Consider the reaction: I₂(g) + Cl₂(g) ⇌ 2 ICl(g) K_p = 81.9 at 25 °C Calculate ΔG_rxn for the reaction at 25 °C under each of the following conditions: b. at equilibrium

Verified step by step guidance

1. Identify the relationship between the equilibrium constant \( K_p \) and the standard Gibbs free energy change \( \Delta G^\circ_{\text{rxn}} \) using the equation: \( \Delta G^\circ_{\text{rxn}} = -RT \ln K_p \).
2. Recognize that at equilibrium, the Gibbs free energy change \( \Delta G_{\text{rxn}} \) is zero because the system is at its lowest energy state.
3. Use the given equilibrium constant \( K_p = 81.9 \) and the temperature \( T = 25^\circ C \) (which is 298 K) to calculate \( \Delta G^\circ_{\text{rxn}} \).
4. Substitute the values into the equation: \( \Delta G^\circ_{\text{rxn}} = - (8.314 \text{ J/mol K}) \times (298 \text{ K}) \times \ln(81.9) \).
5. Since \( \Delta G_{\text{rxn}} = 0 \) at equilibrium, the calculated \( \Delta G^\circ_{\text{rxn}} \) confirms the reaction's spontaneity under standard conditions.

Key Concepts

Gibbs Free Energy (ΔG)

Gibbs Free Energy (ΔG) is a thermodynamic potential that measures the maximum reversible work obtainable from a thermodynamic system at constant temperature and pressure. It indicates the spontaneity of a reaction; a negative ΔG suggests that a reaction can occur spontaneously, while a positive ΔG indicates non-spontaneity. At equilibrium, ΔG is equal to zero, meaning the forward and reverse reactions occur at the same rate.

Equilibrium Constant (Kp)

The equilibrium constant (Kp) is a dimensionless number that expresses the ratio of the concentrations of products to reactants at equilibrium for a given reaction at a specific temperature. For the reaction I2(g) + Cl2(g) ⇌ 2 ICl(g), Kp = 81.9 indicates that at equilibrium, the concentration of ICl is significantly higher than that of I2 and Cl2, suggesting that the formation of ICl is favored under the given conditions.

Relationship between ΔG and Kp

The relationship between Gibbs Free Energy (ΔG) and the equilibrium constant (Kp) is given by the equation ΔG = ΔG° + RT ln(Q), where Q is the reaction quotient. At equilibrium, Q equals Kp, and ΔG becomes zero. This relationship allows us to calculate the standard Gibbs Free Energy change (ΔG°) for a reaction using the equilibrium constant, providing insight into the favorability of the reaction under standard conditions.