Concentration Cells
Concentration Cells
Concentration cells are a special type of electrochemical cell where the electrodes are identical in material and the electrolyte consists of the same ions, but at different concentrations. The driving force for the electrical potential in concentration cells is the tendency for ion concentrations to equalize. This results in the flow of electrons from the electrode in the more concentrated solution to the electrode in the less concentrated solution.
How Concentration Cells Work
In a concentration cell, both electrodes are made of the same material (e.g., copper, silver), and the electrolyte contains the same ions but at different concentrations. The cell generates an electromotive force (EMF) due to the concentration gradient between the two solutions. The electrode in contact with the higher concentration solution becomes the anode (oxidation occurs), while the electrode in contact with the lower concentration solution becomes the cathode (reduction occurs).
The EMF of the cell can be calculated using the Nernst equation:
$$ E = E^0 - \frac{RT}{nF} \ln \frac{[C]{low}}{[C]{high}} $$
where:
- $E$ is the cell potential,
- $E^0$ is the standard electrode potential (which is zero for concentration cells),
- $R$ is the universal gas constant (8.314 J/(mol·K)),
- $T$ is the temperature in Kelvin,
- $n$ is the number of moles of electrons transferred in the reaction,
- $F$ is the Faraday constant (96485 C/mol),
- $[C]_{low}$ is the concentration of ions in the cathode compartment,
- $[C]_{high}$ is the concentration of ions in the anode compartment.
Differences and Important Points
Here is a table summarizing the key aspects of concentration cells:
| Feature | Description |
|---|---|
| Electrodes | Identical in composition |
| Electrolyte | Same ions but different concentrations |
| Cell Potential | Generated due to the concentration gradient |
| Anode | Electrode in contact with the higher concentration solution (oxidation) |
| Cathode | Electrode in contact with the lower concentration solution (reduction) |
| EMF Calculation | Nernst equation is used without a standard electrode potential term |
| Equilibrium | Achieved when the concentrations become equal and the EMF is zero |
Examples
Example 1: Copper Concentration Cell
Consider a concentration cell with copper electrodes and CuSO₄ as the electrolyte. The anode compartment has a 1 M CuSO₄ solution, and the cathode compartment has a 0.01 M CuSO₄ solution. The cell can be represented as:
$$ \text{Cu} | \text{Cu}^{2+} (1 \text{ M}) || \text{Cu}^{2+} (0.01 \text{ M}) | \text{Cu} $$
The half-reactions are:
- Anode: $\text{Cu} \rightarrow \text{Cu}^{2+} + 2e^-$
- Cathode: $\text{Cu}^{2+} + 2e^- \rightarrow \text{Cu}$
Using the Nernst equation at 298 K (25°C):
$$ E = - \frac{8.314 \times 298}{2 \times 96485} \ln \frac{0.01}{1} $$
$$ E \approx - \frac{0.0257}{2} \ln(0.01) $$
$$ E \approx 0.0295 \times 4.6052 $$
$$ E \approx 0.136 \text{ V} $$
The positive sign indicates that the flow of electrons is from the anode to the cathode, as expected.
Example 2: Hydrogen Concentration Cell
A hydrogen concentration cell consists of two hydrogen electrodes in contact with H⁺ ion solutions of different concentrations. If one compartment has a pH of 0 and the other has a pH of 7, the cell can be represented as:
$$ \text{Pt} | \text{H}_2 (\text{g}) | \text{H}^+ (1 \text{ M}) || \text{H}^+ (10^{-7} \text{ M}) | \text{H}_2 (\text{g}) | \text{Pt} $$
The half-reactions are:
- Anode: $\text{H}_2 \rightarrow 2\text{H}^+ + 2e^-$
- Cathode: $2\text{H}^+ + 2e^- \rightarrow \text{H}_2$
Using the Nernst equation at 298 K (25°C):
$$ E = - \frac{0.0257}{2} \ln \frac{10^{-7}}{1} $$
$$ E \approx 0.0591 \times 7 $$
$$ E \approx 0.414 \text{ V} $$
This example illustrates how the pH difference between two solutions can create an EMF in a concentration cell.
Conclusion
Concentration cells are a fascinating application of electrochemistry principles. They demonstrate how a potential difference can be created solely by a difference in ion concentration. Understanding concentration cells is important for fields such as batteries, sensors, and corrosion science. By mastering the concepts and calculations related to concentration cells, students can gain a deeper insight into thermodynamics and kinetics of electrochemical systems.