AP Chemistry
9.10 Cell Potential Under Nonstandard Conditions
9.9 Cell Potential and Free Energy
9.5 Free Energy and Equilibrium
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.
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?
| 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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