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title: "A researcher compares two hypothetical galvanic cells used in metal recovery. Both cells operate at the same temperature and transfer the same number of moles of electrons per mole of reaction. The standard cell potentials satisfy \\(E_2^\\circ=2E_1^\\circ\\), where \\(E_1^\\circ>0\\). The corresponding equilibrium constants are \\(K_1\\) and \\(K_2\\).  The relationships \\(\\Delta G^\\circ=-nFE^\\circ\\) and \\(\\Delta G^\\circ=-RT\\ln K\\) apply. Which of the following correctly relates \\(K_2\\) to \\(K_1\\)?"
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url: "https://nerd-notes.com/ubq/119438/"
date_modified: "2026-08-19T12:40:23+00:00"
---

# A researcher compares two hypothetical galvanic cells used in metal recovery. Both cells operate at the same temperature and transfer the same number of moles of electrons per mole of reaction. The standard cell potentials satisfy \(E_2^\circ=2E_1^\circ\), where \(E_1^\circ>0\). The corresponding equilibrium constants are \(K_1\) and \(K_2\).

The relationships \(\Delta G^\circ=-nFE^\circ\) and \(\Delta G^\circ=-RT\ln K\) apply. Which of the following correctly relates \(K_2\) to \(K_1\)?

A researcher compares two hypothetical galvanic cells used in metal recovery. Both cells operate at the same temperature and transfer the same number of moles of electrons per mole of reaction. The standard cell potentials satisfy \(E_2^\circ=2E_1^\circ\), where \(E_1^\circ>0\). The corresponding equilibrium constants are \(K_1\) and \(K_2\).

The relationships \(\Delta G^\circ=-nFE^\circ\) and \(\Delta G^\circ=-RT\ln K\) apply. Which of the following correctly relates \(K_2\) to \(K_1\)?

- **A.** \(K_2=2K_1\)
- **B.** \(K_2=(K_1)^2\)
- **C.** \(K_2=\sqrt{K_1}\)
- **D.** \(K_2=\dfrac{1}{(K_1)^2}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/119438/*