The equilibrium constant of the reaction,`SO_(2)(g) + 1/2 O_(2)(g) hArr 2SO_(3)(g)` is `5 xx 10^(-2)atm`. The equilibrium constant of the reaction,`2SO_(3)(g) hArr 2SO_(2)(g) + O_(2)(g)`

Options

A. 100 atm
B. 200 atm
C. `4 xx 10^(2) atm`
D. `6.25 xx 10^(4) atm`

Answer

C

Explanation

`SO_(2) + 1/2O_(2) hArr SO_(3)`
`K_(1) = [SO_(3)]/([SO_(2)][O_(2)]^(1/2))`………….(1)
and `K_(1) = 5 xx 10^(-2)atm`
`2SO_(3) hArr 2SO_(2) + O_(2)`
`:. K_(2) = ([SO_(2)]^(2)[O_(2)])/[SO_(3)]^(2)`…………..(2)
From equations (1) and (2), we get
`K_(2) = 1/K_(1)^(2) = 1/(5 xx 10^(-2))^(2) = 1/(25 xx 10^(-4)) = 10^(4)/25 = 100 xx 10^(4)/25 = 4 xx 10^(2) atm`