Electrochemistry: Principles, Calculations, and Applications

Electrochemistry

Introduction to Electrochemistry

Electrochemistry is the branch of chemistry that studies the relationship between chemical reactions and electrical energy. It is fundamental for understanding batteries, corrosion, and electrolysis, and is a key topic in general chemistry.

• Oxidation: The loss of electrons by a substance. Example: $\mathrm{Zn} (s) \rightarrow \mathrm{Zn}^{2+} (aq) + 2e^-$

• Reduction: The gain of electrons by a substance. Example: $\mathrm{Cu}^{2+} (aq) + 2e^- \rightarrow \mathrm{Cu} (s)$

• Oxidizing agent: Causes oxidation by being reduced.

• Reducing agent: Causes reduction by being oxidized.

• Example overall reaction: $\mathrm{Zn} + \mathrm{Cu}^{2+} \rightarrow \mathrm{Zn}^{2+} + \mathrm{Cu}$ - $\mathrm{Cu}^{2+}$ is the oxidizing agent - $\mathrm{Zn}$ is the reducing agent

Oxidation Numbers

Oxidation numbers help track electron transfer in redox reactions. They are assigned based on a set of rules:

• An atom in its elemental state has an oxidation number of 0.

• An atom in a monatomic ion has an oxidation number equal to its charge.

• In polyatomic ions or molecular compounds, oxidation numbers are assigned as if the atom were a monatomic ion:

  • Hydrogen: +1 when bonded to a nonmetal, –1 when bonded to a metal.

  • Oxygen: –2, except in peroxides (e.g., H2O2).

  • Halogens: –1 (unless they are the central atom).

• The sum of oxidation numbers is 0 for a neutral compound and equals the net charge for a polyatomic ion.

Identifying and Balancing Redox Reactions (Half-Reaction Method)

Redox reactions can be balanced using the half-reaction method:

1. Identify which atoms are oxidized and which are reduced.

2. Write the unbalanced half-reactions for oxidation and reduction.

3. Balance each half-reaction for all atoms except oxygen and hydrogen.

4. Balance oxygen by adding H2O; balance hydrogen by adding H+.

5. Balance charge by adding electrons (e–).

6. Multiply half-reactions to equalize electron transfer.

7. Add the half-reactions and cancel electrons and any species appearing on both sides.

Electrochemical Cells: Galvanic vs. Electrolytic

Electrochemical cells convert chemical energy to electrical energy or vice versa. There are two main types:

• Galvanic (Voltaic) Cell: Uses a spontaneous reaction to generate electrical energy.

• Electrolytic Cell: Uses a nonspontaneous reaction driven by an external power source.

• Anode: Site of oxidation (loses electrons); negative in galvanic cells.

• Cathode: Site of reduction (gains electrons); positive in galvanic cells.

• Salt Bridge: Maintains ion balance by allowing ion flow between half-cells.

• Direction of electron flow: From anode to cathode.

Cell Notation and Visual Interpretation

Cell notation is a shorthand way to represent electrochemical cells:

• General format: Anode | Anode solution (M) || Cathode solution (M) | Cathode

• Example: Zn(s) | Zn2+(aq, 1 M) || Cu2+(aq, 1 M) | Cu(s)

• Vertical lines (|) represent phase boundaries; double lines (||) represent the salt bridge.

• Interpret diagrams to identify electron flow and reaction sites.

• Use Pt as an inert electrode for reactions lacking solid metals.

Standard Reduction Potentials and Cell Potential (E°)

Standard reduction potentials (E°) are used to calculate the cell potential:

• Cell potential: $E^\circ_{\text{cell}} = E^\circ_{\text{red}} - E^\circ_{\text{ox}}$

• Standard reduction potential tables list half-reactions as reductions, ordered by decreasing E°.

• If $E^\circ_{\text{cell}}$ is positive, the reaction is spontaneous (stronger oxidizing agent).

• If $E^\circ_{\text{cell}}$ is negative, the reaction is nonspontaneous (stronger reducing agent).

• Example: For $\mathrm{Cu}^{2+} (aq) + \mathrm{Zn} (s) \rightarrow \mathrm{Cu} (s) + \mathrm{Zn}^{2+} (aq)$ $E^\circ (\mathrm{Cu}^{2+}/\mathrm{Cu}) = 0.34\ \mathrm{V}$, $E^\circ (\mathrm{Zn}^{2+}/\mathrm{Zn}) = -0.76\ \mathrm{V}$ $E^\circ_{\text{cell}} = 0.34\ \mathrm{V} - (-0.76\ \mathrm{V}) = 1.1\ \mathrm{V}$

Thermodynamics and Electrochemistry

Electrochemical cell potential is related to thermodynamic quantities:

• Gibbs Free Energy: $\Delta G^\circ = -nFE^\circ$ - $n$: Number of electrons transferred - $F$: Faraday’s constant ($96,500\ \mathrm{C/mol\ e^-}$)

• Equilibrium Constant (K): $\Delta G^\circ = -RT \ln(K)$ $E^\circ = \frac{RT}{nF} \ln(K)$ - $R$: Gas constant ($8.314\ \mathrm{J/mol\cdot K}$) - $T$: Temperature in Kelvin

• Spontaneity relationship: - $\Delta G < 0$, $E > 0$: Spontaneous - $\Delta G > 0$, $E < 0$: Non-spontaneous

Concentration Effects and the Nernst Equation

The Nernst equation allows calculation of cell potential under non-standard conditions:

• Nernst Equation: $E = E^\circ - \frac{RT}{nF} \ln(Q)$

• $Q$: Reaction quotient = [products]/[reactants]

• Effect of concentration:

  • Increase in reactants → E increases

  • Increase in products → E decreases

Summary and Practice

• Balance redox reactions and identify oxidizing and reducing agents.

• Analyze and interpret galvanic cells and their shorthand notations.

• Calculate $E^\circ$, $\Delta G^\circ$, and use the Nernst equation for non-standard conditions.

• Predict how concentration changes affect cell voltage.