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: c. P_ICl = 2.55 atm; P_I2 = 0.325 atm; P_Cl2 = 0.221 atm

Verified step by step guidance

1. Identify the relationship between the equilibrium constant \( K_p \) and the Gibbs free energy change \( \Delta G^\circ \) using the equation \( \Delta G^\circ = -RT \ln K_p \), where \( R \) is the ideal gas constant (8.314 J/mol·K) and \( T \) is the temperature in Kelvin.
2. Convert the temperature from Celsius to Kelvin by adding 273.15 to the given temperature in Celsius (25 °C).
3. Calculate \( \Delta G^\circ \) using the equation from step 1 with the given \( K_p \) value.
4. Use the reaction quotient \( Q_p \) to determine the Gibbs free energy change under non-standard conditions using the equation \( \Delta G = \Delta G^\circ + RT \ln Q_p \).
5. Calculate \( Q_p \) using the partial pressures: \( Q_p = \frac{(P_{\text{ICl}})^2}{P_{\text{I}_2} \cdot P_{\text{Cl}_2}} \), and then substitute \( Q_p \) into the equation from step 4 to find \( \Delta G \).

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 is crucial for predicting the spontaneity of a reaction; a negative ΔG indicates a spontaneous process, while a positive ΔG suggests non-spontaneity. The relationship between ΔG and the equilibrium constant (K) is given by the equation ΔG = ΔG° + RT ln(Q), where Q is the reaction quotient.

Reaction Quotient (Q)

The reaction quotient (Q) is a measure of the relative concentrations of products and reactants at any point in a reaction. It is calculated using the same expression as the equilibrium constant (K), but with the current partial pressures or concentrations. Comparing Q to K helps determine the direction in which a reaction will proceed to reach equilibrium: if Q < K, the reaction shifts to the right (toward products), and if Q > K, it shifts to the left (toward reactants).

Equilibrium Constant (Kp)

The equilibrium constant (Kp) is a dimensionless number that expresses the ratio of the partial pressures 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 products are favored over the reactants. This constant is temperature-dependent and provides insight into the extent of the reaction under specified conditions.