Physical chemistry

Free energy and equilibrium

At constant temperature and pressure, Gibbs free energy determines spontaneity; equilibrium corresponds to a minimum of G subject to composition constraints.

For a change at fixed T,P, $\Delta G<0$ indicates a spontaneous forward direction, $\Delta G>0$ the reverse direction, and $\Delta G=0$ equilibrium.

Model and quantities

Read the relation together with assumptions about state, experimental conditions, and sign conventions. Keep units consistent and check dimensions before interpreting a result.

\Delta G = \Delta H - T\Delta S, \qquad \Delta_r G = \Delta_r G^\circ + RT\ln Q

Definition: Gibbs free energy

G=H−TS is the thermodynamic potential useful for isothermal, isobaric processes. $\Delta H$ reflects energy change, while $T\Delta S$ captures the entropy contribution at temperature T.

Quantities in the relation are defined for the reaction or system at hand. In particular, distinguish standard-state quantities from actual conditions and do not infer a mechanism from a general expression alone.

Example: Worked example

A process has $\Delta H=20$ kJ/mol and $\Delta S=100$ J/(mol·K) at 300 K. Find $\Delta G$ .

Solution

Convert entropy to 0.100 kJ/(mol·K): $\Delta G=20-300(0.100)=-10$ kJ/mol. The negative value indicates the process is favorable under these conditions.

Concept summary
Concept	Description	Unit / note
Key relation	Use under stated conditions	Check units and sign convention
Measured quantity	Relates a state or process	Compare data with model
Scope	Model specific conditions	Check assumptions first

At chemical equilibrium, $\Delta_rG=0$ and $Q=K$ . For a pure substance changing phase, the chemical potentials of the two phases are equal; this underlies phase diagrams.

In the worked example, which result follows from the given data?

Which statement is consistent with this lesson?

References

Peter Atkins, Julio de Paula (2014). Physical Chemistry