Question

Why does Gibbs free energy have to be negative?

Answer 1

For a reaction to happen spontaneously, the total entropy of the system and surroundings must increase:

`DeltaS_(overall)=DeltaS_(sur)+DeltaS_(sys)>0`

The entropy of the system changes by `(DeltaH_(sys))/T`, and because `DeltaH_(sys)=-DeltaH_(sur)`, entropy change of the surroundings can be calculated from the equation

`DeltaS_(sur)=-(DeltaH)/T`

Substituting this for `DeltaS_(sur)` gives

`DeltaS_(overall)=(-DeltaH)/T+DeltaS_(sys)>0`

Multiplying through by `-T` gives

`DeltaG=-TDeltaS_(overall)=DeltaH-TDeltaS_(sys)<0`