# Spontaneity of Reactions- Gibbs Energy or Entropy change

I just wanted to check if I am thinking right:

The reason why we consider the Gibbs energy to be the measurer for spontaneity of a reaction is because it does not depend whether the reaction was exo- or endothermic.

Is it arising because: if the change in entropy were less than zero, the Gibbs change in energy is less than zero? So if that were true, then entropy may not be a measurer for spontaneity, correct?

• The reason why we consider the Gibbs energy to be the indicator for spontaneity of reactions is because it is such an indicator. Let's distinguish facts from interpretations. Entropy is an indicator too, but in different conditions. – Ivan Neretin Feb 28 '17 at 15:48

The only determining factor for spontaneity of a process is the total change in entropy of the universe. This must be non-negative.

For a general process within a system, we can decompose this into: $$\Delta S_{\mathrm{univ}} = \Delta S_{\mathrm{sys}}+\Delta S_{\mathrm{surr}} \geq 0$$

The computation of the system's change in entropy $\Delta S_{\mathrm{sys}}$ is not trivial, but doable. On the other hand, there is no practical way to directly measure or compute the corresponding change for the surroundings. We generally take shortcuts by measuring something else and deriving this value.

For example, for a isothermal, isobaric process, we assume that $$\Delta S_{\mathrm{surr}} = -\frac{\Delta H_{\mathrm{sys}}}{T}$$

Substitution into the first equation gives: $$\Delta S_{\mathrm{univ}} = \Delta S_{\mathrm{sys}} -\frac{\Delta H_{\mathrm{sys}}}{T} \geq 0$$

$$-T\Delta S_{\mathrm{sys}} + \Delta H_{\mathrm{sys}} \leq 0$$

This value is $\Delta G$.

For a constant volume process, you use the Helmholz free energy $\Delta F$ instead and just use internal energy change $\Delta U$ instead of $\Delta H$.

From this perspective, free energy is a convenient way to capture the total entropy change of the universe while only considering your system, but not surprisingly, there are assumptions you make in order for the magic to happen.

Neither enthalpy nor entropy alone can decide the spontaneity of a process.

For example, evaporation of water from oceans is an endothermic process $(\Delta H \gt 0)$, which clearly violates the fact that a system aims for minimum energy, yet this process is spontaneous (or naturally occurring).

To determine the spontaneity of a process the Gibbs-Hemholtz equation was introduced. This combines the effects of both enthalpy and entropy for determining the spontaneity of a process.

$\Delta G=\Delta H-T\Delta S$

A system generally aims for two things; minimum energy and maximum probability to be found in the universe (or more entropy). Therefore, for a spontaneous process, $\Delta H \lt 0$ and $\Delta S \gt 0$, Which gives an overall negative change is Gibbs energy.

For a spontaneous process, $\Delta G$ is negative.

• There is more to it. $\Delta G$ determines the spontaneity of processes at constant $T$ and $P$. Otherwise we have to use something else. – Ivan Neretin Feb 28 '17 at 18:31