Free Nernst Equation Calculator

The Nernst equation is a cornerstone of electrochemistry. This reduction potential calculator (also referred to as a cell potential calculator) applies the Nernst equation to determine the actual potential of a half‑cell or full‑cell reaction under any temperature and concentration conditions. It serves as a comprehensive electrochemistry calculator for students, researchers, and professionals who need quick and accurate results.

Reduction Potential and Standard Electrode Potential

Reduction potential (redox potential) indicates how strongly a chemical species tends to gain electrons and be reduced. A higher potential means a stronger tendency to be reduced, while a lower potential indicates a preference for oxidation. However, a high potential does not guarantee the reaction will occur; some activation energy is typically required. Because absolute potential values are hard to measure, potentials are always reported relative to a reference. The standard electrode potential (often called standard reduction potential) is measured with respect to the standard hydrogen electrode (SHE), which is arbitrarily assigned 0 V. Standard conditions include a temperature of 25 °C, unit activity for each ion, and a pressure of 1 bar for gases.

The Nernst Equation (Cell Potential Equation)

The Nernst equation relates the reduction potential $E$ to the standard electrode potential $E₀$, temperature $T$, the number of electrons transferred $z$, and the ratio of activities (or concentrations) of the reduced and oxidized species:

$$E = E₀ - \frac{RT}{zF} \ln\frac{[\text{red}]}{[\text{ox}]}$$

Where:

• $E$ – reduction potential under non‑standard conditions (V)
• $E₀$ – standard electrode potential (V, relative to SHE)
• $R$ – universal gas constant, $8.314\ \text{J/(K·mol)}$
• $T$ – absolute temperature (K)
• $z$ – moles of electrons transferred in the balanced half‑ or full‑cell reaction
• $F$ – Faraday constant, $96485.3\ \text{C/mol}$
• $[\text{red}]$ – activity (or molar concentration) of the species being reduced
• $[\text{ox}]$ – activity (or molar concentration) of the species being oxidized

In many practical situations, concentrations can replace activities when the solution is dilute.

Worked Example

Consider the spontaneous redox reaction between magnesium and lead ions:

Oxidation (anode): $\text{Mg} \rightarrow \text{Mg}^{2+} + 2e^-$, $E_\text{ox} = +2.38\ \text{V}$
Reduction (cathode): $\text{Pb}^{2+} + 2e^- \rightarrow \text{Pb}$, $E_\text{red} = -0.13\ \text{V}$

Overall: $\text{Pb}^{2+}(aq) + \text{Mg}(s) \rightarrow \text{Mg}^{2+}(aq) + \text{Pb}(s)$
Standard cell potential: $E₀ = 2.38\ \text{V} + (-0.13\ \text{V}) = 2.25\ \text{V}$

Two electrons are transferred ($z = 2$). The temperature is 25 °C (298.15 K). The concentration of Pb²⁺ is 0.200 M and that of Mg²⁺ is 0.020 M.

The reaction quotient for the net cell reaction is:

$$Q = \frac{[\text{Mg}^{2+}]}{[\text{Pb}^{2+}]} = \frac{0.020}{0.200} = 0.1$$

The Nernst equation for the full cell then becomes:

$$\begin{aligned} E &= E₀ - \frac{RT}{zF} \ln Q \\ &= 2.25\ \text{V} - \frac{(8.314\ \text{J/(K·mol)})(298.15\ \text{K})}{(2)(96485.3\ \text{C/mol})} \ln(0.1) \\ &= 2.25\ \text{V} - (0.01285\ \text{V})(-2.303) \\ &= 2.25\ \text{V} + 0.0296\ \text{V} = 2.28\ \text{V} \end{aligned}$$

This calculated cell potential (2.28 V) is slightly higher than the standard value (2.25 V) because the concentration ratio is not 1. Using a dedicated electrochemistry calculator like this Nernst equation tool allows you to quickly evaluate the effect of different temperatures and concentrations on the cell potential.