For the reaction at 298K, A+ B rarr C, DeltaH =400 kJ mol^(-1) and DeltaS = 0.2 kJ K^(-1) mol^(-1) . At what temperature will be thereaction become spontaneous considerting DeltaHand DeltaS to be constant over the temperature range.

For the reaction at 298K, A+ B rarr C, DeltaH =400 kJ mol^(-1) and Del

1.	For the reaction at 298K, A+ B rarr C, DeltaH =400 kJ mol^(-1) and DeltaS = 0.2 kJ K^(-1) mol^(-1) . At what temperature will be thereaction become spontaneous considerting DeltaHand DeltaS to be constant over the temperature range.
Answer» Solution :`DeltaG = DeltaH - T DELTAS` For the reaction to be spontaneous , `DeltaG` should be negative,i.e.,` Delta H - T DeltaSlt0` or `DeltaH lt T Delta S` or `T Delta S gt DeltaH` or `T gt (DeltaH)/( DeltaS) ` or`T gt ( 400 kJ MOL^(-1))/( 0.2 kJ K^(-1)mol^(-1))` or `T gt 2000K` This method can be applied only when `DeltaH ` and `DeltaS` both are `+ve`. ALTERNATIVELY, for equilibrium , `DeltaG= 0 `. Hence, `T DeltaS = DeltH` or `T = ( DeltaH )/( DeltaS = 0.2 = ( 400KJ mol^(-1))/( 0.2 kJ K^(-1) mol^(-1))= 2000 K `. For SPONTANEITY, `DeltaG = -ve`. This can be so only when `T gt 2000K`. ( so that `TDeltaS gt DeltaH`is magnitude).