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Consider the following reactions in whic...

Consider the following reactions in which all the reactants and the products are in gaseous state.
`2PQ hArr P_(2)=Q_(2), K_(1)=2.5xx10^(5)`
`PQ +1//2 R_(2) hArr PQR, K_92) =5xx10^(-3)`
The value of `K_(2)` for the equilibrium
`1//2P_(2)+1//2Q_(2) +1//2R_(2) hArr PQR,` is

A

`2.5 xx10^(-3)`

B

`2.5 xx10^(3)`

C

`1.0 xx10^(-5)`

D

`5 xx10^(3)`

Text Solution

Verified by Experts

The correct Answer is:
C
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)`
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