Consider the following reactions in which all the statements and the products are in gaseous state.
`2PQ 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 equilibirum `(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

Given, `2PQ hArr P_(2) + Q_(2)`,
`K_(1) = ([P_(2)][Q_(2)])/([PQ]^(2)) = 2.5 xx 10^(5)`
`PQ + (1)/(2)R_(2) hArr PQR`,
`K_(2) = ([PQR])/([PQ][R_(2)]^(1//2)) = 5 xx 10^(-3)`
Required equilibrium is
`(1)/(2)P_(2) + (1)/(2) Q_(2) + (1)/(2) R_(2) hArr PQR`
`K_(3) = ([PQR])/([P_(2)]^(1//2)[Q_(2)]^(1//2)[R_(2)]^(1//2))`
On multiplying and dividing by [PQ],
`K_(3) = ([PQR][PQ])/([P_(2)]^(1//2)[Q_(2)]^(1//2)[R_(2)]^(1//2)[PQ])`
or `K_(3) = K_(2) xx sqrt((1)/(K_(1)))`
`= 5 xx 10^(-3) xx sqrt((1)/(2.5 xx 10^(4)))`
`= (5 xx 10^(-3))/(0.5 xx 10^(3)) = 1 xx 10^(-5)`