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Nernst Equation

Electrochemical cell potential — E = E° − (RT/nF) · ln Q

Electrochemistry Physical Chemistry Galvanic Cell Thermodynamics
Preset:
Graph:
E° = +1.100 V Q = 1.000 ln Q = 0.000 E = +1.100 V ΔG = −212.5 kJ/mol

⚡ Nernst Equation

The Nernst equation relates the electrochemical cell potential E to its standard potential E° and the reaction quotient Q:

E = E° − (RT / nF) · ln Q

At 25 °C (298 K) this simplifies to: E = E° − (0.02570 / n) · ln Q  =  E° − (0.05916 / n) · log₁₀ Q

E° — standard reduction potential (both half-cells at 1 M, 25 °C, 1 atm) · R = 8.314 J mol⁻¹ K⁻¹ · F = 96485 C mol⁻¹ · n — electrons transferred · Q = [products] / [reactants].

When Q = 1 (standard conditions), ln Q = 0 and E = E°. As reactant concentration increases, Q decreases, raising E above E°. The cell reaches equilibrium when E = 0 and Q = K_eq. The cell voltage also drives ΔG = −nFE.

About the Nernst Equation Simulator

This simulation shows how the potential of an electrochemical (galvanic) cell depends on concentration and temperature, rather than only on the standard value. It is governed by the Nernst equation, E = E° − (RT/nF)·ln Q, where E° is the standard cell potential, R the gas constant (8.314 J mol⁻¹ K⁻¹), F the Faraday constant (96485 C mol⁻¹), n the electrons transferred, and Q the reaction quotient.

You pick a half-cell preset (Zn/Cu, Fe²⁺/Fe³⁺, H₂/H⁺, or MnO₄⁻/Mn²⁺), then adjust oxidised and reduced species concentrations (10⁻³ to 10 M), temperature (200–400 K) and n (1–6). Live readouts give E°, Q, ln Q, E and ΔG = −nFE, with cell, E vs ln Q, and E vs T views. The principle underpins batteries, fuel cells, pH meters and ion-selective sensors.

Frequently Asked Questions

What is the Nernst equation?

The Nernst equation relates the actual potential of an electrochemical cell to its standard potential and the concentrations of the reacting species. It is written E = E° − (RT/nF)·ln Q, showing that cell voltage shifts away from E° whenever conditions differ from the standard 1 M, 25 °C reference state.

What do E°, n and Q stand for?

E° is the standard cell potential measured with all species at 1 M, 298 K and 1 atm. The value n is the number of electrons transferred in the balanced redox reaction. Q is the reaction quotient, the ratio of product to reactant activities; in this model it is taken as the oxidised over reduced concentration ratio.

How do the controls change the result?

The concentration sliders move on a logarithmic scale from 0.001 M to 10 M, altering Q and therefore E. Raising temperature increases the RT/nF prefactor, steepening the slope of E against ln Q. Increasing n shrinks that prefactor, so each tenfold change in Q shifts E by a smaller amount.

Why does E equal E° when Q is one?

When the oxidised and reduced concentrations are equal, Q = 1 and ln Q = 0, so the entire correction term (RT/nF)·ln Q vanishes. The cell then operates exactly at its standard potential E°. This is why the standard state is defined with all species at 1 M.

What is the 0.05916 figure I see in textbooks?

At 298 K the term RT/F multiplied by ln(10) equals about 0.05916 V. This lets the equation be rewritten as E = E° − (0.05916/n)·log₁₀ Q, a convenient base-10 form. The simulator uses the full natural-log version, so its 0.02570/n coefficient is the same quantity before converting to log₁₀.

How is ΔG calculated here?

The Gibbs free energy change is found from ΔG = −nFE, using the live cell potential E. A positive E gives a negative ΔG, meaning the reaction is spontaneous and the cell can do electrical work. The readout is divided by 1000 to display kilojoules per mole.

Is the simulation physically accurate?

It uses the exact Nernst expression with the correct constants and the standard potentials of common half-cells, so the trends and magnitudes are realistic. It does, however, approximate activities by concentrations and ignores junction potentials, ion pairing and electrode kinetics, which matter at high concentration or extreme conditions.

Why does raising temperature change the voltage?

Temperature appears in the RT/nF factor, so it scales how strongly concentration affects potential. If Q is not equal to one, increasing T moves E further from E°; if Q equals one the temperature has no effect because the whole correction term is zero. The E vs T view illustrates this directly.

How does this relate to a pH meter?

A pH meter is a hydrogen or glass electrode whose potential follows the Nernst equation with respect to H⁺ concentration. The H₂/H⁺ preset shows how voltage tracks the logarithm of hydrogen-ion activity, which is exactly what lets a calibrated electrode read pH from a measured potential.

What happens as the cell approaches equilibrium?

As the reaction proceeds, reactants deplete and Q rises toward the equilibrium constant K. The cell potential E falls until it reaches zero, at which point Q = K and no further net current flows. A dead battery is simply a cell whose reaction quotient has reached its equilibrium value.

Which real systems use these half-cells?

The Zn/Cu Daniell cell is a classic teaching battery, the Fe²⁺/Fe³⁺ couple appears in redox flow batteries and titrations, MnO₄⁻/Mn²⁺ is a strong oxidant used in permanganate titrations, and the hydrogen electrode defines the reference scale for all standard potentials.