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. 49
B. 2401
C. 7
D. 0.02

Answer

C

Explanation

`2AB hArr A_(2) + B_(2)`
`:. K_(1) = [A_(2)][B_(2)]/[AB]^(2)`….(1)
and `K_(1) = 49`
`AB = 1/2A_(2) + 1/2B_(2)`
`K_(2) = [A_(2)]^(1/2)[B_(2)]^(1/2)/[AB]`….(2)
From equation (1) and (2)
`K_(1) = K_(2)^(2)`
`implies K_(2) = sqrt(K_(1)) = sqrt(49) = 7`