Question

Describe two ways that you could measure \(\Delta G^{\circ}\) of a reaction.

Short answer

\(\Delta G^{\circ}\) of a reaction can be measured by two primary means: 1) Direct measurement of equilibrium constants. The standard Gibbs free energy change is related to the equilibrium constant of the reaction by the equation \(\Delta G^{\circ} = -RT \ln K\). 2) Indirect determination through measurement of enthalpy and entropy changes. This is described by the equation \(\Delta G^{\circ} = \Delta H^{\circ} - T \Delta S^{\circ}\).

Step-by-step solution

Method 1: Using Equilibrium Constants

Given a chemical reaction in equilibrium, the equilibrium constant (K) can be directly measured under standard conditions. According to the Gibbs free energy equation, \(\Delta G^{\circ} = -RT \ln K\), where R is the universal gas constant, T is the absolute temperature, and K is the equilibrium constant. Therefore, measure the equilibrium constant of the reaction, substitute it into the equation along with the known values of R and T, and solve for \(\Delta G^{\circ}\).

Method 2: Determination of \(\Delta H^{\circ}\) and \(\Delta S^{\circ}\)

For chemical reactions where direct measurement of the equilibrium constant is not feasible, \(\Delta G^{\circ}\) can be determined by indirectly measuring the enthalpy change (\(\Delta H^{\circ}\)) and the entropy change (\(\Delta S^{\circ}\)). The relationship between these quantities is given by \(\Delta G^{\circ} = \Delta H^{\circ} - T \Delta S^{\circ}\). You measure \(\Delta H^{\circ}\) and \(\Delta S^{\circ}\) for the reaction, substitute them into the equation along with the absolute temperature T, and solve for \(\Delta G^{\circ}\).