Nernst Equation Calculator

Electrochemical Potential & Cell Kinetics Solver

Input Parameters

V
mol
K
Q
Galvanic Cell Live Model Active
Cell Potential (E_cell)
1.0704 V
Reaction is spontaneous under non-standard conditions.
Mathematical Working & Substitutions
E_cell = E°_cell − (RT/nF) × ln(Q)

Understanding the Nernst Equation

What is the Nernst Equation?

The Nernst Equation is a fundamental equation in electrochemistry that calculates the reduction potential of a half-cell or the overall electromotive force (EMF) of a galvanic cell under non-standard concentrations, temperatures, and pressures.

The Mathematical Formula

The general representation of the Nernst equation is:

Ecell = E°cell − (RT / nF) × ln(Q)

Where the parameters are defined as:

Special Case: Standard Temperature (298.15 K / 25°C)

When the temperature is exactly 298.15 K, the term RT/F multiplied by the conversion factor from natural log (ln) to base-10 logarithm (2.302585) simplifies to a constant:

Ecell = E°cell − (0.0592 / n) × log10(Q)

This simplified equation is widely used in school curriculums and exams (such as CBSE, NCERT, JEE, and NEET) for rapid electrochemical evaluations.

Interactive Galvanic Cell Simulation

The simulator above demonstrates the operational state of a galvanic/electrochemical cell based on your inputs:

Solved Examples

Example 1: Daniell Cell Potential at 25°C

Problem: Calculate the potential of a Daniell cell represented by Zn | Zn2+(0.1 M) || Cu2+(0.01 M) | Cu. The standard potential E°cell is 1.10 V.

Solution:

  1. Identify parameters: n = 2 electrons; T = 298.15 K.
  2. Write the cell reaction: Zn(s) + Cu2+(aq) → Zn2+(aq) + Cu(s).
  3. Calculate Reaction Quotient (Q): Q = [Zn2+] / [Cu2+] = 0.1 / 0.01 = 10.
  4. Apply Nernst Equation: E = 1.10 − (0.0592 / 2) × log10(10)
  5. E = 1.10 − 0.0296 × 1 = 1.0704 V.
Example 2: Standard Hydrogen Electrode at pH = 10

Problem: Determine the electrode potential of a hydrogen electrode in contact with a solution whose pH is 10. (Standard potential E° = 0.00 V, hydrogen pressure = 1 bar).

Solution:

  1. Write the half-cell reaction: 2H+(aq) + 2e− → H2(g). Here n = 2.
  2. At pH = 10, the concentration of hydrogen ions [H+] = 10−10 M.
  3. Calculate Q: Q = pH2 / [H+]2 = 1 / (10−10)2 = 1 / 10−20 = 1020.
  4. Substitute values at 298.15 K: E = 0.00 − (0.0592 / 2) × log10(1020)
  5. E = 0.00 − 0.0296 × 20 = −0.592 V.
Example 3: Non-Standard Fe-Ag Redox Potential

Problem: Calculate Ecell at 25°C for the reaction: Fe(s) + 2Ag+(0.1 M) → Fe2+(0.01 M) + 2Ag(s). Given E°cell = 1.24 V.

Solution:

  1. Find electrons transferred: Fe oxidizes to Fe2+ (2 electrons), and two Ag+ reduce to Ag. Thus, n = 2.
  2. Compute Q: Q = [Fe2+] / [Ag+]2 = 0.01 / (0.1)2 = 0.01 / 0.01 = 1.0.
  3. Apply Nernst Equation: E = 1.24 − (0.0592 / 2) × log10(1.0)
  4. Since log10(1) = 0, the log term becomes zero.
  5. E = 1.24 − 0 = 1.24 V (Cell potential equals standard potential when Q = 1).

Frequently Asked Questions

What is the difference between E_cell and E°_cell?
E°cell represents the cell potential measured under standard conditions: all solutions are at 1.0 M concentration, gases are at 1.0 bar pressure, and the temperature is 298.15 K (25°C). Ecell is the actual potential measured under any non-standard concentrations, temperatures, or gas pressures.
What is the reaction quotient (Q) in electrochemistry?
The reaction quotient Q is the ratio of product concentration to reactant concentration at any given moment in the reaction. In the Nernst equation, only aqueous ions and gases are included in Q. Pure solids and pure liquids are assigned an activity of 1 and do not affect Q.
Why does the cell potential decrease as a battery discharges?
As the reaction inside a battery proceeds (discharging), reactants are converted into products. Consequently, the concentration of reactants decreases, and products increase, raising the reaction quotient Q. According to the Nernst equation, a larger Q increases the subtraction term, which drives the cell potential (Ecell) down until it reaches 0 V (equilibrium).
Can cell potential be negative? What does it signify?
Yes, a negative cell potential (Ecell < 0) means the reaction is non-spontaneous in the forward direction. Instead, the reverse reaction is spontaneous. In a galvanic cell, a negative potential indicates that the anode and cathode roles have inverted relative to the assumed cell diagram.