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Nernst Equation Calculator

Cell potential under non-standard conditions.

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Cell Potential

Formula first

Overview

The Nernst equation defines the relationship between the reduction potential of an electrochemical cell and the activities of the chemical species involved under non-standard conditions. It effectively relates the thermodynamics of a reaction to its voltage output by incorporating the reaction quotient and temperature.

Symbols

Variables

E = Cell Potential, E^\theta = Standard Potential, R = Gas Constant, T = Temperature, n = Moles of Electrons

Cell Potential
Standard Potential
Gas Constant
Temperature
Moles of Electrons
Faraday Constant
Reaction Quotient

Apply it well

When To Use

When to use: Apply the Nernst equation when calculating cell voltage for solutions where concentrations are not 1 M or gas pressures are not 1 atm. It is essential when the system is not at standard state or when determining the concentration of ions using a measured potential.

Why it matters: This equation explains why batteries lose voltage as they run out of reactants and allows scientists to calculate the pH of solutions. In biology, it is used to determine the electrical potential across cell membranes, which is vital for nerve signaling.

Avoid these traps

Common Mistakes

  • Using log10 instead of ln.
  • Forgetting to include n.

One free problem

Practice Problem

Calculate the cell potential (E) for a Zn-Cu galvanic cell at 298 K where the reaction quotient (Q) is 50. The standard cell potential (E0) is 1.10 V and the reaction involves the transfer of 2 electrons.

Standard Potential1.1 V
Gas Constant8.314 J/mol K
Temperature298 K
Moles of Electrons2
Faraday Constant96485 C/mol
Reaction Quotient50

Solve for:

Hint: Calculate the term (RT/nF) first, then multiply by the natural log of Q before subtracting from E0.

The full worked solution stays in the interactive walkthrough.

References

Sources

  1. Atkins' Physical Chemistry
  2. IUPAC Gold Book: Nernst equation
  3. Wikipedia: Nernst equation
  4. NIST CODATA
  5. IUPAC Gold Book
  6. Halliday, Resnick, and Walker, Fundamentals of Physics
  7. Atkins' Physical Chemistry, 11th Edition
  8. IUPAC Gold Book (Compendium of Chemical Terminology)