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Calculate the standard free energy chang...

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)(JK^(-1) mol^(-1)): C("graphite") = 5.70, H_(2)(g) = 130.7 CH_(4)(g) = 186.3`

Text Solution

Verified by Experts

`Delta_(r)G^(@)` can be calculated from the relation :
`Delta_(r)G^(@) = Delta_(r)H^(@) - T Delta_(r)S^(@)`
`C("graphite") + 2H_(2)(g) to CH_(4)(g)`
`Delta_(r)H^(@) = Delta_(f)H^(@)(CH_(4)) - [Delta_(f)H^(@)(C) + 2Delta_(f)H^(@)(H_(2)]`
` = -74.81 - 0-0 = - 74.81 kJ "mol"^(-1)`
`Delta_(r)S^(@) = S_(m)^(@)(CH_(4))-[S_(M)^(@)(C) + 2S_(M)^(@)(H_(2))]`
` = 186.3 - [5.70 + 2 xx 130.7]`
` = 186.3 -267.1`
` = -80.8 J K^(-1) "mol"^(-1)`
`therefore Delta_(r)G^(@) = Delta_(r)H^(@) - TDelta_(r)S^(@)`
`= -74.81 - 298 xx (80.8 xx 10^(-3))`
` = -74.81 + 24.08 = -50.73 kJ "mol"^(-1)`
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