Gibbs Free Energy (G) | Thermodynamics Class 11

Gibbs Free Energy ($\Delta G$)

Predicting Spontaneity & Useful Work | Thermodynamics

1. Definition & Significance

Gibbs Free Energy ($G$) is a thermodynamic state function defined as the maximum amount of energy available to do useful work (non-expansion work) by a system.

$$ G = H - TS $$

Change in Gibbs Energy at constant temperature:

$$ \Delta G = \Delta H - T \Delta S $$

Physical Significance:

• $-\Delta G = w_{useful}$ (Maximum useful work obtainable).
• It combines the effects of Enthalpy ($\Delta H$, energy factor) and Entropy ($\Delta S$, randomness factor).

2. Criteria for Spontaneity

At constant temperature and pressure, the sign of $\Delta G$ determines the direction of a reaction.

• $\Delta G < 0$ (Negative): The process is Spontaneous (Feasible).
• $\Delta G > 0$ (Positive): The process is Non-Spontaneous (Reverse is spontaneous).
• $\Delta G = 0$ (Zero): The system is at Equilibrium.

3. Effect of Temperature on Spontaneity

Based on $\Delta G = \Delta H - T \Delta S$, four cases arise:

$\Delta H$ (Enthalpy)	$\Delta S$ (Entropy)	$\Delta G$	Conclusion
Negative (Exo)	Positive (Disorder $\uparrow$)	Always Negative	Spontaneous at All Temperatures
Positive (Endo)	Negative (Disorder $\downarrow$)	Always Positive	Non-Spontaneous at All Temperatures
Negative (Exo)	Negative (Disorder $\downarrow$)	-ve at Low T +ve at High T	Spontaneous only at Low Temperatures
Positive (Endo)	Positive (Disorder $\uparrow$)	+ve at Low T -ve at High T	Spontaneous only at High Temperatures

4. Standard Gibbs Energy & Equilibrium Constant

For a reversible reaction, standard free energy change ($\Delta G^\circ$) is related to the equilibrium constant ($K_{eq}$ or $K_c$).

$$ \Delta G^\circ = -RT \ln K_{eq} $$ $$ \Delta G^\circ = -2.303 RT \log K_{eq} $$

• If $K > 1$, then $\Delta G^\circ < 0$ (Products favored).
• If $K < 1$, then $\Delta G^\circ > 0$ (Reactants favored).

5. Relation with Electrical Work

In electrochemistry, electrical work done by a cell is equal to the decrease in Gibbs Free Energy.

$$ \Delta G^\circ = -nFE^\circ_{cell} $$

Where $n$ is moles of electrons, $F$ is Faraday constant, and $E^\circ$ is standard cell potential.

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