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)

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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.