Gibbs Energy Change and Equilibrium

NCERT Reference: Chapter 5 – Thermodynamics – Page 147 onward

Quick Notes

G = H − T·S
ΔG = ΔH − T·ΔS

ΔG < 0 → Spontaneous
ΔG = 0 → System at Equilibrium
ΔG > 0 → Non-Spontaneous

At equilibrium, ΔG = 0 and Δ_rG° = −RT ln K
For calculations in base 10 logs: Δ_rG° = −2.303 RT log K
At equilibrium: ΔG = ΔH − TΔS = −RT ln K

Full Notes

How is ΔG related to equilibrium?

Gibbs free energy (ΔG) is calculated using:

NCERT 11 Chemistry equation card showing ΔG equals ΔH minus TΔS for Gibbs free energy change.

At equilibrium, ΔG = 0, because there's no net change in the system. The rates of the forward and reverse reactions are equal, so there’s no further driving force in either direction – this state is only possible when ΔG = 0.

As a reaction proceeds, ΔG becomes less negative or less positive, gradually approaching zero.

Understanding the link between ΔG and equilibrium:

Chemical reactions naturally move toward more stable states — in thermodynamic terms, this means lower Gibbs free energy.
As the reaction progresses and the concentrations of reactants and products change, ΔG changes too:
- When the system is far from equilibrium, ΔG is large (positive or negative).
- The reaction proceeds in the direction that reduces ΔG.
- Over time, ΔG decreases until it reaches zero — the system reaches equilibrium.

At Equilibrium:

Forward and reverse reaction rates are equal.
Free energy is at its lowest possible value.
ΔG = 0 meaning there is no net driving force.

This is why equilibrium is established: the system has reached its most energetically favorable position.

If the system is not at equilibrium, then ΔG ≠ 0, and the reaction will shift to reduce ΔG.

Gibbs Energy and Equilibrium Constant

For a general reaction: aA + bB ⇌ cC + dD

The reaction Gibbs energy is given by:

NCERT 11 Chemistry expression for reaction Gibbs energy ΔrG equals ΔrG° plus RT ln Q relating free energy to the reaction quotient.

(This equation tells us how the Gibbs free energy of a reaction (Δ_rG) changes depending on the actual conditions (like concentrations or pressures) compared to standard conditions.)

At equilibrium: Q = K and Δ_rG = 0, so:

0 = Δ_rG° + RT ln K ⇒ Δ_rG° = −RT ln K

If using base 10 logs (common in data tables): Δ_rG° = −2.303 RT log K

This relationship allows us to calculate the equilibrium constant (K) from Δ_rG° and predict how favorable a reaction is:

Large K means Δ_rG° is large and negative = spontaneous
Small K means Δ_rG° is positive = not spontaneous

Unified Equation: ΔG and Equilibrium

You can now write:

NCERT 11 Chemistry unified relation showing ΔG equals ΔH minus TΔS and equals −RT ln K at equilibrium linking thermodynamics and equilibrium constant.

(Equation 5.24)

This equation shows how thermodynamics (ΔH, ΔS), temperature (T) and chemical equilibrium (K) are all related by a single, unified expression.

Summary

ΔG links enthalpy and entropy to predict direction of change.
Equilibrium occurs when ΔG equals zero.
Δ_rG° relates to K via −RT ln K.
Base 10 form uses −2.303 RT log K.