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title: "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}\\).  | 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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url: "https://nerd-notes.com/ubq/120359/"
date_modified: "2026-08-23T04:23:23+00:00"
---

# 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 \(298\text{ K}\).

| 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?

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 \(298\text{ K}\).

| 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?

- **A.** Reaction 2 involves more reactant particles colliding simultaneously, which lowers the activation energy of the forward pathway and increases the value of \(K\).
- **B.** Reaction 2 produces a greater total number of moles of product particles, which increases \(\Delta S^\circ\) and makes \(\Delta G^\circ\) more negative independently of electrical work.
- **C.** Reaction 2 transfers \(6\text{ mol } e^-\text{/mol}_{\text{rxn}}\) compared to \(2\text{ mol } e^-\text{/mol}_{\text{rxn}}\) for Reaction 1; because \(\Delta G^\circ = -nFE^\circ\) and \(\ln K = \dfrac{nFE^\circ}{RT}\), the larger product \(nE^\circ\) for Reaction 2 produces a more negative \(\Delta G^\circ\) and a greater \(K\).
- **D.** Standard cell potential is an extensive property that is divided by the number of electrons transferred; therefore, the electrical energy delivered per electron is greater in Reaction 2.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120359/*