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 xx10^(-3)`
B. `2.5 xx10^(3)`
C. `1.0 xx10^(-5)`
D. `5 xx10^(3)`

Answer

C

Explanation

Given, `2PQ hArr P_2 +Q_2`
`K_1 =([P_2][Q_2])/([PQ]^2)=2.5 xx10^5`
`PQ +1//2R_2 hArr PQR`
`K_2 =([PQR])/([PQ][R_2]^(1//2))=5 xx10^(-3)`
Required equilibrium is :
`1//2P_2 +1//2Q_2 +1//2R_2 hArrPQR`
`K_3 =([PQR])/([P_2]^(1//2)[Q_2]^(1//2)[R_2]^(1//2))`
`K_3=K_2xxsqrt(1/K_1)`
`=5 xx10^(-3)xxsqrt(1/(2.5 xx10^5))=(5xx10^(-3))/(0.5xx10^(3))=1xx10^(-5)`