For the reaction,
`4C(s) +5H_(2)(g) rarr nC_(4)H_(10)(g)`,
`DeltaH^(Theta) =- 124.73 kJ mol^(-1), DeltaS^(Theta) =- 365.8 J K^(-1) mol^(-1)`
`4C(s) +5H_(2)(g) rarr iso-C_(4)H_(10)(g)`
`DeltaH^(Theta) =- 131.6 kJ mol^(-1), DeltaS^(Theta) =- 381.079 J K^(-1) mol^(-1)`
Indicate whether normal butane can be spontaneously converted to iso-butane or not.

Answer

yes, `DeltaG^(@)=-2.32kJ`

Explanation

For `nC_(4)H_(10)`,
`DeltaG^(@)=DeltaH^(@)-TDeltaS^(@)`
`=-124.73-298(-365.8xx10^(-3))=-15.72kJ`
For iso-butane (iso-`C_(4)H_(10)`)
`DeltaG^(@)=-131.6-298(-381.079xx10^(-3))`
`=18.04kJ`
For conversion of `nC_(4)H_(10)toiso-C_(4)H_(10)`.
`DeltaG^(@)=-18.04-(-15.72)=-2.32kJ`
Negative value shows that the process is spontaneous.