g)K=(1/(K_1K_2))^(1//2)`