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"#
