Spontaneous process

Commonly, the logic is inverted[3] and a (hypothetical or real) process with a predicted decrease of free energy at constant temperature is termed spontaneous. In that sense, the spontaneity of a process only determines whether or not a process can occur and makes no indication as to whether or not the process will occur. In other words, spontaneity is a necessary, but not sufficient, condition for a process to actually occur. Furthermore, spontaneity makes no implication as to the speed at which as spontaneous may occur. As an example, the conversion of a diamond into graphite is a spontaneous process at room temperature and pressure. Despite being spontaneous, this process does not occur since the energy to break the strong carbon-carbon bonds is larger than the release in free energy.

On the other hand, a process that is predicted to result in an increase in free energy at constant temperature and pressure (or volume) is forbidden under the conditions considered if there is no input of electrical energy.

For a process that occurs at constant temperature and pressure, spontaneity (according to the inverted logic) can be determined using the change in Gibbs free energy, which is given by:

$${\displaystyle \Delta G=\Delta H-T\Delta S\,,}$$

where the sign of ΔG depends on the signs of the changes in enthalpy (ΔH) and entropy (ΔS). The sign of ΔG will change from positive to negative (or vice versa) at the temperature given by T = ΔH/ΔS.

In cases where ΔG is:

• negative, the process is spontaneous and may proceed in the forward direction as written.
• positive, the process is non-spontaneous as written, but it may proceed spontaneously in the reverse direction.
• zero, the process is at equilibrium, with no net change taking place over time.

This set of rules can be used to determine four distinct cases by examining the signs of ΔS and ΔH.

• When ΔS > 0 and ΔH < 0, the exothermic process is spontaneous as written, at any temperature.
• When ΔS < 0 and ΔH > 0, the process is never spontaneous, but the reverse process is always spontaneous.
• When ΔS > 0 and ΔH > 0, the endothermic process will be spontaneous at high temperatures and non-spontaneous at low temperatures.
• When ΔS < 0 and ΔH < 0, the exothermic process will be spontaneous at low temperatures and non-spontaneous at high temperatures.

For the latter two cases, the temperature at which the spontaneity changes will be determined by the relative magnitudes of ΔS and ΔH.

When analyzing the entropy change of a process to assess spontaneity, it is important to carefully consider the definition of the system and surroundings. The second law of thermodynamics states that for a spontaneous process in an isolated system the entropy of the system increases over time. For open or closed systems, however, the statement must be modified to say that the total entropy of the combined system and surroundings must increase, or,

$${\displaystyle \Delta S_{\text{total}}=\Delta S_{\text{system}}+\Delta S_{\text{surroundings}}\geq 0\,.}$$

This criterion can then be used to explain how it is possible for the entropy of an open or closed system to decrease during a spontaneous process. A decrease in system entropy can only occur spontaneously if the entropy change of the surroundings is both positive in sign and has a larger magnitude than the entropy change of the system:

$${\displaystyle \Delta S_{\text{surroundings}}>\left|\Delta S_{\text{system}}\right|.}$$

For a closed system, the increase in entropy of the surroundings is accomplished via heat transfer from the system to the surroundings (i.e. the process is exothermic).

• Endergonic reaction reactions, which are not spontaneous at standard temperature, pressure, and concentrations.
• Diffusion, a spontaneous phenomenon that minimizes the Gibbs free energy.