Electrochemistry: Principles, Cells, and Applications

Electrochemistry

Introduction to Electrochemistry

Electrochemistry is the branch of chemistry that studies the interconversion of chemical and electrical energy. It is fundamentally concerned with the movement of electrons in redox (reduction-oxidation) reactions, which can be harnessed to generate electricity or drive chemical changes using electrical energy.

• Electricity is the flow of electrons through a conductor.

• Redox reactions involve the transfer of electrons between chemical species.

Types of Electrochemical Cells

Electrochemical cells are devices that either generate electrical energy from chemical reactions or use electrical energy to drive chemical reactions. They are classified based on the spontaneity of the reaction:

	Spontaneous Reaction	Non-spontaneous Reaction
Cell Type	Galvanic/Voltaic Cell	Electrolytic Cell
Energy Flow	Electricity is generated by a chemical reaction	Electricity is required for the reaction to proceed
Anode	Negative (−)	Positive (+)
Cathode	Positive (+)	Negative (−)
Cell Potential ($E_{cell}$)	$E_{cell} > 0$	$E_{cell} < 0$

• Galvanic/Voltaic Cell: Converts chemical energy to electrical energy via a spontaneous redox reaction.

• Electrolytic Cell: Uses electrical energy to drive a non-spontaneous chemical reaction.

Electrode Potentials

Cell Potential and Electromotive Force (emf)

The cell potential (also called electromotive force, emf, or $E_{cell}$) is the voltage produced by an electrochemical cell. It is measured in volts (V) and reflects the tendency of a redox reaction to occur.

• Cell Diagram: A shorthand notation to represent the components of an electrochemical cell.

• Example: Cu(s) | Cu2+ (aq) || Ag+ (aq) | Ag(s)

• The double vertical line || represents the salt bridge, which maintains electrical neutrality.

Standard Electrode Potentials ($E^ ext{o}$)

The standard electrode potential ($E^ ext{o}$) is the potential of a half-cell under standard conditions (1 M concentration, 1 atm pressure, 25°C) relative to the standard hydrogen electrode (SHE), which is assigned a potential of 0 V.

• Standard Hydrogen Electrode (SHE): $2H^+(aq, 1M) + 2e^- \rightarrow H_2(g, 1~atm)$, $E^ ext{o} = 0$ V

• A more positive $E^ ext{o}$ means a greater tendency to be reduced.

• A more negative $E^ ext{o}$ means a greater tendency to be oxidized.

Calculating Standard Cell Potentials

The standard cell potential ($E^ ext{o}_{cell}$) is calculated from the standard reduction potentials of the cathode and anode:

• $E^ ext{o}_{cell} = E^ ext{o}_{cathode} - E^ ext{o}_{anode}$

• The cathode is where reduction occurs; the anode is where oxidation occurs.

Example: For the cell: Zn(s) + Cl2(g) → Zn2+(aq) + 2Cl−(aq)

• Zn(s) → Zn2+(aq) + 2e− $E^ ext{o} = -0.76$ V

• Cl2(g) + 2e− → 2Cl−(aq) $E^ ext{o} = +1.36$ V

• $E^ ext{o}_{cell} = 1.36 - (-0.76) = 2.12$ V

Identifying Oxidation and Reduction

To determine which species is oxidized or reduced, compare their standard electrode potentials:

• The species with the higher (more positive) $E^ ext{o}$ is reduced (acts as the oxidizing agent).

• The species with the lower (more negative) $E^ ext{o}$ is oxidized (acts as the reducing agent).

Effect of Concentration: The Nernst Equation

Nernst Equation

The Nernst equation relates the cell potential to the standard cell potential and the concentrations (activities) of the reactants and products:

$E_{cell} = E^ ext{o}_{cell} - \frac{RT}{nF} \ln Q$

• $R$ = gas constant (8.314 J·mol−1·K−1)

• $T$ = temperature in Kelvin

• $n$ = number of moles of electrons transferred

• $F$ = Faraday constant (96485 C·mol−1)

• $Q$ = reaction quotient

At 25°C (298 K), the equation simplifies to:

$E_{cell} = E^ ext{o}_{cell} - \frac{0.0257}{n} \ln Q$

Example Calculation

For a cell with non-standard concentrations:

• Zn(s) + Cu2+(2.0 M) → Cu(s) + Zn2+(0.10 M)

• $E^ ext{o}_{cell} = 1.10$ V

• Use the Nernst equation to find $E_{cell}$ under these conditions.

Relationship Between $E_{cell}$, $9G$, and $K$

Thermodynamic Relationships

• Gibbs Free Energy and Cell Potential:

  • $\Delta G = -nFE_{cell}$

• Gibbs Free Energy and Equilibrium Constant:

  • $\Delta G = -RT \ln K$

• Cell Potential and Equilibrium Constant:

  • $E_{cell} = \frac{RT}{nF} \ln K$

Where $K$ is the equilibrium constant for the cell reaction.

Electrolysis

Electrolytic Cells and Industrial Applications

Electrolysis is the process of using electrical energy to drive a non-spontaneous chemical reaction. It is widely used in industry for:

• Electrorefining of metals

• Electroplating of metals

Quantitative Aspects: Faraday's Laws of Electrolysis

The amount of substance produced or consumed at an electrode during electrolysis is proportional to the quantity of electric charge passed through the cell.

• $Q = I \times t$

• $Q$ = charge (coulombs, C)

• $I$ = current (amperes, A)

• $t$ = time (seconds, s)

• 1 Faraday ($F$) = 1 mole of electrons = 96485 C

Steps for Electrolysis Calculations

1. Calculate total charge: $Q = I \times t$

2. Convert charge to moles of electrons: $\text{mol e}^- = Q / F$

3. Use stoichiometry to find moles of substance produced or consumed

4. Convert moles to mass if required: $\text{mass} = \text{moles} \times \text{molar mass}$

Example: Electrolysis of Molten CaCl2

• Current: 0.452 A

• Time: 1.50 hours = 5400 s

• Total charge: $Q = 0.452 \times 5400 = 2440$ C

• Moles of electrons: $2440 / 96485 = 0.0253$ mol e−

• For Ca2+ + 2e− → Ca(s): $0.0253 / 2 = 0.0127$ mol Ca

• Mass of Ca: $0.0127 \times 40.08 = 0.509$ g