Equilibirum constants `K_(1)` and `K_(2)` for the following equilibria
`NO(g) + (1)/(2)O_(2)hArrNO_(2)(g)` and `2NO_(2)(g)hArr`
`2NO(g) + O_(2)(g)` are related as

Options

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

Answer

A

Explanation

`K_(1) = ([NO_(2)])/([NO][O_(2)])` and `K_(2) = ([NO]^(2)[O_(2)])/([NO_(2)]^(2))`
If eqn. is multiplied by n, then new equilibrium constant is `K_(1)n` and if equ. Is reversed, then new equilibrium constant is reciprocal of pervious.
`:. K_(2) = (1)/(K_(1)^(2))`