Calculate the standard free energy change for the formation of methane at `300K`:
`C("graphite") +2H_(2) (g) rarr CH_(4)(g)`
The following data are given:
`Delta_(f)H^(Theta) (kJ mol^(-1)): CH_(4)(g) =- 74.81`
`Delta_(f)S^(Theta)(kJ mol^(-1)): C("graphite") = 5.70, H_(2)(g) = 130.7 CH_(4)(g) = 186.3`

Explanation

`Delta_(r)G^(Theta)` can be calculated form the relation:
`Delta_(r)G^(Theta) = Delta_(r)H^(Theta) - TDelta_(r)S^(Theta)`
`C("graphite") +2H_(2)(g) rarr CH_(4)(g)`
`Delta_(f)H^(Theta) = Delta_(f)H^(Theta) (CH_(4)) -[Delta_(f)H^(Theta)(C ) +2Delta_(f)H^(Theta)(H_(2))]`
`=- 74.81 -0 -0 =- 74.81 kJ mol^(-1)`
`Delta_(r)S^(Theta) S_(m)^(Theta) (CH_(4)) -[S_(m)^(Theta) (C )+2S_(m)^(Theta)(H_(2))]`
`= 186.3 -[5.70 +2 xx 130.7]`
`= 180.3 - 267.1`
`=- 80.8 J K^(-1) mol^(-1)`
`:. Delta_(r)G^(Theta) = Delta_(r)H^(Theta) -TDelta_(r)S^(Theta)`
`=- 74.81 -300 xx (-80.0 xx 10^(-3))`
`=- 74.81 +24.4 =- 50.57 kJ mol^(-1)`