Criteria for Equilibrium — Revision Notes

⚡ 30-Second Revision

Equilibrium (Constant T, P): — $\Delta G = 0$
Equilibrium (Constant T, V): — $\Delta A = 0$
Equilibrium (Isolated System): — $\Delta S_{system} = 0$ (at maximum entropy)
Spontaneity (Constant T, P): — $\Delta G < 0$
Spontaneity (Isolated System): — $\Delta S_{system} > 0$
Gibbs Free Energy Equation: — $\Delta G = \Delta H - TDelta S$
Equilibrium Temperature: — $T_{eq} = \frac{\Delta H}{\Delta S}$ (when $\Delta G = 0$)
Relationship with K: — $\Delta G^\circ = -RT \ln K$

2-Minute Revision

Equilibrium is a dynamic state where forward and reverse process rates are equal, leading to no net change in macroscopic properties. The key thermodynamic criteria depend on the system's conditions. For most chemical reactions at constant temperature and pressure, equilibrium is achieved when the Gibbs free energy change ($\Delta G$) is zero, signifying the system is at its minimum Gibbs free energy.

If $\Delta G < 0$, the process is spontaneous, moving towards equilibrium. For systems at constant temperature and volume, the Helmholtz free energy change ($\Delta A$) is zero at equilibrium. In an isolated system, equilibrium corresponds to the maximum entropy of the system, meaning $\Delta S_{system} = 0$.

Remember that $\Delta G^\circ$ (standard Gibbs free energy change) is related to the equilibrium constant (K) by $\Delta G^\circ = -RT \ln K$, which tells us about the extent of the reaction at equilibrium, not the $\Delta G$ at equilibrium itself (which is always zero).

For numerical problems, the equilibrium temperature can be found using $T_{eq} = \frac{\Delta H}{\Delta S}$, ensuring consistent units.

5-Minute Revision

Understanding the criteria for equilibrium is fundamental to chemical thermodynamics. Equilibrium is a dynamic state where opposing processes occur at equal rates, resulting in no net change in observable properties. It's crucial not to confuse this with a static state where all activity has ceased. The specific thermodynamic criterion for equilibrium depends on the conditions under which the system operates:

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Constant Temperature and Pressure (most common): — The system is at equilibrium when the Gibbs free energy change ($\Delta G$) is zero. This means the system has reached its minimum Gibbs free energy. If $\Delta G < 0$, the process is spontaneous (moves towards equilibrium); if $\Delta G > 0$, it's non-spontaneous (the reverse process is spontaneous).

* Equation: $\Delta G = \Delta H - TDelta S$. At equilibrium, $0 = \Delta H - T_{eq}\Delta S$, so $T_{eq} = \frac{\Delta H}{\Delta S}$. * Example: Water at $0^\circ\text{C}$ and $1\,\text{atm}$ (melting point) is in equilibrium, so $\Delta G = 0$ for $H_2O(s) \rightleftharpoons H_2O(l)$.

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Constant Temperature and Volume: — The system is at equilibrium when the Helmholtz free energy change ($\Delta A$) is zero. This means the system is at its minimum Helmholtz free energy.

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Isolated System: — The system is at equilibrium when its entropy ($S_{system}$) is at a maximum. For any infinitesimal change at equilibrium, $\Delta S_{system} = 0$.

Key Relationships:

$\Delta G^\circ$ and K: — The standard Gibbs free energy change ($\Delta G^\circ$) is related to the equilibrium constant (K) by $\Delta G^\circ = -RT \ln K$. A large positive $\Delta G^\circ$ means $K \ll 1$ (reactants favored), while a large negative $\Delta G^\circ$ means $K \gg 1$ (products favored). Remember, $\Delta G^\circ$ is for standard conditions, while $\Delta G$ is for actual conditions and is zero at equilibrium.

Common Pitfalls:

Confusing $\Delta G < 0$ (spontaneity) with $\Delta G = 0$ (equilibrium).
Forgetting to convert units (e.g., kJ to J) when calculating $T_{eq}$.
Assuming concentrations of reactants and products are equal at equilibrium; they are constant, but their ratio is determined by K.

Focus on understanding these criteria and their applications, especially for phase transitions and chemical reactions.

Prelims Revision Notes

Equilibrium Definition: — Dynamic state where forward rate = reverse rate; no net change in macroscopic properties.
Thermodynamic Criteria for Equilibrium:

- Constant Temperature (T) & Pressure (P): $\Delta G = 0$ (Gibbs free energy is at a minimum). - Constant Temperature (T) & Volume (V): $\Delta A = 0$ (Helmholtz free energy is at a minimum). - Isolated System: $\Delta S_{system} = 0$ (Entropy of the system is at a maximum).

Spontaneity vs. Equilibrium:

- Spontaneous: $\Delta G < 0$ (constant T, P); $\Delta S_{universe} > 0$. Drives towards equilibrium. - Equilibrium: $\Delta G = 0$ (constant T, P); $\Delta S_{universe} = 0$. The state where spontaneity ceases.

Gibbs Free Energy Equation: — $\Delta G = \Delta H - TDelta S$.

- At equilibrium, $\Delta H = T_{eq}\Delta S \implies T_{eq} = \frac{\Delta H}{\Delta S}$. - Crucial: Ensure $\Delta H$ and $\Delta S$ units are consistent (e.g., both in J or kJ) for calculations.

Relationship with Equilibrium Constant (K):

- $\Delta G^\circ = -RT \ln K$. - If $\Delta G^\circ < 0 \implies K > 1$ (products favored at equilibrium). - If $\Delta G^\circ > 0 \implies K < 1$ (reactants favored at equilibrium). - If $\Delta G^\circ = 0 \implies K = 1$ (reactants and products roughly equal at equilibrium).

Phase Transitions: — At the normal melting point, boiling point, or sublimation point, the two phases are in equilibrium, so $\Delta G = 0$ at that specific temperature and pressure.
Common Misconceptions:

- Equilibrium is dynamic, not static (reactions continue). - Concentrations are constant, not necessarily equal, at equilibrium. - $\Delta G = 0$ is for actual conditions at equilibrium, while $\Delta G^\circ$ is for standard conditions and relates to K.

Vyyuha Quick Recall

GET A S.I.T.E. for Equilibrium!

Gibbs = 0 for Equilibrium at constant Temperature, Pressure. A = 0 for constant Temperature, Volume. System Isolated: $\Delta S_{system}$ is Top (maximum), so $\Delta S_{system}$ Equals 0.