Consider the following reactions in which all the reactants and the products are in gasous state
` 2 PQ hArr P_(2) + Q_(2) , K_(1) = 2.5 xx 10^(5)`
` PQ + 1/2 R_(2) hArr PQR, K_(2) = 5 xx 10^(-3)`
The value of `K_(3)` for the equilibrium
` 1//2 P_(2) + 1//2 Q_(2) + 1//2 R_(2) hArr PQR, ` is

Options

A. `2.5 xx 10^(-3)`
B. `2.5 xx 10^(3)`
C. `1.0 xx 10^(-5)`
D. ` 5 xx 10^(3)`

Answer

C

Explanation

For `2 PQ hArr P_(2) + Q_(2) , K_(1) = ([P_(2)] [Q_(2)])/([PQ]^(2))`
For ` PQ + 1/2 R_(2) hArr PQR, `
`K_(2) = ([PQR])/([PQ] [R_(2)]^(1//2))`
For the required equilibrium
` 1/2 P_(2) + 1/2 Q_(2) + 1/2 R_(2) hArr PQR`
` K = ([PQR])/([P_(2)]^(1//2) [Q_(2)]^(1//2) [R_(2)]^(1//2))=(K_(2))/(sqrt(K_(1)))`
` = ( 5xx 10^ (3))/(sqrt(2*5 xx 10^(5) ))=(5xx 10^(-3))/(5xx 10^(2))= 10^(-5)`