Galvanic Cells and Cell Potentials

Introduction

Key Concepts

1. Galvanic Cells: Definition and Components

A galvanic cell is an electrochemical cell that derives electrical energy from spontaneous redox reactions taking place within the cell. It consists of two electrodes: the anode and the cathode, each immersed in an electrolyte solution. These electrodes are connected via an external circuit and a salt bridge or a porous membrane that maintains electrical neutrality by allowing ion flow.

- Anode: The electrode where oxidation occurs. Electrons are released here. - Cathode: The electrode where reduction takes place. Electrons are consumed here. - Salt Bridge: A pathway containing a salt solution that maintains charge balance by allowing ions to migrate between the two half-cells.

2. Redox Reactions in Galvanic Cells

Redox (reduction-oxidation) reactions are central to the operation of galvanic cells. In these reactions, one species loses electrons (oxidation) while another gains electrons (reduction). The flow of electrons from the anode to the cathode through an external circuit generates electrical energy.

For example, consider the classic Daniell cell:

$$ \text{Zn (s)} + \text{Cu}^{2+} (\text{aq}) \rightarrow \text{Zn}^{2+} (\text{aq}) + \text{Cu (s)} $$

Here, zinc is oxidized at the anode: $$ \text{Zn (s)} \rightarrow \text{Zn}^{2+} (\text{aq}) + 2e^- $$

Copper ions are reduced at the cathode: $$ \text{Cu}^{2+} (\text{aq}) + 2e^- \rightarrow \text{Cu (s)} $$

3. Cell Potential (Electromotive Force - EMF)}

The cell potential, or electromotive force (EMF), is the voltage generated by a galvanic cell. It is a measure of the cell's ability to perform electrical work. The standard cell potential ($E^\circ_{\text{cell}}$) is calculated using standard electrode potentials ($E^\circ$) of the cathode and anode: $$ E^\circ_{\text{cell}} = E^\circ_{\text{cathode}} - E^\circ_{\text{anode}} $$

For the Daniell cell: $$ E^\circ_{\text{cell}} = E^\circ_{\text{Cu}^{2+}/\text{Cu}} - E^\circ_{\text{Zn}^{2+}/\text{Zn}} \\ E^\circ_{\text{cell}} = +0.34\, \text{V} - (-0.76\, \text{V}) = +1.10\, \text{V} $$

4. Nernst Equation

While the standard cell potential is measured under standard conditions (1 M concentration, 1 atm pressure, 25°C), actual cell potentials can vary based on the concentrations of the reactants and products. The Nernst equation quantifies this relationship: $$ E = E^\circ_{\text{cell}} - \frac{RT}{nF} \ln Q $$

At 25°C, the equation simplifies to: $$ E = E^\circ_{\text{cell}} - \frac{0.05916}{n} \log Q $$

Where:

• E: Cell potential under non-standard conditions
• E°_cell: Standard cell potential
• R: Gas constant (8.314 J/mol.K)
• T: Temperature in Kelvin
• n: Number of moles of electrons transferred
• F: Faraday's constant (96485 C/mol)
• Q: Reaction quotient

5. Relationship Between Gibbs Free Energy and Cell Potential

The spontaneity of a galvanic cell reaction is directly related to Gibbs free energy ($\Delta G$). The relationship is given by: $$ \Delta G = -nFE $$

A negative $\Delta G$ indicates a spontaneous reaction, which corresponds to a positive cell potential ($E > 0$).

6. Calculating Cell Potentials

To calculate the cell potential, follow these steps:

1. Identify the oxidation and reduction half-reactions.
2. Determine the standard electrode potentials ($E^\circ$) for each half-reaction.
3. Calculate the standard cell potential: $$ E^\circ_{\text{cell}} = E^\circ_{\text{cathode}} - E^\circ_{\text{anode}} $$
4. Use the Nernst equation to find the cell potential under non-standard conditions if necessary.

**Example:** Calculate the standard cell potential for the reaction: $$ \text{MnO}_4^- (\text{aq}) + 8\text{H}^+ (\text{aq}) + 5\text{e}^- \rightarrow \text{Mn}^{2+} (\text{aq}) + 4\text{H}_2\text{O (l)} $$ $$ \text{Fe}^{2+} (\text{aq}) \rightarrow \text{Fe}^{3+} (\text{aq}) + \text{e}^- $$

Given standard electrode potentials:

• $E^\circ_{\text{MnO}_4^-/\text{Mn}^{2+}} = +1.51\, \text{V}$
• $E^\circ_{\text{Fe}^{3+}/\text{Fe}^{2+}} = +0.77\, \text{V}$

- MnO₄^- is reduced at the cathode. - Fe²⁺ is oxidized at the anode.

Thus: $$ E^\circ_{\text{cell}} = E^\circ_{\text{cathode}} - E^\circ_{\text{anode}} \\ E^\circ_{\text{cell}} = +1.51\, \text{V} - (+0.77\, \text{V}) = +0.74\, \text{V} $$

7. Factors Affecting Cell Potential

Several factors can influence the cell potential of a galvanic cell:

• Concentration of Reactants and Products: According to the Nernst equation, changes in concentration affect $E$.
• Temperature: An increase in temperature can alter reaction kinetics and thermodynamics, impacting $E$.
• Pressure: Particularly relevant for reactions involving gases, where pressure changes can shift equilibrium.
• Nature of Electrodes: Different electrode materials can influence the cell potential based on their inherent properties.

8. Applications of Galvanic Cells

Galvanic cells have a wide range of applications in everyday life and industrial processes:

• Batteries: Primary (non-rechargeable) and secondary (rechargeable) batteries operate based on galvanic cell principles.
• Electroplating: Uses galvanic cells to deposit a layer of material onto a surface for protection or aesthetic purposes.
• Corrosion Prevention: Understanding galvanic cells helps in designing strategies to prevent metal corrosion.
• Bioelectrochemistry: Biological systems, such as nerve impulses, involve galvanic-type processes.

9. Limitations and Challenges

While galvanic cells are crucial in many applications, they come with certain limitations:

• Energy Density: Some galvanic cells may have lower energy densities compared to other energy storage systems.
• Lifespan: The capacity of galvanic cells can diminish over time due to side reactions and electrode degradation.
• Cost: High-performance materials required for efficient cell operation can be expensive.
• Environmental Impact: Disposal of certain galvanic cells poses environmental challenges due to hazardous materials.

Comparison Table

Summary and Key Takeaways