Chemical Equilibrium and Thermodynamics

Relationship Between Equilibrium Constant and Gibbs Free Energy

Chemical equilibrium is a fundamental concept in chemistry, describing the state where the concentrations of reactants and products remain constant over time. The equilibrium constant (K) and Gibbs free energy (G) are closely related and provide insight into the spontaneity and outcome of chemical reactions.

• Equilibrium Constant (K): Indicates the ratio of product to reactant concentrations at equilibrium. A large K favors products; a small K favors reactants.

• Gibbs Free Energy (G): Combines enthalpy and entropy to predict whether a reaction is spontaneous.

• Standard Gibbs Energy Change (ΔrG𝐎): The change in Gibbs energy under standard conditions.

• Relationship: The connection between ΔrG𝐎 and K is given by the equation:

• Where R is the gas constant (8.314 J mol–1 K–1), T is temperature in Kelvin, and K is the equilibrium constant.

• If ΔrG𝐎 is large and negative, K is large and products are favored.

• If ΔrG𝐎 is large and positive, K is small and reactants are favored.

Thermodynamic Quantities

Understanding enthalpy, entropy, and Gibbs free energy is essential for predicting reaction behavior.

• Enthalpy (H): The heat content of a system at constant pressure.

• Change in Enthalpy (ΔH): Difference in heat between products and reactants.

  • ΔH > 0: Endothermic (heat absorbed)

  • ΔH < 0: Exothermic (heat released)

• Standard Enthalpy of Reaction (ΔrH𝐎): Enthalpy change under standard conditions (most stable form, 1 bar, 1 mol L–1).

• Entropy (S): Measure of energy dispersal in a system; higher entropy means more possible microstates.

• Change in Entropy (ΔS): Difference in entropy between products and reactants.

• Gibbs Free Energy (G): Predicts spontaneity of a reaction:

• ΔG < 0: Spontaneous (exergonic)

• ΔG > 0: Nonspontaneous (endergonic)

Equilibrium and Phase Changes

Phase changes (e.g., melting, freezing) are governed by Gibbs free energy and equilibrium.

• At the melting point (0 °C for water), ΔG = 0 and equilibrium exists between solid and liquid phases.

• Below 0 °C, freezing is spontaneous (ΔG < 0 for H2O(l) → H2O(s)).

• Above 0 °C, melting is spontaneous (ΔG < 0 for H2O(s) → H2O(l)).

Response of Equilibrium Systems to Changes

Le Châtelier’s Principle

Le Châtelier’s principle states that a system at equilibrium will adjust to counteract any external change, seeking to restore equilibrium.

• Disturbance: Adding/removing reactants or products, changing pressure or temperature, or adding a catalyst.

• Reaction Quotient (Q): Used to predict direction of shift:

  • Q < K: Reaction shifts toward products.

  • Q > K: Reaction shifts toward reactants.

Effects of Concentration Changes

• Adding reactant or removing product: Q decreases, reaction shifts toward products.

• Removing reactant or adding product: Q increases, reaction shifts toward reactants.

Effects of Pressure Changes in Gaseous Reactions

• Changing Volume: Alters concentrations and Q.

  • Increase volume: Favors side with more moles of gas.

  • Decrease volume: Favors side with fewer moles of gas.

  • If moles are equal, no effect.

• Adding Inert Gas at Constant Volume: Increases total pressure but does not affect equilibrium position.

Effects of Temperature Changes

• Only temperature changes alter the equilibrium constant (K).

• For endothermic reactions (ΔrH > 0): Increasing temperature increases K, favoring products.

• For exothermic reactions (ΔrH < 0): Increasing temperature decreases K, favoring reactants.

Addition of a Catalyst

• Catalysts increase the rate at which equilibrium is reached but do not affect the equilibrium position or the value of K.

Summary Table: Effects on Chemical Equilibrium

Example Calculation

For a reaction with ΔrG𝐎 = –140 kJ mol–1 at 25 °C:

This large negative ΔrG𝐎 yields a large K, indicating products are strongly favored.

Additional info: The notes above expand on the brief points in the original material, providing definitions, equations, and context for each concept. The summary table is inferred from the text and standard chemistry knowledge.