---
title: "A student investigates the relationship between ion concentration and cell potential by constructing a series of \\(\\text{Ag/Ag}^+\\) concentration cells at \\(298 \\text{ K}\\). Each cell consists of two \\(\\text{Ag(s)}\\) electrodes in separate beakers connected by a salt bridge and a voltmeter. The cathode compartment contains \\([\\text{Ag}^+] = 1.0 \\text{ M}\\) in every trial, while the anode compartment contains \\(\\text{AgNO}_3\\text{(aq)}\\) at various concentrations. The initial cell potential, \\(E_{\\text{cell}}\\), recorded for each trial is shown in the table below.  | Trial | \\([\\text{Ag}^+]_{\\text{anode}}\\) (M) | \\([\\text{Ag}^+]_{\\text{cathode}}\\) (M) | \\(E_{\\text{cell}}\\) (V) | | :—: | :—: | :—: | :—: | | 1 | \\(1.0 \\times 10^{-1}\\) | \\(1.0\\) | \\(+0.059\\) | | 2 | \\(1.0 \\times 10^{-2}\\) | \\(1.0\\) | \\(+0.118\\) | | 3 | \\(1.0 \\times 10^{-3}\\) | \\(1.0\\) | \\(+0.177\\) | | 4 | Unknown \\(X\\) | \\(1.0\\) | \\(+0.236\\) |  Based on the data, what is \\([\\text{Ag}^+]\\) in the unknown solution, and what condition explains why \\(E_{\\text{cell}}\\) becomes \\(0.000 \\text{ V}\\) after the cell is allowed to operate for a long period of time?"
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url: "https://nerd-notes.com/ubq/123946/"
date_modified: "2026-09-28T12:32:26+00:00"
---

# A student investigates the relationship between ion concentration and cell potential by constructing a series of \(\text{Ag/Ag}^+\) concentration cells at \(298 \text{ K}\). Each cell consists of two \(\text{Ag(s)}\) electrodes in separate beakers connected by a salt bridge and a voltmeter. The cathode compartment contains \([\text{Ag}^+] = 1.0 \text{ M}\) in every trial, while the anode compartment contains \(\text{AgNO}_3\text{(aq)}\) at various concentrations. The initial cell potential, \(E_{\text{cell}}\), recorded for each trial is shown in the table below.

| Trial | \([\text{Ag}^+]_{\text{anode}}\) (M) | \([\text{Ag}^+]_{\text{cathode}}\) (M) | \(E_{\text{cell}}\) (V) |
| :—: | :—: | :—: | :—: |
| 1 | \(1.0 \times 10^{-1}\) | \(1.0\) | \(+0.059\) |
| 2 | \(1.0 \times 10^{-2}\) | \(1.0\) | \(+0.118\) |
| 3 | \(1.0 \times 10^{-3}\) | \(1.0\) | \(+0.177\) |
| 4 | Unknown \(X\) | \(1.0\) | \(+0.236\) |

Based on the data, what is \([\text{Ag}^+]\) in the unknown solution, and what condition explains why \(E_{\text{cell}}\) becomes \(0.000 \text{ V}\) after the cell is allowed to operate for a long period of time?

A student investigates the relationship between ion concentration and cell potential by constructing a series of \(\text{Ag/Ag}^+\) concentration cells at \(298 \text{ K}\). Each cell consists of two \(\text{Ag(s)}\) electrodes in separate beakers connected by a salt bridge and a voltmeter. The cathode compartment contains \([\text{Ag}^+] = 1.0 \text{ M}\) in every trial, while the anode compartment contains \(\text{AgNO}_3\text{(aq)}\) at various concentrations. The initial cell potential, \(E_{\text{cell}}\), recorded for each trial is shown in the table below.

| Trial | \([\text{Ag}^+]_{\text{anode}}\) (M) | \([\text{Ag}^+]_{\text{cathode}}\) (M) | \(E_{\text{cell}}\) (V) |
| :---: | :---: | :---: | :---: |
| 1 | \(1.0 \times 10^{-1}\) | \(1.0\) | \(+0.059\) |
| 2 | \(1.0 \times 10^{-2}\) | \(1.0\) | \(+0.118\) |
| 3 | \(1.0 \times 10^{-3}\) | \(1.0\) | \(+0.177\) |
| 4 | Unknown \(X\) | \(1.0\) | \(+0.236\) |

Based on the data, what is \([\text{Ag}^+]\) in the unknown solution, and what condition explains why \(E_{\text{cell}}\) becomes \(0.000 \text{ V}\) after the cell is allowed to operate for a long period of time?

- **A.** \([\text{Ag}^+] = 1.0 \times 10^{-4} \text{ M}\); the cell potential reaches \(0.000 \text{ V}\) because all \(\text{Ag}^+\text{(aq)}\) ions at the cathode are completely consumed.
- **B.** \([\text{Ag}^+] = 1.0 \times 10^{-4} \text{ M}\); the cell potential reaches \(0.000 \text{ V}\) because the system reaches dynamic equilibrium where \(Q = K = 1\) and \(\Delta G = 0\).
- **C.** \([\text{Ag}^+] = 1.0 \times 10^{-5} \text{ M}\); the cell potential reaches \(0.000 \text{ V}\) because the system reaches dynamic equilibrium where \(Q = K = 1\) and \(\Delta G = 0\).
- **D.** \([\text{Ag}^+] = 1.0 \times 10^{-5} \text{ M}\); the cell potential reaches \(0.000 \text{ V}\) because all \(\text{Ag}^+\text{(aq)}\) ions at the cathode are completely consumed.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/123946/*