Use data from Appendix IIB to calculate the equilibrium constants at 25 °C for each reaction. ΔG°f for BrCl(g) is -1.0 kJ/mol. a. 2 NO2(g) ⇌ N2O4(g) b. Br2(g) + Cl2(g) ⇌ 2 BrCl(g)

Verified step by step guidance

1. Identify the relationship between the standard Gibbs free energy change (\( \Delta G^\circ \)) and the equilibrium constant (\( K \)) using the equation: \( \Delta G^\circ = -RT \ln K \), where \( R \) is the 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 (25 °C).
3. For reaction (a), use Appendix IIB to find the \( \Delta G^\circ_f \) values for \( \text{NO}_2(g) \) and \( \text{N}_2\text{O}_4(g) \). Calculate \( \Delta G^\circ \) for the reaction using the formula: \( \Delta G^\circ = \sum \Delta G^\circ_f(\text{products}) - \sum \Delta G^\circ_f(\text{reactants}) \).
4. For reaction (b), use the given \( \Delta G^\circ_f \) for \( \text{BrCl(g)} \) and find \( \Delta G^\circ_f \) values for \( \text{Br}_2(g) \) and \( \text{Cl}_2(g) \) from Appendix IIB. Calculate \( \Delta G^\circ \) for the reaction using the same formula as in step 3.
5. Solve for the equilibrium constant \( K \) for each reaction by rearranging the equation from step 1 to \( K = e^{-\Delta G^\circ / RT} \) and substituting the calculated \( \Delta G^\circ \) values.

Key Concepts

Gibbs Free Energy and Equilibrium

Gibbs Free Energy (ΔG) is a thermodynamic potential that helps predict the direction of chemical reactions. At equilibrium, ΔG is zero, indicating that the forward and reverse reactions occur at the same rate. The relationship between ΔG and the equilibrium constant (K) is given by the equation ΔG° = -RT ln(K), where R is the gas constant and T is the temperature in Kelvin.

Equilibrium Constant (K)

The equilibrium constant (K) quantifies the ratio of the concentrations of products to reactants at equilibrium for a given reaction. It is temperature-dependent and can be calculated using the formula K = [products]^[coefficients] / [reactants]^[coefficients]. A larger K value indicates a greater concentration of products at equilibrium, while a smaller K suggests a preference for reactants.

Standard Gibbs Free Energy of Formation (ΔG°f)

The standard Gibbs Free Energy of formation (ΔG°f) is the change in Gibbs Free Energy when one mole of a compound is formed from its elements in their standard states. It is a crucial value for calculating the ΔG of a reaction and, consequently, the equilibrium constant. In this question, the ΔG°f for BrCl(g) is provided, which will be used to determine the equilibrium constant for the reaction involving Br2 and Cl2.