Consider the following gaseous equilibria with equilibrium constants `K_(1)` and `K_(2)` respectively.
`SO_(2(g))+(1)/(2)O_(2(g))hArr SO_(3(g))`
`2SO_(3(g))hArr 2SO_(2(g))+O_(2(g))`
The equilibrium constants are related as ………….

Options

A. `2K_(1)=K_(2)^(2)`
B. `K_(1)^(2)=(1)/(K_(2))`
C. `K_(2)^(2)=(1)/(K_(1))`
D. `K_(2)=(2)/(K_(1)^(2))`

Answer

B

Explanation

`SO_(2)+(1)/(2)O_(2)hArrSO_(3)`…(i)
`2SO_(3)hArr2SO_(2)+O_(2)`……..(ii)
Reaction (ii) is double of (i) and reverse of (i), Hence
`K_(2)=(1)/(K_(1)^(2))thereforeK_(1)^(2)(1)/(K_(2))`