AP Chemistry
9.9 Cell Potential and Free Energy
9.5 Free Energy and Equilibrium
9.3 Gibbs Free Energy and Thermodynamic Favorability
A student studying the relationship between electrical work, standard free energy, and chemical equilibrium compiles the data in the table below for three redox reactions carried out at \(298\text{ K}\).
Which of the following best explains why Reaction 2 is more thermodynamically favorable under standard conditions and has a larger equilibrium constant than Reaction 1, even though \(E^\circ\) for Reaction 2 is smaller?
| Reaction | Balanced equation | \(n\) | \(E^\circ\text{ (V)}\) | \(\Delta G^\circ\text{ (kJ/mol}_{\text{rxn}}\text{)}\) | \(K\text{ at } 298\text{ K}\) |
|---|---|---|---|---|---|
| 1 | \(\text{X}^{2+}\text{(aq)} + \text{Y(s)} \rightarrow \text{X(s)} + \text{Y}^{2+}\text{(aq)}\) | \(2\) | \(+0.40\) | \(-77\) | \(3.3 \times 10^{13}\) |
| 2 | \(2\,\text{W}^{3+}\text{(aq)} + 3\,\text{Z(s)} \rightarrow 2\,\text{W(s)} + 3\,\text{Z}^{2+}\text{(aq)}\) | \(6\) | \(+0.20\) | \(-116\) | \(1.9 \times 10^{20}\) |
| 3 | \(\text{Q}^{2+}\text{(aq)} + \text{R(s)} \rightarrow \text{Q(s)} + \text{R}^{2+}\text{(aq)}\) | \(2\) | \(-0.15\) | \(+29\) | \(8.5 \times 10^{-6}\) |
Which of the following best explains why Reaction 2 is more thermodynamically favorable under standard conditions and has a larger equilibrium constant than Reaction 1, even though \(E^\circ\) for Reaction 2 is smaller?
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