`DeltaG^(@)` for `(1)/(2)N_(2)+(3)/(2)H_(2)hArrNH_(3)` is `-16.5 kJ mol^(-1)` at `25^(@)C`. Find out `K_(p)` for the reaction. Also report `K_(p)` and `DeltaG^(@)` for:
`N_(2)+3H_(2)hArr2NH_(3)` at `25^(@)C`

Explanation

`-DeltaG^(@)=2.303RTlogK_(p)`
`-(-16.5xx10^(3))=2.303xx8.314xx298 logK_(p)`
`logK_(p)=(16500)/(2.303xx8.314xx298)`
`:. K_(p)=779.41 atm^(-1)`
Also , `K_(P_(1))` for `N_(2)+3H_(2)hArr2NH_(3)`
`K_(p_(1))=(K_(p))^(2)=(779.41)^(2)`
`K_(p_(1))=6.07xx10^(5)atm^(-2)`
Also, `-DeltaG_(1)^(@)=2.303xx8.314xx298 log (6.07xx10^(5))J`
`=32.998 kJ`
`:. DeltaG_(1)^(@)=-32.998 kJ mol^(-1)`