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: a. standard conditions

Verified step by step guidance

1. Identify the given values: The equilibrium constant, Kp, is 81.9, and the temperature, T, is 25 °C (which is 298 K when converted to Kelvin).
2. Recall the relationship between the Gibbs free energy change (ΔG) and the equilibrium constant (K) at a given temperature (T) using the formula: ΔG = -RT ln(K), where R is the gas constant (8.314 J/mol·K).
3. Convert the temperature from Celsius to Kelvin by adding 273.15 to the Celsius temperature.
4. Substitute the values of R, T, and K into the formula to calculate ΔG under standard conditions.
5. Since the reaction is at standard conditions, the partial pressures of the reactants and products are 1 atm, and thus the reaction quotient, Q, equals 1. This simplifies the calculation as ln(1) equals 0, which directly gives ΔG = -RT ln(K).

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 a crucial concept in 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 = -RT ln(K), where R is the universal gas constant and T is the temperature in Kelvin.

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 standard conditions. This constant is essential for calculating ΔG under different conditions.

Standard Conditions

Standard conditions refer to a set of specific parameters used to measure and compare thermodynamic properties, typically defined as 1 bar of pressure and a specified temperature, usually 25 °C (298 K). Under these conditions, the standard Gibbs free energy change (ΔG°) can be calculated using the equilibrium constant (Kp) and is essential for determining the spontaneity of reactions. Understanding standard conditions is vital for accurately calculating ΔG for reactions in a consistent manner.