Nernst Equation Calculator

Calculate electrode (cell) potential with the Nernst equation.

Input the standard electrode potential, temperature, number of electrons, and the concentrations and coefficients for all products and reactants. The calculator will compute the cell potential using the Nernst equation.

Try an example: Zn/Cu cell, H+ reduction, Cl- oxidation, biological membrane...
Nernst Equation Examples

Explore common electrochemical scenarios:

Zn/Cu Galvanic Cell

Zn/Cu Galvanic Cell

Zn2+ (0.01 M), Cu2+ (1.0 M), z = 2, E° = 1.10 V, 25°C

Standard Electrode Potential (E°): 1.1 V | Temperature: 25 °C | Number of Electrons (z): 2
Products:Name: Cu2+, Concentration: 1, Coefficient: 1
Reactants:Name: Zn2+, Concentration: 0.01, Coefficient: 1

Hydrogen Ion Reduction

Hydrogen Ion Reduction

2H+ (0.001 M), H2 (1 atm), z = 2, E° = 0.00 V, 25°C

Standard Electrode Potential (E°): 0 V | Temperature: 25 °C | Number of Electrons (z): 2
Products:Name: H2, Concentration: 1, Coefficient: 1
Reactants:Name: H+, Concentration: 0.001, Coefficient: 2

Chloride Oxidation

Chloride Oxidation

Cl2 (1 atm), Cl- (0.1 M), z = 2, E° = 1.36 V, 25°C

Standard Electrode Potential (E°): 1.36 V | Temperature: 25 °C | Number of Electrons (z): 2
Products:Name: Cl2, Concentration: 1, Coefficient: 1
Reactants:Name: Cl-, Concentration: 0.1, Coefficient: 2

Biological Membrane Potential

Biological Membrane Potential

K+ (140 mM inside, 4 mM outside), z = 1, E° = 0.00 V, 37°C

Standard Electrode Potential (E°): 0 V | Temperature: 37 °C | Number of Electrons (z): 1
Products:Name: K+ (outside), Concentration: 0.004, Coefficient: 1
Reactants:Name: K+ (inside), Concentration: 0.14, Coefficient: 1
Other Titles
Understanding the Nernst Equation: A Comprehensive Guide
Master the concept, calculation, and applications of the Nernst equation in electrochemistry.

What is the Nernst Equation?

  • Definition and Importance
  • Physical Meaning in Electrochemistry
  • Role in Cell Potentials
The Nernst equation relates the reduction potential of an electrochemical cell to the standard electrode potential, temperature, and activities (concentrations) of the chemical species involved.
Why is the Nernst Equation Important?
It allows chemists to predict cell voltages under non-standard conditions and is fundamental in electrochemistry, biology, and physiology.

Nernst Equation in Practice

  • A Zn/Cu cell with non-standard ion concentrations.
  • Membrane potential in nerve cells.

Step-by-Step Guide to Using the Nernst Equation Calculator

  • Inputting Standard Potential and Temperature
  • Adding Products and Reactants
  • Interpreting Results
To use the calculator, enter the standard electrode potential, temperature, and number of electrons. Add all products and reactants with their concentrations and coefficients. The calculator computes the reaction quotient (Q) and the cell potential (E).
How to Read the Results
The result shows the calculated cell potential and the value of Q. The formula used is E = E° - (RT/zF) ln Q.

Step-by-Step Examples

  • For Zn/Cu: E° = 1.10 V, [Cu2+] = 1.0 M, [Zn2+] = 0.01 M, z = 2, T = 25°C.
  • For H+ reduction: E° = 0.00 V, [H+] = 0.001 M, [H2] = 1 atm, z = 2, T = 25°C.

Real-World Applications of the Nernst Equation

  • Batteries and Fuel Cells
  • Biological Membranes
  • Analytical Chemistry
The Nernst equation is used to calculate the voltage of batteries, fuel cells, and biological membranes. It is also essential in analytical techniques such as potentiometry and pH measurement.
Where is the Nernst Equation Used?
From industrial electrolysis to nerve impulse transmission, the Nernst equation is a key tool in science and engineering.

Applications in Science and Industry

  • Calculating the voltage of a lead-acid battery.
  • Estimating the membrane potential of a neuron.

Common Misconceptions and Correct Methods

  • Misunderstanding Q Calculation
  • Ignoring Temperature Effects
  • Incorrect Coefficient Usage
A common mistake is to omit coefficients or use incorrect concentrations in Q. Always use the correct stoichiometry and ensure all concentrations are in mol/L. Temperature must be in Kelvin for the general formula.
Best Practices for Accurate Results
Double-check all input values and units. For biological systems, use the correct temperature (e.g., 37°C for humans).

Avoiding Calculation Errors

  • Forgetting to convert °C to K.
  • Using partial pressures instead of concentrations for gases.

Mathematical Derivation and Examples

  • The Nernst Equation Formula
  • Worked Calculation Examples
  • Interpreting the Results
The Nernst equation is derived from thermodynamic principles and relates the Gibbs free energy change to the cell potential. It quantifies how cell voltage depends on ion concentrations and temperature.
Example Calculation
For a Zn/Cu cell: E = 1.10 - (0.05916/2) log([Zn2+]/[Cu2+]) at 25°C.

Mathematical Examples

  • For Cl- oxidation: E = 1.36 - (0.05916/2) log([Cl-]^2/[Cl2]) at 25°C.
  • For K+ membrane: E = 0.00 - (0.0615/1) log([K+ inside]/[K+ outside]) at 37°C.