D41.3 Concentration Cells

A concentration cell is a special type of voltaic cell where the electrodes are the same material but the half-cells have different concentrations of soluble species. Because one or both half-cells are not under standard-state conditions, the half-cell potentials are unequal, and there is a potential difference between the half-cells. That potential difference can be calculated using the Nernst equation.

For example, consider this concentration cell at 25 °C:

Zn(s) | Zn2+(aq, 0.10 M) || Zn2+(aq, 0.50 M) | Zn(s)

The standard cell potential is 0 V because the anode and cathode involve the same reaction. However, if equal volumes of the two half-cell solutions were mixed, the concentration of Zn2+ would change to the average of the initial concentrations, namely, to 0.30 M. The cell can do work because the concentrations of Zn2+ change.

Oxidation: Zn(s) Zn2+(aq, 0.10 M) + 2e‾ E°anode = -0.763 V
Reduction : Zn2+(aq, 0.50 M) + 2e‾ Zn(s) E°cathode = -0.763 V
Overall: Zn2+(aq, 0.50 M) Zn2+(aq, 0.10 M) E°cell = 0 V

The Nernst equation verifies that the process is spontaneous at the given conditions, because it shows that Ecell > 0 V:

 E_{\text{cell}} = 0\;\text{V}\;-\;\dfrac{\left(8.314\frac{\text{J}}{\text{K}{\cdot}\text{mol}}\right)(298.15\;\text{K})}{(2)\left(96485\frac{\text{J}}{\text{V}{\cdot}\text{mol}}\right)}\;\text{ln}\left(\dfrac{0.10\;\text{M}}{0.50\;\text{M}}\right) = +0.021\;\text{V}

In a concentration cell, the standard cell potential (E°cell) is always zero. In order to have a spontaneous forward reaction, and hence have a positive cell potential (Ecell), the reaction quotient Q must be less than 1 (when Q < 1, ln(Q) < 0). As the reaction proceeds, the concentrations change, Q approaches 1 and Ecell approaches 0 V.

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