For the reaction at `298 K`
`2A+B rarr C`
`DeltaH=400 kJ mol^(-1)` and `DeltaS=0.2 kJ K^(-1) mol^(-1)`
At what temperature will the reaction becomes spontaneous considering `DeltaH` and `DeltaS` to be contant over the temperature range.

Explanation

`DeltaG = DeltaH - T DeltaS`
For the reaction to be spontaneous , `DeltaG` should be negative ,i.e.,` Delta H - T DeltaS lt 0` 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).