Show that free energy `(Delta G)` as a criterion for spontaneous and non-spontaneous processes.

Explanation

Effect of temperature on the spontaneity of chemical reaction using Gibb's-Helmholtz equation : `Delta G = Delta H - T.Delta S`
Case I : For an exothermic process, `Delta H` is negative.
(a) If `Delta S` is positive, `Delta G` is always negative. The process is always spontaneous.
(b) If `Delta S` is negative,
(i) If the temperature is low such that `T Delta S lt Delta H`, then `Delta G` is negative. The process is spontaneous.
(ii) If the temperature is high such that `T Delta S gt Delta H`, then `Delta G` is positive. The process is not spontaneous
Thus, an exothermic process which is not spontaneous at a given temperature may become spontaneous at low temperatures.
Case II : For an endothermic process, `Delta H` is positive.
(a) If `Delta S` is negative, `Delta G` is always positive. `:.` The process is not spontaneous
(b) If `Delta S` is positive,
(i) If the temperature is low such that `TDelta S lt Delta H`, then `Delta G` is positive. The process is not spontaneous.
(ii) If the temperature is high such that `T Delta S gt Delta H`, the `Delta G` is negative. The process is spontaenous.
Thus, an endothermic process which is not spontaneous at a given temperature may become spontaneous at high temperatures.
Case III : When any process attains equilibrium, `T Delta S gt Delta H, Delta G = 0`
i.e., `Delta G = Delta H - T Delta S = 0` or `Delta H = T Delta S` at equilibrium
For a chemical reaction, `A + B rarr C + D`, Gibb's energy change is given by, `Delta G = SigmaG_(2) - Sigma G_(1)`. It is the difference between the total free energies of all the products and the total free energies of all the reactants.