Cell Potential Calculator

Calculate electrochemical cell potential, EMF, and Gibbs free energy. Use the Nernst equation for non-standard conditions.

Standard Cell Potential
Nernst Equation
Electrode Comparison
Cathode (Reduction Half-Cell)
Anode (Oxidation Half-Cell)
Cathode (Reduction Half-Cell)
Anode (Oxidation Half-Cell)
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Cell Potential Calculation Results

Nernst Equation Calculator

Calculate cell potential under non-standard conditions using the Nernst equation:

E = E° - (RT/nF) ln Q
V
°C

Understanding Cell Potential

Cell potential (Ecell), also known as electromotive force (EMF), is the measure of the potential difference between two half-cells in an electrochemical cell. It determines the direction of spontaneous redox reactions and the amount of electrical work the cell can perform.

Key Insight: A positive cell potential indicates a spontaneous reaction, while a negative value indicates a non-spontaneous reaction that would require energy input to occur.

Types of Cell Potentials

1

Standard Cell Potential (E°cell): Measured under standard conditions (1 M concentrations, 1 atm pressure, 25°C). Calculated as E°cell = E°cathode - E°anode.

2

Non-Standard Cell Potential (Ecell): Calculated using the Nernst equation to account for non-standard conditions such as different concentrations or temperatures.

3

Equilibrium Cell Potential: The cell potential when the system is at equilibrium (Ecell = 0 V). At this point, the forward and reverse reaction rates are equal.

The Nernst Equation

The Nernst equation relates the cell potential to the standard cell potential and the reaction quotient (Q):

E = E° - (RT/nF) ln Q

Where:

  • E = Cell potential under non-standard conditions
  • E° = Standard cell potential
  • R = Universal gas constant (8.314 J/mol·K)
  • T = Temperature in Kelvin
  • n = Number of electrons transferred in the redox reaction
  • F = Faraday's constant (96485 C/mol)
  • Q = Reaction quotient

Standard Electrode Potentials

Half-Reaction E° (V) Reducing Power
Li⁺ + e⁻ → Li (s) -3.04 Strong
K⁺ + e⁻ → K (s) -2.93 Strong
Ca²⁺ + 2e⁻ → Ca (s) -2.87 Strong
Na⁺ + e⁻ → Na (s) -2.71 Strong
Mg²⁺ + 2e⁻ → Mg (s) -2.37 Strong
Al³⁺ + 3e⁻ → Al (s) -1.66 Moderate
Zn²⁺ + 2e⁻ → Zn (s) -0.76 Moderate
Fe²⁺ + 2e⁻ → Fe (s) -0.44 Weak
Pb²⁺ + 2e⁻ → Pb (s) -0.13 Weak
2H⁺ + 2e⁻ → H₂ (g) 0.00 Reference
Cu²⁺ + 2e⁻ → Cu (s) +0.34 Weak
Ag⁺ + e⁻ → Ag (s) +0.80 Moderate
Au⁺ + e⁻ → Au (s) +1.68 Strong

Relationship to Thermodynamics

Cell potential is directly related to the Gibbs free energy change (ΔG) of the redox reaction:

ΔG = -nFEcell

Where:

  • ΔG = Gibbs free energy change (J/mol)
  • n = Number of electrons transferred
  • F = Faraday's constant (96485 C/mol)
  • Ecell = Cell potential (V)

A negative ΔG (positive Ecell) indicates a spontaneous reaction, while a positive ΔG (negative Ecell) indicates a non-spontaneous reaction.

Practical Application: Cell potential calculations are essential in designing batteries, fuel cells, and corrosion prevention systems. They help predict which metals will corrode when in contact and determine the voltage output of electrochemical cells.

Frequently Asked Questions

Cell potential (Ecell) is the theoretical maximum voltage an electrochemical cell can produce under specific conditions. The actual voltage measured may be lower due to factors like internal resistance, concentration polarization, and activation overpotential.

Temperature affects cell potential through the Nernst equation. As temperature increases, the (RT/nF) term increases, which can either increase or decrease the cell potential depending on the reaction quotient Q. For most reactions, cell potential decreases slightly with increasing temperature.

The standard hydrogen electrode (SHE) is assigned a potential of 0.00 V by convention. It provides a consistent reference point against which all other electrode potentials can be measured. The SHE consists of a platinum electrode in contact with H₂ gas at 1 atm and H⁺ ions at 1 M concentration.

Yes, a negative cell potential indicates that the reaction is non-spontaneous under the given conditions. To make the reaction occur, energy would need to be supplied to the system (electrolysis). A positive cell potential indicates a spontaneous reaction that can produce electrical energy.

Cell potential determines the voltage of a battery, but it doesn't directly determine battery life. Battery life (capacity) depends on the amount of active material available for the redox reaction. However, as a battery discharges, the cell potential gradually decreases due to changes in concentration and other factors, which is why batteries eventually "die."