Calculate the value of `log K_(p)` for the reaction, `N_(2(g))+3H_(2(g))hArr2NH_(3(g))` at `25^(@)C`. The standard enthalpy of formation of `NH_(3(g))` is `-46kJ` and standard entropies of `N_(2(g))`, `H_(2(g))` and `NH_(3(g))` are `191`, `130`, `192` `JK^(-1) mol^(-1)`. respectively. (`R=8.3JK^(-1)mol^(-1)`)

Explanation

`Delta_(f)G^(@) (NH_(3)) = DeltaH^(@) - TDeltaS^(@) = -46000- ( 298 xx192) J mol^(-1) = - 103.2 kJ mol^(-1)`
`Delta_(f)G^(@) (N_(2))= DeltaH^(@) - T DeltaS^(@) = 0 -298 xx191 J mol^(-1) = -56.9 kJ mol^(-1)`
`Delta_(f)G^(@) ( H_(2)) = DeltaH^(@) - T DeltaS^(@) =0 - 298 xx 130 J mol^(-1) = - 38.74kJ mol^(-1)`
`DeltaG^(@)` for reaction
`Delta _(r)G^(@) = 2 xx Delta_(f)G^(@) ( NH_(3)) - Delta_(f)G^(@) ( N_(2))-3Delta_(f)(H_(2)) =- 206.4 +56.9 +116.2 = - 33.28 kJ mol^(-1)- DeltaG^(@) =2.303 RT log K`
` 33.28 = 2.303 xx (8.314 xx 10^(-3)) log K` or `log K =1.738 xx 10^(3)`