Gibbs Free Energy & Spontaneity
Discover the ultimate criteria for spontaneous reactions. Master the Gibbs-Helmholtz equation, the Spontaneity Matrix, and predict equilibrium shifts effortlessly.
Module Focus
According to the Second Law of Thermodynamics, a reaction is spontaneous if the entropy of the universe increases ($\Delta S_{\text{universe}} > 0$). However, calculating the entropy change of the entire universe is practically impossible. Gibbs Free Energy ($G$) solves this problem by allowing us to predict spontaneity using only the properties of the system.
1. Gibbs Free Energy ($G$)
Gibbs Free Energy is a thermodynamic state function defined as $G = H - TS$. For a process occurring at constant temperature and pressure, the change in free energy is given by the famous Gibbs-Helmholtz equation.
Criteria for Spontaneity (at Constant T, P)
- If $\mathbf{\Delta G < 0}$ (Negative): The process is Spontaneous (exergonic).
- If $\mathbf{\Delta G = 0}$ (Zero): The process is at Equilibrium (reversible).
- If $\mathbf{\Delta G > 0}$ (Positive): The process is Non-spontaneous (endergonic). It will be spontaneous in the reverse direction.
The decrease in Gibbs Free Energy ($-\Delta G$) represents the maximum amount of useful work (non-expansion work) that can be extracted from a closed system operating at constant T and P.
Example: Electrical work done by a galvanic cell ($-\Delta G = nFE_{cell}$).
2. The Spontaneity Matrix (Temperature Dependence)
Because $\Delta G = \Delta H - T\Delta S$, the spontaneity of a reaction depends on the signs of Enthalpy change ($\Delta H$) and Entropy change ($\Delta S$), and often the Temperature ($T$).
| $\Delta H$ | $\Delta S$ | $-T\Delta S$ Term | $\Delta G$ | Result |
|---|---|---|---|---|
| $(-)$ Exothermic | $(+)$ Disorder $\uparrow$ | $(-)$ | Always $(-)$ | Spontaneous at all $T$ |
| $(+)$ Endothermic | $(-)$ Disorder $\downarrow$ | $(+)$ | Always $(+)$ | Non-spontaneous at all $T$ |
| $(-)$ Exothermic | $(-)$ Disorder $\downarrow$ | $(+)$ | $(-)$ at Low $T$ | Spontaneous ONLY at Low $T$ (Enthalpy Driven) |
| $(+)$ Endothermic | $(+)$ Disorder $\uparrow$ | $(-)$ | $(-)$ at High $T$ | Spontaneous ONLY at High $T$ (Entropy Driven) |
Examiners will ask: "Above what temperature does the reaction become spontaneous?"
Solution: Set $\Delta G = 0$ (the equilibrium point).
In questions, $\Delta H$ is almost always given in Kilojoules (kJ), while $\Delta S$ is given in Joules (J). You MUST convert $\Delta H$ to Joules (multiply by 1000) before dividing, or your temperature will be off by a factor of 1000!
3. Standard Gibbs Energy & Equilibrium Constant
The Free Energy change of a reaction under non-standard conditions ($\Delta G$) is related to the Standard Free Energy change ($\Delta G^\circ$) and the reaction quotient ($Q$).
At Thermodynamic Equilibrium:
The reaction can do no more work, so $\mathbf{\Delta G = 0}$ (Note: $\Delta G^\circ$ is NOT zero). Also, the reaction quotient $Q$ becomes the equilibrium constant $\mathbf{K_{eq}}$.
$\mathbf{\Delta G^\circ = -RT \ln K_{eq}} \quad \text{or} \quad \mathbf{\Delta G^\circ = -2.303 RT \log_{10} K_{eq}}$
Relation Between $\Delta G^\circ$ and $K_{eq}$:
- If $\mathbf{\Delta G^\circ < 0}$: Then $\ln K_{eq}$ is positive, meaning $\mathbf{K_{eq} > 1}$. The reaction is spontaneous in the forward direction, and products are favored at equilibrium.
- If $\mathbf{\Delta G^\circ > 0}$: Then $\ln K_{eq}$ is negative, meaning $\mathbf{K_{eq} < 1}$. The reaction is non-spontaneous in the forward direction, and reactants are heavily favored.
- If $\mathbf{\Delta G^\circ = 0}$: Then $\mathbf{K_{eq} = 1}$. Both reactants and products are equally favored.
NEET Grand Test: Free Energy
15 High-Order Thinking Questions testing temperature cutoffs, unit traps, and spontaneity logic.
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