Electrochemistry: Cell Potentials, Voltaic Cells, and Applications

Electrochemistry and Cell Potentials

Introduction to Electrochemistry

Electrochemistry is the study of chemical processes that involve the movement of electrons, typically through redox (reduction-oxidation) reactions. These processes are fundamental to the operation of batteries, fuel cells, and many biological systems.

• Cell potential is a measure of the driving force (free energy change) for a cell reaction.

• It is composed of the oxidation potential (anode) and the reduction potential (cathode).

• The overall cell potential is given by:

$E_{cell} = E_{oxidation} + E_{reduction}$

• Since standard electrode potentials are tabulated as reduction potentials, the oxidation potential for a half-reaction is the negative of the reduction potential for the reverse half-reaction:

$E_{oxidation} = -E_{anode}$ $E_{cell} = E_{cathode} - E_{anode}$

• Electrode potentials are a measure of the oxidizing ability of the reactant.

Standard Electrode Potentials

Standard electrode potentials (E°) are measured under standard conditions (25°C, 1 M concentration, 1 atm pressure) and are referenced to the standard hydrogen electrode (SHE), which is assigned a potential of 0.00 V.

Cathode (Reduction) Half-Reaction	Standard Potential, E° (V)
Li+(aq) + e- → Li(s)	-3.04
Na+(aq) + e- → Na(s)	-2.71
Mg2+(aq) + 2e- → Mg(s)	-2.37
Al3+(aq) + 3e- → Al(s)	-1.66
Zn2+(aq) + 2e- → Zn(s)	-0.76
Fe2+(aq) + 2e- → Fe(s)	-0.44
Cu2+(aq) + 2e- → Cu(s)	0.34
2H+(aq) + 2e- → H2(g)	0.00
Ag+(aq) + e- → Ag(s)	0.80
Cl2(g) + 2e- → 2Cl-(aq)	1.36
F2(g) + 2e- → 2F-(aq)	2.87

Additional info: Table truncated for brevity; see full table in textbook for more values.

Predicting Spontaneity of Redox Reactions

• To determine if a redox reaction is spontaneous, calculate the cell potential using standard reduction potentials.

• If $E_{cell} > 0$, the reaction is spontaneous under standard conditions.

• Example 1: Does Li+ react with Cu2+ spontaneously at RT?

• Example 2: Can Fe3+ react with Pb spontaneously at RT?

Electrochemistry and Life

• Electrochemical energy sources are exploited by organisms for metabolism.

• Combinations of oxidants and reductants support various metabolic lifestyles.

• Electrochemistry is also important in the search for extraterrestrial life (e.g., Europa's habitability).

Voltaic (Galvanic) Cells

Components and Representation

A voltaic cell is an electrochemical cell that generates electrical energy from a spontaneous redox reaction.

• Anode: Site of oxidation (loss of electrons).

• Cathode: Site of reduction (gain of electrons).

• Salt bridge: Maintains electrical neutrality by allowing ion flow.

• External circuit: Pathway for electron flow from anode to cathode.

Example: Zn(s) | Zn2+(aq) || Cu2+(aq) | Cu(s)

Cell Notation

• The oxidation half-cell (anode) is written on the left; the reduction half-cell (cathode) on the right.

• Phase boundaries are shown with a single vertical bar (|).

• The salt bridge is represented by a double vertical bar (||).

• Inert electrodes (e.g., Pt) are used when a gas or nonmetal is involved.

• Concentrations and pressures are specified in parentheses.

Example: Cu(s) | Cu2+(1.0 M) || F2(1.0 atm) | F-(1.0 M) | Pt

Thermodynamics and Cell Potentials

Relationship Between Free Energy and Cell Potential

• The change in Gibbs free energy ($\Delta G$) is related to the cell potential by:

$\Delta G = -nFE_{cell}$

• Where n is the number of moles of electrons transferred, and F is the Faraday constant (96,485 C/mol).

Nernst Equation: Dependence on Concentration

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

$E_{cell} = E_{cell}^\circ - \frac{RT}{nF} \ln Q$

• At 25°C (298 K):

$E_{cell} = E_{cell}^\circ - \frac{0.02568}{n} \ln Q$

• Or, using base-10 logarithms:

$E_{cell} = E_{cell}^\circ - \frac{0.0592}{n} \log Q$

• Where Q is the reaction quotient.

Equilibrium and Cell Potentials

• At equilibrium, $E_{cell} = 0$ and $Q = K$ (equilibrium constant).

• The relationship between standard cell potential and equilibrium constant is:

$E_{cell}^\circ = \frac{0.0592}{n} \log K$

Applications of Electrochemistry

Determination of pH

• pH can be determined by measuring the cell potential of a cell involving the hydrogen ion.

• This is the principle behind the pH meter, which uses a glass electrode sensitive to [H+].

Commercial Voltaic Cells

Zinc–Carbon Dry Cell (Leclanché Cell)

• Anode: Zn(s) → Zn2+(aq) + 2e-

• Cathode: 2NH4+(aq) + 2MnO2(s) + 2e- → Mn2O3(s) + H2O(l) + 2NH3(aq)

• Initial voltage: ~1.5 V, but decreases rapidly in cold weather due to kinetic limitations.

Zinc–Carbon Dry Cell: Alkaline

• Uses Zn powder and KOH electrolyte (aqueous paste).

• Performs better in cold weather than regular Zn–C batteries.

• Still disposable; side reactions can increase self-discharge and corrosion.

Lithium–Iodine Battery

• Solid-state battery with electrodes separated by a thin crystalline layer of lithium iodide.

• High resistance, low voltage at mA range, but very reliable (used in pacemakers, lasts ~10 years).

Fuel Cells

• Fuel cells require a continuous supply of reactants (fuel and oxidant).

• Anode reaction: $H_2(g) \rightarrow 2H^+(aq) + 2e^-$

• Cathode reaction: $O_2(g) + 4H^+(aq) + 4e^- \rightarrow 2H_2O(l)$

• Originally used in space applications; now used in some cars.

Summary of Key Concepts

• Balancing oxidation-reduction reactions in acidic and basic solutions.

• Components and construction of voltaic cells.

• Cell notation for voltaic cells.

• How to determine which reaction occurs at the cathode and anode.

• Definition and use of standard cell and electrode potentials.

• Calculating equilibrium constants from cell potentials and vice versa.

• Dependence of cell potentials on concentration (Nernst equation).

• Calculating maximum work from cell reactants.

• Determining relative strengths of oxidizing and reducing agents and spontaneity direction.

Applied Electrochemistry: Everyday and Biological Relevance

• Fuel cells as clean energy sources (e.g., cars producing water instead of greenhouse gases).

• Battery performance affected by temperature (e.g., phone batteries drain faster in cold, cars start slower below 0°C).

• Medical applications require reliable, long-lasting batteries (e.g., lithium–iodine batteries in pacemakers).

Practice Examples

• Example 3: What happens if a battery in a flashlight has reached equilibrium? (No current flows; the flashlight will not light up.)

• Example 4: Why does a heavy-duty zinc-carbon battery have thicker zinc walls? (Provides more zinc for oxidation, increasing battery life and output.)

• Example 5: In a redox reaction between Cu and Al, which is oxidized and which is reduced? (Al is oxidized, Cu2+ is reduced; determined by their standard reduction potentials.)