Nernst Equation Calculator

The Nernst Equation Calculator computes the actual cell potential of an electrochemical (galvanic) cell when conditions are not standard — that is, when concentrations, pressures, or temperature differ from the reference state. Standard reduction potentials only tell you the voltage at 1 M concentrations and 25 °C; in the real world a battery's voltage drifts as it discharges and concentrations change. The Nernst equation captures exactly that drift, and this tool turns it into a cell voltage, a Gibbs free energy ΔG, an equilibrium constant K, and a clear spontaneity verdict — complete with an interactive plot of E versus log Q.

What Is the Nernst Equation?

The Nernst equation links the measured cell potential \( E \) to the standard cell potential \( E^{\circ} \) and the composition of the cell through the reaction quotient \( Q \). Named after the German chemist Walther Nernst, it is one of the cornerstones of electrochemistry, used in batteries, pH meters, ion-selective electrodes, corrosion science, and biology (nerve and membrane potentials).

where:

• \( E \) — the actual cell potential (volts)
• \( E^{\circ} \) — the standard cell potential (volts)
• \( R \) — the universal gas constant, 8.314 J mol⁻¹ K⁻¹
• \( T \) — the temperature in kelvin (K)
• \( n \) — the number of moles of electrons transferred in the balanced reaction
• \( F \) — the Faraday constant, 96485 C mol⁻¹
• \( Q \) — the reaction quotient (ratio of product to reactant activities)

The Simplified Form at 25 °C

At the standard laboratory temperature of 25 °C (298.15 K), the group of constants \( \frac{2.303\,RT}{F} \) evaluates to about 0.0592 V. Converting the natural log to base-10 log gives the version most students memorize:

This is why a tenfold change in the reaction quotient shifts the cell potential by 0.0592/n volts. Because the slope depends on temperature, this calculator does not hard-code 0.0592 — it recomputes the slope for whatever temperature you enter, so results stay correct for warm or cold cells.

How to Use the Nernst Equation Calculator

1. Enter the standard cell potential E°: This is the difference between the cathode and anode standard reduction potentials (E°cathode − E°anode), in volts.
2. Enter the number of electrons n: Use the number of electrons transferred in the balanced overall cell reaction.
3. Set the temperature: Defaults to 25 °C. Change it for non-ambient cells.
4. Provide the reaction quotient: Either enter Q directly, or switch to concentration mode and enter the combined product and reactant concentration terms.
5. Click Calculate: Read the cell potential, the spontaneity verdict, ΔG, and K, and explore the Nernst line chart and the animated galvanic-cell diagram.

Worked Example: The Daniell Cell

Consider a zinc–copper (Daniell) cell, Zn | Zn²⁺ || Cu²⁺ | Cu, with \( E^{\circ} = 1.10 \) V and \( n = 2 \). Suppose [Zn²⁺] = 1.0 M and [Cu²⁺] = 0.001 M, so \( Q = \frac{[\text{Zn}^{2+}]}{[\text{Cu}^{2+}]} = 1000 \). At 25 °C:

The lowered copper concentration pulls the voltage down slightly from the standard 1.10 V. As the cell discharges and [Cu²⁺] falls further, the voltage keeps dropping until it reaches zero — the point at which the cell is "dead" and the reaction has reached equilibrium.

Reaction Quotient Q and the Equilibrium Constant K

The reaction quotient \( Q \) has the same algebraic form as the equilibrium constant \( K \), but uses the current (non-equilibrium) concentrations. When \( Q < K \), the forward reaction is favored and \( E > 0 \); when \( Q > K \), the reverse reaction is favored and \( E < 0 \); and when \( Q = K \), the cell is at equilibrium with \( E = 0 \). Setting \( E = 0 \) in the Nernst equation gives the elegant link between standard potential and equilibrium:

Cell Potential, Spontaneity, and Free Energy

What Affects the Cell Potential?

Common Applications

• Batteries and fuel cells — predicting how voltage falls as reactants are consumed.
• pH and ion-selective electrodes — the glass pH electrode is a direct application of the Nernst equation.
• Concentration cells — generating voltage purely from a concentration difference (E° = 0).
• Corrosion — assessing whether a metal will oxidize under specific environmental conditions.
• Biology — resting membrane potentials of neurons follow the same equation.

Frequently Asked Questions

What is the Nernst equation?

The Nernst equation relates the actual cell potential of an electrochemical cell to the standard cell potential and the concentrations of the species involved. It is written E = E° − (RT/nF) ln Q, where E° is the standard cell potential, R is the gas constant, T is the temperature in kelvin, n is the number of electrons transferred, F is the Faraday constant, and Q is the reaction quotient.

How do you calculate cell potential under non-standard conditions?

Start from the standard cell potential E°, then subtract the correction term (RT/nF) ln Q. At 25 °C this simplifies to E = E° − (0.0592/n) log10 Q. Enter your reaction quotient or the product and reactant concentrations, the number of electrons, and the temperature, and the calculator does the rest.

What is the reaction quotient Q in the Nernst equation?

Q is the ratio of product activities to reactant activities for the cell reaction, each raised to its stoichiometric coefficient. For dilute solutions, concentrations in mol/L are used. When all species are at standard conditions Q equals 1, so ln Q is 0 and the cell potential equals E°.

Why is the Nernst slope 0.0592 divided by n?

At 25 °C (298.15 K) the term 2.303RT/F equals about 0.0592 volts. Dividing by n gives the change in cell potential per tenfold change in the reaction quotient. At other temperatures the slope changes because it is proportional to T, so this calculator recomputes it for the temperature you enter.

How is the equilibrium constant related to the Nernst equation?

At equilibrium the cell potential E is zero and Q equals the equilibrium constant K. Setting E = 0 in the Nernst equation gives log10 K = nFE°/(2.303RT). A positive standard potential therefore corresponds to a large equilibrium constant and a product-favored reaction.

What does a positive or negative cell potential mean?

A positive cell potential (E > 0) means the reaction is spontaneous as written and the cell behaves like a battery (galvanic). A negative cell potential (E < 0) means the reaction is non-spontaneous and needs an external voltage to be driven (electrolytic). When E is zero the cell is at equilibrium and delivers no net current.

Additional Resources

• Nernst Equation - Wikipedia
• Galvanic Cell - Wikipedia