Given that equilibrium constant for the reaction `2SO_(2)(g) + O_(2)(g)hArr2SO_(3)(g)` has a value of 278 at a particular temperature. What is the value of the equilibrium constant for the following reaction at the same temperature ? `SO_(3)(g)hArrSO_(2)(g) + (1)/(2)O_(2)(g)`

Options

A. `1.8 xx 10^(-3)`
B. `3.6 xx 10^(-3)`
C. `6.0 xx 10^(-2)`
D. `1.3 xx 10^(-5)`

Explanation

For the reaction,
`2SO_(2) (g)+O_(2) (g) Leftrightarrow 2SO_(3) (g) K`
`=([SO_(3)]^(2))/([SO_(2)]^(2) [O_(2)])=278`
`SO_(3) (g) Leftrightarrow SO_(2) (g)+1/2 O_(2) (g)`
`K.=([SO_(2)] [O_(2)]^(1//2))/([SO_(3)])=(1/K)^(1//2)`
`=((1)/(278))^(1//2)=6 xx 10^(-2)`