Cell Potential Calculator

Calculate standard cell potential (E°cell), apply the Nernst equation for non-standard conditions, and explore the relationship between cell potential and thermodynamics.

Calculation Mode

Reduction Potential (E°red) in V

Standard reduction potential for the cathode (reduction half-reaction)

Oxidation Potential (E°ox) in V

Standard reduction potential for the anode (oxidation half-reaction)

Electrons Transferred (n)

What is Cell Potential?

Cell potential (also called electromotive force, EMF, or E°cell) is the measure of the potential difference between two half-cells in an electrochemical cell. It represents the driving force for electron transfer in redox reactions and is measured in volts (V).

Standard Cell Potential Calculation:

E°cell = E°cathode - E°anode

E°cell = E°reduction - E°oxidation

E°cathode: Standard reduction potential where reduction occurs (gains electrons)
E°anode: Standard reduction potential where oxidation occurs (loses electrons)
Positive E°cell: Spontaneous reaction (galvanic/voltaic cell)
Negative E°cell: Non-spontaneous reaction (requires external energy, electrolytic cell)

The Nernst Equation

The Nernst equation allows us to calculate cell potential under non-standard conditions (when concentrations are not 1 M, pressures not 1 atm, or temperature not 25°C).

E = E° - (RT/nF) ln(Q)

At 25°C (298.15 K), this simplifies to:

E = E° - (0.0592/n) log(Q)

Where:

E: Cell potential under non-standard conditions (V)
E°: Standard cell potential (V)
R: Universal gas constant = 8.314 J/(mol·K)
T: Temperature (K)
n: Number of moles of electrons transferred
F: Faraday constant = 96,485 C/mol
Q: Reaction quotient = [products]/[reactants]

Relationship to Thermodynamics

Cell potential is directly related to Gibbs free energy and the equilibrium constant through fundamental thermodynamic relationships.

Gibbs Free Energy

ΔG° = -nFE°

• E° > 0 → ΔG° < 0 (spontaneous)
• E° < 0 → ΔG° > 0 (non-spontaneous)
• E° = 0 → ΔG° = 0 (equilibrium)

Equilibrium Constant

E° = (RT/nF) ln(K)

At 25°C: E° = (0.0592/n) log(K)

• Large K → Large positive E°
• Small K → Negative E°

Common Standard Reduction Potentials (25°C)

Standard reduction potentials (E°) are measured relative to the standard hydrogen electrode (SHE), which is assigned a value of 0.00 V.

Half-Reaction (Reduction)	E° (V)
F₂(g) + 2e⁻ → 2F⁻	+2.87
MnO₄⁻ + 8H⁺ + 5e⁻ → Mn²⁺ + 4H₂O	+1.51
Au³⁺ + 3e⁻ → Au(s)	+1.50
Cl₂(g) + 2e⁻ → 2Cl⁻	+1.36
O₂(g) + 4H⁺ + 4e⁻ → 2H₂O	+1.23
Br₂(l) + 2e⁻ → 2Br⁻	+1.07
Ag⁺ + e⁻ → Ag(s)	+0.80
Fe³⁺ + e⁻ → Fe²⁺	+0.77
I₂(s) + 2e⁻ → 2I⁻	+0.54
Cu²⁺ + 2e⁻ → Cu(s)	+0.34
2H⁺ + 2e⁻ → H₂(g)	0.00
Pb²⁺ + 2e⁻ → Pb(s)	-0.13
Sn²⁺ + 2e⁻ → Sn(s)	-0.14
Ni²⁺ + 2e⁻ → Ni(s)	-0.25
Fe²⁺ + 2e⁻ → Fe(s)	-0.44
Zn²⁺ + 2e⁻ → Zn(s)	-0.76
Al³⁺ + 3e⁻ → Al(s)	-1.66
Mg²⁺ + 2e⁻ → Mg(s)	-2.37
Na⁺ + e⁻ → Na(s)	-2.71
Li⁺ + e⁻ → Li(s)	-3.05

Note: More positive E° values indicate stronger oxidizing agents (better at gaining electrons). More negative E° values indicate stronger reducing agents (better at losing electrons).

Example Calculations

Example 1: Zinc-Silver Galvanic Cell

Cell reaction: Zn(s) + 2Ag⁺(aq) → Zn²⁺(aq) + 2Ag(s)

Half-reactions:

Cathode (reduction): Ag⁺ + e⁻ → Ag, E° = +0.80 V
Anode (oxidation): Zn → Zn²⁺ + 2e⁻, E° = -0.76 V

E°cell = E°cathode - E°anode

E°cell = (+0.80) - (-0.76) = +1.56 V

Result: E°cell = +1.56 V (spontaneous reaction, galvanic cell)

Example 2: Non-Standard Conditions

Given: Same Zn-Ag cell at 25°C with [Zn²⁺] = 0.10 M and [Ag⁺] = 2.0 M

E° = 1.56 V, n = 2, Q = [Zn²⁺]/[Ag⁺]² = 0.10/(2.0)² = 0.025

E = E° - (0.0592/n) log(Q)

E = 1.56 - (0.0592/2) log(0.025)

E = 1.56 - (0.0296) × (-1.602)

E = 1.56 + 0.047 = 1.607 V

Result: E = 1.61 V (higher than standard due to low product/high reactant concentrations)

Example 3: Calculate E° from ΔG°

Given: ΔG° = -301.3 kJ/mol for a reaction with n = 2

ΔG° = -nFE°

E° = -ΔG° / (nF)

E° = -(-301,300 J/mol) / (2 × 96,485 C/mol)

E° = 301,300 / 192,970 = 1.56 V

Result: E° = 1.56 V (positive, confirming spontaneous reaction)

Galvanic vs Electrolytic Cells

Galvanic (Voltaic) Cells

E°cell: Positive (+)
ΔG°: Negative (-)
Nature: Spontaneous
Function: Converts chemical energy to electrical energy
Examples: Batteries, fuel cells
Anode: Negative electrode
Cathode: Positive electrode

Electrolytic Cells

E°cell: Negative (-)
ΔG°: Positive (+)
Nature: Non-spontaneous
Function: Converts electrical energy to chemical energy
Examples: Electrolysis, electroplating
Anode: Positive electrode
Cathode: Negative electrode

Note: All calculations assume ideal conditions. Real electrochemical cells may have additional factors such as overpotential, internal resistance, concentration polarization, and junction potentials that can affect the measured cell potential. Standard reduction potentials are measured at 25°C (298.15 K), 1 M concentration, and 1 atm pressure relative to the standard hydrogen electrode (SHE).

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Nernst Equation Calculator Oxidation State Calculator Gibbs Free Energy Calculator Enthalpy Change Calculator