For reactions carried out under standard-state conditions.

Chapter 18, Problem 66AP

(choose chapter or problem)

For reactions carried out under standard-state conditions, Equation 18.10 takes the form \(\Delta G^{\circ}=\Delta H^{\circ}-T \Delta S^{\circ}\).

(a) Assuming \(\Delta H^{\circ}\) and \(\Delta S^{\circ}\) are independent of temperature, derive the equation

\(\ln \frac{K_2}{K_1}=\frac{\Delta H^{\circ}}{R}\left(\frac{T_2-T_1}{T_1 T_2}\right)\)

where \(K_1\) and \(K_2\) are the equilibrium constants at \(T_1\) and \(T_2\), respectively. (b) Given that at \(25^{\circ} \mathrm{C} K_{\mathrm{c}}\) is \(4.63 \times 10^{-3}\) for the reaction

\(\mathrm{N}_2 \mathrm{O}_4(g) \rightleftarrows 2 \mathrm{NO}_2(g) \quad \Delta H^{\circ}=58.0 \mathrm{~kJ} / \mathrm{mol}\)

calculate the equilibrium constant at \(65^{\circ} \mathrm{C}\).