Electrochemical Cells and Half-Reactions

Introduction

Key Concepts

1. Electrochemical Cells

An electrochemical cell is a device that converts chemical energy into electrical energy through redox reactions. It consists of two electrodes: the anode and the cathode, connected by an electrolyte that allows ion flow to balance charge during the reaction.

1.1. Types of Electrochemical Cells

There are two main types of electrochemical cells:

• Galvanic Cells (Voltaic Cells): These cells generate electrical energy spontaneously from spontaneous redox reactions. The anode undergoes oxidation, and the cathode undergoes reduction.
• Electrolytic Cells: These cells require an external electrical source to drive non-spontaneous redox reactions. Here, the anode is positive, and the cathode is negative.

1.2. Components of an Electrochemical Cell

• Anode: The electrode where oxidation occurs. In galvanic cells, it is the negative electrode.
• Cathode: The electrode where reduction occurs. In galvanic cells, it is the positive electrode.
• Electrolyte: A medium containing ions that facilitates ion transfer between electrodes, maintaining electrical neutrality.
• Salt Bridge: A device that connects the two half-cells, allowing the flow of ions to complete the electrical circuit and prevent charge buildup.

1.3. Cell Potential (E°)

The cell potential, or standard electromotive force (E°), measures the voltage produced by an electrochemical cell under standard conditions (1 M concentration, 1 atm pressure, and 25°C). It is calculated using the standard reduction potentials of the cathode and anode: $$ E°_{\text{cell}} = E°_{\text{cathode}} - E°_{\text{anode}} $$ A positive E° indicates a spontaneous reaction in galvanic cells, while a negative E° implies a non-spontaneous reaction in electrolytic cells.

1.4. Nernst Equation

The Nernst equation relates the cell potential to the concentrations of the reactants and products, allowing the calculation of cell potential under non-standard conditions: $$ E = E° - \frac{RT}{nF} \ln Q $$ Where:

• E = cell potential
• E° = standard cell potential
• R = universal 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

2. Half-Reactions

Half-reactions depict the oxidation and reduction processes separately in an electrochemical reaction. Each half-reaction includes only the species undergoing oxidation or reduction, along with electrons to balance charge.

2.1. Oxidation and Reduction

• Oxidation: The loss of electrons by a substance. It is represented in the half-reaction by electrons being a product.
• Reduction: The gain of electrons by a substance. It is represented in the half-reaction by electrons being a reactant.

2.2. Balancing Redox Reactions

Balancing redox reactions involves ensuring the conservation of mass and charge. The steps include:

1. Separate the overall reaction into two half-reactions (oxidation and reduction).
2. Balance all elements except hydrogen and oxygen.
3. Balance oxygen atoms by adding $H_2O$ molecules.
4. Balance hydrogen atoms by adding $H^+$ ions.
5. Balance the charge by adding electrons ($e^-$).
6. Multiply each half-reaction by appropriate coefficients to equalize the number of electrons.
7. Add the half-reactions together, cancelling out electrons and any other species that appear on both sides.

2.3. Standard Electrode Potentials

Standard electrode potentials (E°) indicate the tendency of a species to gain electrons. They are measured under standard conditions and listed in reduction tables. The higher (more positive) the E°, the greater the species' affinity for electrons and its tendency to undergo reduction.

2.4. Applications of Electrochemical Cells

• Batteries: Portable energy sources that convert stored chemical energy into electrical energy through galvanic cells.
• Corrosion Prevention: Understanding electrochemical principles helps in designing methods to prevent the oxidation of metals.
• Electroplating: Using electrolytic cells to deposit a layer of metal onto a surface for protection or aesthetic purposes.
• Fuel Cells: Devices that convert chemical energy from fuels directly into electrical energy through electrochemical reactions.

2.5. Faraday’s Laws of Electrolysis

Faraday’s laws quantify the relationship between the amount of electricity passed through an electrolyte and the amount of substance that undergoes oxidation or reduction:

• First Law: The mass of a substance altered at an electrode during electrolysis is directly proportional to the quantity of electricity passed.
• Second Law: The mass of different substances altered by the same quantity of electricity is proportional to their equivalent weights.

2.6. Electromotive Force (EMF) and Cell Efficiency

The electromotive force (EMF) of a cell is a measure of its ability to do work. However, not all the energy from a cell’s reaction is converted into electrical energy due to inefficiencies like internal resistance. The efficiency ($\eta$) of an electrochemical cell can be expressed as: $$ \eta = \frac{E_{\text{useful}}}{E_{\text{total}}} \times 100\% $$ Where $E_{\text{useful}}$ is the electrical energy output and $E_{\text{total}}$ is the total chemical energy available from the reaction.

Comparison Table

Summary and Key Takeaways