Cell Potential Calculator

Calculator Inputs

Example Data Table

Sample copper-zinc cell values illustrate how conditions shift voltage.

Formula Used

Standard cell potential: E°_cell = E°_cathode − E°_anode, using standard reduction potentials for both half-reactions.

Nernst equation:

• E = E° − (RT/nF) ln(Q)
• E = E° − (2.303RT/nF) log₁₀(Q)

Reaction quotient: Q = Π(a_products^ν) / Π(a_reactants^ν) where ν is the stoichiometric coefficient and a is activity (or concentration approximation).

Gibbs energy: ΔG = −nFE.

Equilibrium constant: ln(K) = (nFE°)/(RT).

How to Use This Calculator

1. Select whether to compute E°cell from half-cells or enter E°cell directly.
2. Enter n (electrons) and your temperature in °C or K.
3. Choose log form and calculation style (exact or 25°C shortcut).
4. Either enter Q directly or fill the activities table to build Q.
5. Press Calculate to view E°cell, Ecell, ΔG, and K above the form.

Professional Article

1) Why cell potential matters

Cell potential is the voltage produced by a redox reaction. Many practical cells sit around 0.1–3.0 V. A positive value indicates thermodynamic spontaneity for the stated conditions, while a negative value signals the reverse direction is favored. In labs, open‑circuit voltage is often used to validate reaction setup.

2) Standard potentials as a baseline

Standard reduction potentials (E°) are tabulated at reference conditions, commonly 1 M solutes and 1 bar gases. When you enter two reduction potentials, the calculator uses E°cell = E°cathode − E°anode. For instance, 0.80 V − 0.34 V gives 0.46 V.

3) Electron transfer number n

The electron count n shapes sensitivity to composition. The Nernst correction is divided by n, so a two‑electron process shifts about half as much as a one‑electron process for the same Q. Typical aqueous examples often use n = 1, 2, or 4.

4) Reaction quotient Q from activities

Q summarizes how far conditions are from standard state. Build it from activities using Π(a_products^ν) divided by Π(a_reactants^ν). Solids and liquids are usually treated as activity 1. At 25°C with n = 2, changing Q from 1 to 10 lowers E by about 0.03 V.

5) Temperature dependence with real constants

Temperature enters through RT/F. At 298.15 K, RT/F ≈ 0.0257 V and 2.303RT/F ≈ 0.05916 V, producing the familiar 0.05916/n factor for log10(Q) at 25°C. Higher temperature increases the magnitude of the Q correction.

6) Free energy connection

Voltage links directly to Gibbs energy: ΔG = −nFE. With F = 96485 C/mol, even moderate voltages represent large energy changes. For n = 2 and E = 0.46 V, ΔG is about −88.8 kJ/mol.

7) Equilibrium constant insight

From standard conditions, ln(K) = nFE°/(RT). A larger positive E° means a much larger K, so products dominate at equilibrium. If E° is near zero, K is near one and concentration changes can flip the direction easily.

8) Practical accuracy notes

Use positive activities and correct stoichiometric powers. Concentrations can approximate activities for dilute solutions, but high ionic strength can require activity coefficients. Measured voltages may be lower due to internal resistance, mass transport limits, and electrode kinetics, even when E is favorable. Record conditions, units, and assumptions for reproducible comparisons across experiments.

FAQs

1) What is E°cell and how is it computed?

E°cell is the standard cell potential. If you enter two standard reduction potentials, the calculator uses E°cell = E°cathode − E°anode. Ensure both values are reduction potentials from the same table.

2) What does Q represent in the Nernst equation?

Q is the reaction quotient built from activities (or concentration approximations). It compares product “strength” to reactant “strength” using stoichiometric powers. Q shifts the voltage away from E° as conditions change.

3) When should I use ln(Q) versus log10(Q)?

Use ln(Q) for the natural‑log form and log10(Q) for common textbook form. Both are equivalent when the correct coefficient is used. Choose the one that matches your source data and workflow.

4) Why does n (electrons) matter so much?

The Nernst correction is divided by n, so larger n reduces how much the voltage changes for the same Q. n also scales ΔG through −nFE, affecting the energy magnitude for the reaction.

5) Can I use concentrations instead of activities?

Yes, for dilute solutions concentrations often approximate activities. At higher ionic strength, activity coefficients deviate from one, and concentration-based Q becomes less accurate. Treat results as estimates unless activity data are available.

6) What does a negative Ecell mean?

A negative Ecell indicates the forward reaction is not spontaneous under the entered conditions. Reversing the reaction (or swapping anode/cathode) would yield a positive voltage, assuming the same magnitude and conditions.

7) Why might my measured voltage differ from the calculated value?

Measured voltage can be lower due to internal resistance, polarization, and slow kinetics. Concentration gradients and non‑ideal activities also shift Q. The calculator gives the thermodynamic expectation, not performance losses.