Editing Spontaneous process (section)

==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:

<math display="block">\Delta G = \Delta H - T \Delta S \,,</math>

where the sign of Δ''G'' depends on the signs of the changes in [[enthalpy]] (Δ''H'') and [[entropy]] (Δ''S''). If these two signs are the same (both positive or both negative), then the sign of Δ''G'' will change from positive to negative (or vice versa) at the temperature {{nowrap|1=''T'' = Δ''H''/Δ''S''.}}

In cases where Δ''G'' 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 Δ''S'' and Δ''H''.
* When Δ''S'' > 0 and Δ''H'' < 0, the process is always spontaneous as written.
* When Δ''S'' < 0 and Δ''H'' > 0, the process is never spontaneous, but the reverse process is always spontaneous.
* When Δ''S'' > 0 and Δ''H'' > 0, the process will be spontaneous at high temperatures and non-spontaneous at low temperatures. 
* When Δ''S'' < 0 and Δ''H'' < 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 Δ''S'' and Δ''H''.