The standard Gibbd energies `(Delta_(f)S^(Theta))` for the formation of `SO_(2)(g)` and `SO_(3)(g)` are `-300.0` and `-371.0 kJ mol^(-1)` at `300K`, respectively. Calculate `DeltaG` and equilibrium constant for the following reaction at `300K`:

Explanation

`2SO_(2)(g) +O_(2)(g) hArr 2SO_(2)(g)`
`Delta_(r)G^(Theta) = 2Delta_(f)G^(Theta) (SO_(3)) - 2Delta_(f)G^(Theta) (SO_(2)) -Delta_(f)G^(Theta) (O_(2))`
`= 2(-371) -2(-300)-0`
`= -742 +600 =- 142 kJ mol^(-1)`
Now `log K = (Delta_(r)G)/(2.303 RT)`
`Delta_(r)G^(Theta) =- 142 kJ mol^(-1), R = 8.314 xx 10^(-3) kJ mol^(-1)K^(-1)`,
`T = 300K`
`log K = (-142)/(2.303 xx 8.314 xx 10^(-3) xx 300) = 24.72`
`:. K = Antilog (24.72) = 5.248 xx 10^(24)`