Physical Chemistry ★★☆ Medium

⚡ Nernst Equation

Animate a galvanic cell and watch cell potential E change as you vary temperature, ion concentrations, and electrode material. Grounded in E = E° − (RT/nF) ln Q with live ΔG and equilibrium constant readouts.

Cations (to cathode) Anions (to anode) Anode (oxidation) Cathode (reduction)
Nernst Equation E = E° − (RT/nF) ln Q

Electrode Pair

E° (standard)1.100 V
n (electrons)2

Conditions

Live Readouts

Q (reaction quotient)1.000
ln Q0.000
RT/nF—
E (cell potential)1.100 V
ΔG = −nFE—
K = exp(nFE°/RT)—

About the Nernst Equation

Derivation from Gibbs Energy

For a half-cell or full cell reaction, the Gibbs free energy change is ΔG = ΔG° + RT ln Q. The electrical work done by the cell equals ΔG = −nFE, so E = E°−(RT/nF) ln Q. At 25 °C (298.15 K) and using log base 10, RT/F ≈ 0.02569 V, giving the common approximation E = E°−(0.0592/n) log Q.

The Daniell Cell

The historic Daniell cell (1836) uses a zinc anode in ZnSO&sub4; solution and a copper cathode in CuSO&sub4; solution, connected by a salt bridge. Zn oxidises (Zn → Zn²&sup+; + 2e−, E° = −0.76 V) and Cu²&sup+ reduces (Cu²&sup+; + 2e− → Cu, E° = +0.34 V), giving E° = 1.10 V. As Zn ion concentration rises and Cu ion concentration falls, Q increases and E decreases until equilibrium (E = 0).

Equilibrium and the EMF

At equilibrium ΔG = 0 and E = 0, so ln K = nFE°/RT. This connects the thermodynamic equilibrium constant K to the standard cell potential E°. A cell with E° > 0 has K > 1 (products favoured), while E° < 0 means K < 1. The Nernst equation quantifies how far Q is from K and hence how much remaining driving force the cell retains.

Temperature Dependence

The RT/nF prefactor increases linearly with T. At higher temperatures concentration effects are amplified: a tenfold change in Q shifts E by (RT/nF) ln 10 ≈ (0.0592 V/n) × T/298. Industrial electrochemical processes (aluminium smelting, chlor-alkali electrolysis, lithium-ion batteries) all rely on precise Nernst-equation calculations to optimise operating voltages and efficiencies.

About this simulation

This simulation animates a galvanic (voltaic) cell and evaluates the Nernst equation E = E° − (RT/nF)·ln Q live as you change conditions. Ions visibly migrate between half-cells, the anode bar shrinks as it oxidises, and the cathode bar grows as metal deposits on it, while a graph plots cell potential E against ln Q so you can see the logarithmic relationship directly rather than just reading a formula.

🔬 What it shows

Choose from real electrode pairs — Zn/Cu (the classic 1836 Daniell cell), Zn/SHE, Fe²⁺/Fe³⁺, or Ag/Au — each with its own standard potential E° and electron count n. The reaction quotient Q is computed from the oxidant and reductant concentration sliders, then combined with temperature to give the working cell potential E, Gibbs free energy ΔG, and equilibrium constant K.

🎮 How to use

Pick an electrode pair from the dropdown, then drag T (temperature), [Red] (reductant concentration) and [Ox] (oxidant concentration) to see E, ln Q, ΔG and K update instantly, along with the animated ion migration and electrode growth. The E vs ln(Q) graph traces the live operating point along the Nernst line as you adjust concentrations.

💡 Did you know?

At standard conditions (298 K, 1 M concentrations), Q = 1 so ln Q = 0 and E simply equals E° — this is exactly why standard reduction potential tables are measured at 1 M and 25°C. Push concentrations away from 1 M and the cell voltage drifts from the textbook value in a way you can watch happen in real time.

Frequently asked questions

What does each term in E = E° − (RT/nF)·ln Q mean?

E° is the standard cell potential for the chosen electrode pair, R is the gas constant, T is absolute temperature, n is the number of electrons transferred per reaction (set by the electrode preset), F is Faraday's constant, and Q is the reaction quotient built from the current oxidant and reductant concentrations.

Why does raising [Ox] or lowering [Red] increase the cell voltage?

Increasing oxidant concentration or decreasing reductant concentration lowers Q. Since E subtracts a term proportional to ln Q, a smaller Q means a smaller subtraction and therefore a higher E — physically, the reaction has more driving force left to reach equilibrium.

How is the Daniell cell (Zn/Cu) actually wired?

Zinc oxidises at the anode (Zn → Zn²⁺ + 2e⁻, E° = −0.76 V) while Cu²⁺ reduces at the cathode (Cu²⁺ + 2e⁻ → Cu, E° = 1.10 V), joined by a salt bridge to complete the circuit. As the reaction proceeds, Zn²⁺ concentration rises and Cu²⁺ falls, so Q increases and E gradually decreases toward zero at equilibrium.

What does ΔG tell you that E doesn't?

ΔG = −nFE converts the cell potential into Gibbs free energy, the standard thermodynamic measure of whether a reaction is spontaneous. A positive E (spontaneous galvanic cell) always corresponds to a negative ΔG, and the equilibrium constant K is the point where ΔG = 0 and E = 0.

Why does temperature affect the cell voltage?

Temperature appears directly in the RT/nF prefactor, so raising T amplifies how much ln Q shifts the potential away from E°. At higher temperatures, the same concentration imbalance produces a larger deviation from the standard potential than it would at room temperature.