If the equilibrium constant for the reaction `2AB hArr A_(2) + B_(2)` is 49 what is the value of equilibrium constant for `AB hArr 1/2 A_(2) + 1/2 B_(2)`?

Options

A. 7
B. `1/7`
C. 24.5
D. 49

Answer

A

Explanation

(i) `2AB hArr A_(2) + B_(2)`
`K_(1) = [A_(2)][B_(2)]/[AB]^(2)`
(ii)`AB hArr 1/2A_(2) + 1/2B_(2)`
`K_(2) = [A_(2)]^(1/2)[B_(2)]^(1/2)/[AB]`
`:. K_(1) = (K_(2))^(2)`
` implies K_(2) = sqrt(K_(1)) = sqrt(49) = 7`