List three different ways to calculate the standard free energy change, \(\Delta G^{\circ}\), for a reaction at \(25^{\circ} \mathrm{C}\). How is \(\Delta G^{\circ}\) estimated at temperatures other than \(25^{\circ} \mathrm{C}\) ? What assumptions are made?

There are three ways to calculate ΔG° for a reaction at $25^{\circ}\mathrm{C}$: 1) Using the standard enthalpy change (ΔH°) and the standard entropy change (ΔS°) with the equation \( \Delta G^\circ = \Delta H^\circ - T\Delta S^\circ \); 2) Using the equilibrium constant (K) with the equation \( \Delta G^\circ = -RT \ln K \); 3) For redox reactions, using the standard electrode potential (E°) with the equation \( \Delta G^\circ = -nFE^\circ \). To estimate ΔG° at temperatures other than $25^{\circ}\mathrm{C}$, the van't Hoff equation \( \frac{\Delta G_2^\circ - \Delta G_1^\circ}{T_2 - T_1} = -\frac{\Delta H^\circ}{R}(\frac{1}{T_2} - \frac{1}{T_1}) \) can be used. The assumptions made are: 1) Standard state conditions are considered; 2) ΔH° and ΔS° are temperature-independent or their temperature-dependence is negligible; 3) The van't Hoff equation assumes ΔH° is constant over the temperature range considered.