Calculate `|Delta_(f)G^(@)|` for `(NH_(4)Cl, s)` at `350 K`.
Given : `Delta_(f)H^(@) (NH_(4)Cl, s)=-314.5" kJ/mol"`
`{:(S_(N_(2)(g))^(@)=192 JK^(-1) mol^(-1),,S_(H_(2)(g))^(@)=130.5 JK^(-1) mol^(-1),),(S_(Cl_(2)(g))^(@)=223 JK^(-1) mol^(-1),,S_(NH_(4)Cl(s))^(@)=94.5 JK^(-1) mol^(-1),,"All given data at 300 K".),(Delta_(r)C_(P)=-20" J/mol-K",,ln(350/300)=0.15,):}`

Explanation

`Delta_(f)S^(@)(NH_(4)Cl, s)` at `300 K=S_(NH_(4)Cl(s))^(@)-[1/2 S_(N_(2))^(@)+2S_(H_(2))+1/2 S_(Cl_(2))^(@)]`
`=94.5-(1/2xx192+2xx130.5+1/2xx223)`
`=94.5-(96+261+111.5)`
`Delta_(f)S_(300)^(@)" "=-374 JK^(-1) mol^(-1)`
`Delta_(f)S_(310)^(@)" "=Delta_(f)S_(300)^(@)+Delta_(r)C_(p)ln (350/300)`
`=-374-20xx(0.15)=-377 JK^(-1) mol^(-1)`
`Delta_(f)H_(310)^(@)" "=Delta_(f)H_(300)^(@)+Delta_(r)C_(p) [350-300]`
`=-314.5-(20xx50)/(1000)=-315.5`
`Delta_(f) G_(350)^(@)" "=Delta_(f)H^(@)-T. Delta_(f) S^(@)`
`=-315.5-(350xx(-377))/(1000) " "rArr-183.55" kJ/mol"`
`|Delta_(f) G_(350)^(@)|" "=183.55" kJ/mol "rArr" "183" kJ/mol"`