Gibbs Free Energy and Equilibrium

Relationship Between Gibbs Free Energy and Equilibrium Constant

The Gibbs free energy is a thermodynamic quantity that determines the spontaneity of a chemical reaction. Its relationship with the equilibrium constant (Keq) is fundamental in chemical thermodynamics and equilibrium studies.

• Gibbs Free Energy Change (ΔG°): Indicates whether a reaction is spontaneous under standard conditions.

• Equilibrium Constant (Keq): Describes the ratio of product to reactant concentrations at equilibrium.

• The relationship is given by the formula:

• R: Universal gas constant (8.314 J/mol·K)

• T: Temperature in Kelvin

• Keq: Equilibrium constant

Example

A certain reaction takes place at 25°C and has an equilibrium constant of 2.1 × 104. Determine the Gibbs free energy of the reaction.

• Calculation steps:

• Convert temperature to Kelvin: 25°C + 273.15 = 298.15 K

• Plug values into the formula:

Result: -24.3 kJ/mol

Practice Problem

For the reaction Ag2CO3 (s) ⇌ 2Ag+ (aq) + CO32− (aq), ΔH° = 79.14 kJ/mol, ΔS° = 102.2 J/mol·K. Determine the equilibrium constant at the temperature 298.15 K.

• First, calculate ΔG° using:

• Then, use:

Result: 7.62

Gibbs Free Energy and Reaction Quotient (Q)

Relationship Between Gibbs Free Energy and Reaction Quotient

When a reaction is not at equilibrium, the reaction quotient (Q) is used instead of Keq. The Gibbs free energy change under non-standard conditions is given by:

• Q: Reaction quotient, calculated from current concentrations or partial pressures.

• ΔG: Gibbs free energy change under non-standard conditions.

Example

The given reaction has a ΔG° of -374 kJ, and partial pressures of SF6, SF4, S2F2 are 0.43 atm, 0.56 atm, 1.7 atm respectively. Calculate the ΔG for the reaction:

SF6 (g) ⇌ SF4 (g) + S2F2 (g)

• Calculate Q using partial pressures:

• Plug values into the formula for ΔG:

Result: -370.8 kJ

Practice Problem

Consider a hypothetical reaction at 35°C: X (aq) + 2 Y (aq) ⇌ Z (aq), with ΔG° = -3.2 kJ, and ΔG = -8.4 kJ. Concentrations of reactants and products: [X] = 1.1 M, [Y] = 0.34 M, [Z] = 0.54 M. Calculate Keq of the given reaction.

• First, calculate Q:

• Then, use the relationship between ΔG, ΔG°, and Q to solve for Keq:

Result: 87.4

Summary Table: Gibbs Free Energy Relationships

Additional info: These relationships are essential for understanding chemical equilibrium, spontaneity, and the effect of concentration or pressure changes on reaction direction.