Remember
DeltaG = DeltaH - TDeltaS
Thus DeltarG = DeltarH - TDeltarS because Change in a system is proportional to overall enthalpy, entropy or Gibbs free energy.
Thus for the reaction
COCl_2 rarr CO + Cl_2
We know everything except DeltarS so take it as x. Now write down the equation
("-206 kJ")/"mol "= "-220kJ"/"mol" - 298.15K xx x
Solve for x
298.15 xx x = ("-220 kJ/mol") - ("-206 kJ/mol")
298.15 xx x = -14
x = -14 /(298.15K)
= DeltarS = "-046.95623kJ"/"mol"
As we are assuming that the DeltarS which we have found and DeltarH remains constant at 450K too we can now set up the equation
DeltarG^@ = "-220kJ"/"mol" - (450K xx "-046.95623kJ/mol")
DeltarG^@ = "-220kJ"/"mol" - (450K xx "-046.95623kJ/mol")
DeltarG^@ = "-220 kJ"/"mol"-(-21.130.3035)
DeltarG^@ = "-220kJ"/"mol"+21.1303035
DeltarG^@ = "-198.8696965kJ"/"mol"
Now we know that entropy or enthalpy cannot remain constant at different temerature so
DeltarG^@ ~~ "-198.8696965kJ"/"mol"
