Nernst Equation Calculator

The Nernst equation adjusts cell potential for actual concentrations.

How the Math Works

The Nernst Equation calculates cell potential under non-standard conditions by adjusting the standard electrode potential (E°) based on reaction conditions. The formula E = E° - (RT/nF) ln Q incorporates temperature (T), the gas constant (R), Faraday's constant (F), the number of electrons transferred (n), and the reaction quotient (Q). At 25°C, this simplifies to E = E° - (0.0592V/n) log Q, where the natural logarithm converts to a base-10 logarithm for practical computation. The term (RT/nF) acts as a correction factor that accounts for how temperature and stoichiometry influence the voltage deviation from standard conditions.

Practical Applications

To apply this calculation, first determine the standard cell potential by subtracting the cathode's E° from the anode's E°. Calculate the reaction quotient Q using product concentrations divided by reactant concentrations, each raised to their stoichiometric coefficients. For example, in a Zn-Cu cell with [Zn²⁺] = 0.1M and [Cu²⁺] = 0.01M, Q = [Zn²⁺]/[Cu²⁺] = 10. Plug these values into the Nernst Equation to find the actual cell potential, which will differ from the standard 1.10V due to the concentration imbalance driving the reaction to proceed in the direction that restores equilibrium.

Day-to-Day Use

This calculation helps explain everyday phenomena like why car batteries fail in cold weather—the reduced temperature lowers cell potential, requiring more voltage to start the engine. It also clarifies why saltwater is more corrosive than fresh water: higher ion concentrations change the electrochemical potential, accelerating metal degradation. Understanding these principles aids in designing better batteries, selecting appropriate materials for wiring and plumbing, and even predicting the shelf life of packaged foods by analyzing their internal electrochemical stability.

Worked example

E° 1.1 V, n 2, Q 0.1 → ~1.13 V.

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