Gibbs energy
Gibbs free energy combines enthalpy and entropy into one criterion for processes at constant temperature and pressure. The key distinction is between standard free energy, which belongs to a chosen reference state, and the actual ΔG, which depends on the current composition.
The criterion at constant temperature and pressure
G = H − TS
ΔG = ΔH − TΔS
If ΔG < 0, the process is thermodynamically favorable in the forward direction under those conditions. If ΔG > 0, the reverse direction is favored. At equilibrium, ΔG = 0 for an infinitesimal advance of the reaction.
“Favorable” does not mean “fast.” Thermodynamics sets direction; kinetics sets rate.
Four sign combinations
| ΔH | ΔS | Temperature effect |
|---|---|---|
| − | + | ΔG is negative at all T |
| + | − | ΔG is positive at all T |
| − | − | favored at sufficiently low T |
| + | + | favored at sufficiently high T |
This table is only as good as the assumption that ΔH and ΔS do not change much over the temperature range considered.
Composition enters through Q
For a reaction at nonstandard composition:
ΔG = ΔG° + RT ln Q
Q is the reaction quotient formed from activities raised to stoichiometric powers. If Q is small enough, the forward reaction can be favorable even when ΔG° is positive.
At equilibrium, ΔG = 0 and Q = K, giving ΔG° = −RT ln K. A large K corresponds to a negative standard free-energy change.
Maximum useful work and electrochemistry
At constant T and p, the decrease in Gibbs energy gives the maximum non-expansion work available from a reversible process. In an electrochemical cell:
ΔG = −nFE.
A positive cell potential therefore corresponds to negative ΔG for the cell reaction as written. Real devices deliver less useful work because they operate irreversibly and have internal losses.
Common interpretation errors
ΔG is not the energy “stored in bonds.” It is a state function for the whole system. A negative ΔG also does not imply that products go to 100% completion; it says the current composition can lower G by moving forward until equilibrium is reached.
Likewise, ΔG° = 0 means K = 1, not that every composition is at equilibrium.
Reading free energy quantitatively
Standard conditions are not the current conditions
ΔG° describes a reaction when reactants and products are in their standard states. A beaker rarely has that composition. The RT ln Q term corrects the standard value for the actual activities present at that moment.
This is why a reaction with positive ΔG° can still proceed forward if products are continually removed or reactants are supplied at sufficiently high activity. Thermodynamic direction belongs to the current state, not to the equation printed in a table.
Coupled reactions
Biochemical and industrial processes often become favorable by coupling an unfavorable step to a more favorable one. Because Gibbs energy is a state function, the ΔG values add. If the combined ΔG is negative, the coupled overall process can proceed spontaneously.
ATP hydrolysis is a familiar biochemical example, but the principle is general: coupling works only when the reactions share a mechanistic link so that one process actually drives the other.
Free energy and useful work
For a reversible process at constant T and p, −ΔG is the maximum non-expansion work. A battery approaching reversible operation can convert part of a chemical free-energy decrease into electrical work; a rapidly discharging real battery loses some of that potential as heat and overpotential.
Free energy therefore measures opportunity, not guaranteed performance. Kinetics, resistance, transport and irreversibility determine how much of that opportunity a real device captures.
Worked example: temperature threshold
Suppose ΔH = +40 kJ mol⁻¹ and ΔS = +120 J mol⁻¹ K⁻¹. Convert entropy to kJ: 0.120 kJ mol⁻¹ K⁻¹. Setting ΔG = 0 gives T = ΔH/ΔS = 40/0.120 ≈ 333 K.
Below about 333 K, ΔH dominates and ΔG is positive. Above it, the favorable TΔS term is larger. This threshold is approximate because ΔH and ΔS themselves vary somewhat with temperature.
Chemical potential: the local form of Gibbs energy
In a mixture, each component has a chemical potential μ: the change in G associated with adding a small amount of that component at fixed T, p and amounts of the others. Reaction direction can be expressed in terms of how the stoichiometric sum of chemical potentials changes as reaction advances.
This is the deeper reason activities appear in ΔG = ΔG° + RT ln Q. Changing concentration changes chemical potential, and chemical potential changes the thermodynamic driving force.
Phase equilibrium
At liquid–vapor equilibrium, the chemical potential of a substance is the same in both phases. If one phase had lower μ, matter would transfer into it. Boiling, melting and osmosis can therefore all be described with the same free-energy language.
Exercises
Temperature
A reaction has ΔH > 0 and ΔS > 0. When can it become favorable?
Solution
At sufficiently high temperature, where TΔS exceeds ΔH.
Equilibrium constant
If ΔG° is strongly negative, is K usually greater or less than 1?
Solution
Greater than 1, because ΔG° = −RT ln K.
Kinetics
Does ΔG < 0 guarantee an observable reaction rate?
Solution
No. A large activation barrier can make a thermodynamically favorable reaction extremely slow.