- Gibbs free energy is defined as G=H-TS.
- When temperature and pressure are constant, ΔG is directly proportional to ΔSuniv and can thus be used to predict spontaneity.
The 2nd Law of Thermodynamics can predict whether a reaction or process is spontaneous (ΔSuniv>0), at equilibrium (ΔSuniv=0) or not spontaneous (ΔSuniv<0). However, using the 2nd Law of Thermodynamics to make a prediction requires measurements of the entropy change for both the system and the surroundings (a challenging feat!). Defining Gibbs free energy will allow us to predict a reaction's spontaneity using measurements of the system only.
Gibbs free energy, G, is defined as:
where is the enthalpy of the system,
is the temperature of the system, and
is the entropy of the system. The change in Gibbs free energy is given by
and, under the common conditions of constant temperature, by
Gibbs free energy is defined in this way precisely so that at constant temperature and pressure (common reaction conditions), is directly proportional to ΔSuniv via
and thus can be used to predict the spontaneity of a reaction.
To understand why the relationship in Equation 2 is true, and why the conditions of constant temperature and constant pressure are necessary in order for this equation to hold, consider the derivation below:
First, since , ΔG relates to ΔSsurr and ΔSsys via
By comparison to Equation 1, we can see that the rightmost term in Equation 3 (-TΔSsys) already corresponds to the rightmost term in Equation 1 at constant temperature. It must be, then, that -TΔSsurr relates to ΔH.
Under conditions of constant temperature, ΔSsurr is given by
See Part 1 Section 3.2 to review this formula. Any heat that flows into the surroundings must come from the system, such that
At constant pressure, the heat flow from the system, qsys, is equal to ΔH and thus (at constant T and P)
Plugging this new term into Equation 3 gives
That is, we've proven that Equation 3 and Equation 1 are equivalent, and thus that
Complete the activity below to explore how the sign of ΔG relates to the spontaneity of a process or reaction.
Interactive:
Explanation (try yourself before you check the explanation!):
Below its boiling point, methanol gas will spontaneous condense to methanol liquid. Thus, we know that Δ G<0 for this process at this temperature.
In order to turn a liquid into a gas, we must add energy (e.g. as heat) to break the intermolecular bonds. Thus, phase changes in the direction from solid to liquid to gas are endothermic. The opposite direction (e.g. the condensation here) releases heat when intermolecular bonds form. Phase changes in the direction gas to liquid to solid are exothermic. Thus, here Δ H<0.
As a gas becomes a liquid, the entropy of the system (the methanol) decreases. Thus, ΔSsys<0.
The entropy of the surroundings is related to the enthalpy change at constant pressure and temperature by . Since here Δ H<0, it must be that ΔSsurr>0.