Calculate non-standard cell potentials using the Nernst equation with concentration, temperature, and pH effects on electrode and cell potentials.
The Nernst equation extends the standard cell potential to non-standard conditions, accounting for the actual concentrations (activities) of reactants and products, temperature, and the number of electrons transferred. Named after Walther Nernst, who derived it in 1889, this equation is indispensable for predicting real-world electrochemical behavior.
The equation E = E° − (RT/nF)·ln(Q) relates the actual cell potential E to the standard potential E°, temperature T, electrons transferred n, and the reaction quotient Q. At 25°C, this simplifies to E = E° − (0.05916/n)·log(Q), showing that a tenfold increase in product concentration reduces the cell potential by 59.16/n millivolts — the famous Nernstian slope.
This calculator handles both full cell and half-cell Nernst calculations, supports concentration cells (where the driving force comes entirely from concentration differences), pH-dependent redox potentials, and temperature effects. It's essential for understanding pH meters, ion-selective electrodes, biological redox systems, corrosion prediction, and battery behavior under real operating conditions.
This calculator makes non-standard electrochemistry accessible — input your actual concentrations and instantly see how they shift the cell potential. Essential for pH calculations, corrosion prediction, and understanding battery discharge behavior. This nernst equation calculator helps you compare outcomes quickly and reduce avoidable mistakes when making day-to-day care decisions. Use the estimate as a planning baseline and confirm final decisions with a qualified professional when risk is high.
Nernst Equation: E = E° − (RT/nF)·ln(Q) = E° − (0.05916/n)·log₁₀(Q) at 25°C, where R = 8.314 J/(mol·K), T = temperature (K), n = electrons transferred, F = 96,485 C/mol, Q = reaction quotient ([products]/[reactants]).
Result: E = 1.159 V
For the Daniell cell at Q = 0.01 (excess reactants): E = 1.10 − (0.05916/2)·log(0.01) = 1.10 − (0.02958)(−2) = 1.10 + 0.059 = 1.159 V. Lower Q increases the cell potential.
Standard potentials (E°) are measured under ideal conditions: 1 M concentrations, 1 atm gas pressures, 25°C. Real electrochemical systems rarely operate under these conditions. A car battery at −20°C with partially discharged electrolyte, a neuron maintaining ion gradients across its membrane, or a corroding steel pipe in seawater — all require the Nernst equation to predict actual potentials. The correction can be small (a few millivolts) or large (hundreds of millivolts), depending on how far conditions deviate from standard.
The glass electrode pH meter is the most widespread application of the Nernst equation. The potential across the glass membrane responds to the hydrogen ion activity with a theoretical Nernstian slope of 59.16 mV per pH unit at 25°C. Modern pH meters digitally compensate for temperature (ATC) because the slope is proportional to absolute temperature. Understanding this Nernst relationship is essential for calibrating pH meters and recognizing when electrodes are degrading (sub-Nernstian response).
Concentration cells generate potential purely from concentration gradients — no different metals needed. Biological systems like neurons exploit this principle: the ~60 mV resting membrane potential arises from K⁺ concentration differences across the membrane, described by the Nernst equation for potassium ions. The Goldman-Hodgkin-Katz equation extends this to multiple ions simultaneously, but the Nernst equation for each ion individually provides the equilibrium potential (reversal potential) that governs ion channel behavior.
It predicts the voltage of an electrochemical cell under non-standard conditions by adjusting E° for actual concentrations, temperature, and other factors using the reaction quotient Q. This keeps planning practical and lowers the chance of preventable errors.
Q has the same form as the equilibrium constant expression but uses actual, instantaneous concentrations instead of equilibrium values. Q = [products]^coeff / [reactants]^coeff.
At 25°C, the cell potential changes by 59.16/n mV per tenfold change in Q. For a pH electrode (n = 1), this gives 59.16 mV per pH unit — the basis of pH measurement.
When the cell reaches equilibrium, Q = K and E = 0. The cell can no longer do work. This is why batteries go "dead" — they reach chemical equilibrium.
A cell where both electrodes are the same material but in solutions of different concentrations. E° = 0, so the potential comes entirely from the Nernst correction: E = −(RT/nF)·ln(Q).
The Nernstian slope (RT/F) increases linearly with temperature. At 37°C (body temp), it's 61.54/n mV per decade instead of 59.16/n mV at 25°C.