Given `S^@` for `C_("Graphite"), H_(2(g))` and `CH_(4(g))` are `5.70, 130.7` and `186.3 JK^(-1) mol^(-1)`. Also standard heat of formation of `CH_4` is `-74.81kJmol^(-1).` Calculate the standard Gibbs energy change for the formation of methane at `298K.`
`C_("Graphite")+2H_(2(g))toCH_(4(g))`

Explanation

`Delta_(f)H^(@)CH_(4)=H_(CH_(4))^(@)=-74.81kJmol^(-1)`
Also `H^(@)` for `C_("graphite")` and `H_(2(g))=0`
(standard state of elements)
`C_("graphite")+2H_(2(g))toCH_(4(g)),`
`:. DeltaH^(@)=DeltaH_(CH_(4))^(@)-H_(C_("graphite"))^(@)-2xxH_(H_(2))^(@)`
`=74.81`
Also `DeltaS^(@)` (for the reaction)
`=S_(CH_(4))^(@)-S_(C_("graphite"))^(@)-2xxS_(H_(2))^(@)`
`=186.3-5.70-130.7xx2=-80.8JK^(-1)mol^(-1)`
Using `DeltaG^(@)=DeltaH^(@)-TDeltaS^(@)`
`=-74.81-298xx[-80.8xx10^(-3)]`
`=-50.73 kJ`