Criteria for Spontaneity of a Process

Spontaneity of any process depends on three interacting factors, all of which are pulled together in the criterion at the end:

• If a process's enthalpy change is NEGATIVE (exothermic), the process MAY be spontaneous.
• If a process's entropy change is POSITIVE, the process MAY occur spontaneously.
• Gibbs free energy combines both of these into the single necessary-and-sufficient condition: for a reaction to be spontaneous, $\Delta H-T\Delta S$ must be negative, i.e. $\Delta G<0$.

Table 7.5 works through all four sign combinations of $\Delta H_r$ and $\Delta S_r$ (assuming both stay roughly constant across the temperature range considered):

• $\Delta H_r$ negative, $\Delta S_r$ positive $\Rightarrow$ $\Delta G_r$ negative at ALL temperatures -- spontaneous at all temperature (example: $2O_3(g)\rightarrow3O_2(g)$).
• $\Delta H_r$ negative, $\Delta S_r$ negative $\Rightarrow$ $\Delta G_r$ negative at LOW $T$, positive at HIGH $T$ -- spontaneous at low temperature, non-spontaneous at high temperature (example: adsorption of gases).
• $\Delta H_r$ positive, $\Delta S_r$ positive $\Rightarrow$ $\Delta G_r$ positive at LOW $T$, negative at HIGH $T$ -- non-spontaneous at low temperature, spontaneous at high temperature (example: melting of a solid).
• $\Delta H_r$ positive, $\Delta S_r$ negative $\Rightarrow$ $\Delta G_r$ positive at ALL temperatures -- non-spontaneous at all temperatures (example: $2H_2O(g)+O_2(g)\rightarrow2H_2O_2(l)$).

Two caveats the book is careful to add: this table assumes $\Delta H$ and $\Delta S$ genuinely stay the way indicated across the whole temperature range -- which is not always true in practice. And "spontaneity" of a reaction only describes the reaction's THERMODYNAMIC POTENTIAL to proceed as written; the actual RATE at which such a process happens is governed by kinetic factors that lie entirely outside thermodynamic prediction. …