Spontaneous process

Using free energy to determine spontaneity

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

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

where the sign of ΔG depends on the signs of the changes in enthalpy (ΔH) and entropy (ΔS). If these two signs are the same (both positive or both negative), then the sign of ΔG will change from positive to negative (or vice-versa) at the temperature 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 the ΔS and ΔH.

• When ΔS > 0 and ΔH < 0, the process is always spontaneous as written.
• 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 process will be spontaneous at high temperatures and non-spontaneous at low temperatures.
• When ΔS < 0 and ΔH < 0, the 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.

Using entropy to determine spontaneity

When using 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 a process involving an isolated system will be spontaneous if 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, $${\displaystyle \mathrm{\Delta }{S}_{\text{total}}=\mathrm{\Delta }{S}_{\text{system}}+\mathrm{\Delta }{S}_{\text{surroundings}}\ge 0.}$$

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: $${\displaystyle \mathrm{\Delta }{S}_{\text{surroundings}}>0}$$ and $${\displaystyle \left|\mathrm{\Delta }{S}_{\text{surroundings}}\right|>\left|\mathrm{\Delta }{S}_{\text{system}}\right|}$$

In many processes, the increase in entropy of the surroundings is accomplished via heat transfer from the system to the surroundings (i.e. an exothermic process).