Nernst Equation Calculator

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

Understanding the Nernst Equation

The Nernst equation is fundamental in electrochemistry, allowing us to calculate the cell potential under non-standard conditions. It relates the cell potential to the standard electrode potential, temperature, and activities (or concentrations) of the chemical species involved in the reaction.

The Nernst Equation Formula

E = E° - (RT/nF) × ln(Q)

At 25°C (298.15 K): E = E° - (0.0592/n) × log(Q)

E = Cell potential (V)

The actual voltage of the cell under given conditions

E° = Standard cell potential (V)

The voltage when all species are at standard state (1 M, 1 atm, 25°C)

R = Gas constant = 8.314 J/(mol·K)

Universal gas constant

T = Temperature (K)

Usually 298.15 K (25°C) for standard laboratory conditions

n = Electrons transferred

Number of moles of electrons exchanged in the balanced redox reaction

F = Faraday constant = 96,485 C/mol

Charge per mole of electrons

Q = Reaction quotient

Q = [products] / [reactants]

Practical Example

Copper-Zinc Daniell Cell

Zn(s) + Cu²⁺(aq) → Zn²⁺(aq) + Cu(s)

  • E° = 1.10 V
  • n = 2 electrons
  • T = 298.15 K
  • [Cu²⁺] = 0.01 M
  • [Zn²⁺] = 1.0 M
  • Q = [Zn²⁺]/[Cu²⁺] = 1.0/0.01 = 100

E = 1.10 - (8.314 × 298.15)/(2 × 96485) × ln(100)
E = 1.10 - 0.0296 × 4.605
E = 1.10 - 0.136 = 0.964 V

Key Concepts

📊 Concentration Effects

Higher product concentration or lower reactant concentration decreases cell potential

🌡️ Temperature Dependence

Higher temperature increases the magnitude of the concentration correction term

⚡ Standard Potential

E° is characteristic of each redox couple and found in tables

⚖️ Equilibrium

At equilibrium, E = 0 and Q = K (equilibrium constant)

Applications

  • 🔋
    Battery Design: Predict battery voltage under various charge states and conditions
  • 🧪
    pH Measurement: pH electrodes use the Nernst equation to convert voltage to pH
  • ⚗️
    Corrosion Science: Calculate corrosion potential in different environments
  • 🔬
    Analytical Chemistry: Determine ion concentrations using potentiometry
  • 💊
    Biochemistry: Understand redox processes in cellular respiration and metabolism

⚡Quick Reference

Units:

V (volts), K (kelvin)

Formula:

E = E° - (RT/nF) × ln(Q)

Constants:

R = 8.314 J/(mol·K)
F = 96485 C/mol

Level:

College Chemistry

🔗Related Calculators

📐Related Formulas

🎯Where It's Used

  • 🔋

    Battery Technology

    Battery voltage prediction

  • 🧪

    Analytical Chemistry

    Potentiometric measurements

  • ⚗️

    Corrosion Studies

    Corrosion potential analysis

  • 💊

    Biochemistry

    Cellular redox processes