1.1592
V
0.0592
V
-223.68
kJ/mol
1.1592
V
0.0592
V
-223.68
kJ/mol
The Nernst Equation Calculator computes the cell potential under non-standard conditions by accounting for temperature and concentration effects through the reaction quotient (Q). While standard reduction potentials describe cells at 25°C with 1 M concentrations, real electrochemical systems operate under varying conditions. The Nernst equation, developed by Nobel laureate Walther Nernst in 1889, provides the essential link between thermodynamics and electrochemistry for real-world scenarios. This calculator is indispensable for understanding battery voltage variation, pH electrode operation, corrosion prediction, and membrane potential in biological systems. By entering the standard potential, number of electrons transferred, temperature, and reaction quotient, you can determine the actual driving force for any electrochemical reaction.
The Nernst equation relates the cell potential to the reaction quotient:
$$E = E° - \frac{RT}{nF} \ln Q$$
where E is the cell potential under non-standard conditions, E° is the standard cell potential, R = 8.314 J/(mol·K) is the universal gas constant, T is the absolute temperature in kelvin, n is the number of moles of electrons transferred, F = 96,485 C/mol is the Faraday constant, and Q is the reaction quotient.
At 25°C, the equation can be simplified using base-10 logarithm:
$$E = E° - \frac{0.05916}{n} \log_{10} Q$$
When Q < 1 (reactants dominate), the correction term is positive and E > E°. When Q > 1 (products dominate), the correction is negative and E < E°. At equilibrium, Q = K (equilibrium constant), E = 0, and:
$$E° = \frac{RT}{nF} \ln K$$
The associated Gibbs free energy under non-standard conditions is:
$$\Delta G = -nFE$$
When Q < 1, reactant concentrations exceed product concentrations, and the cell potential is higher than E° — the reaction has extra driving force. When Q > 1, product concentrations are high, and the cell potential decreases below E°. When Q = 1, E equals E° exactly (standard conditions). As the reaction proceeds toward equilibrium (Q → K), E approaches zero. The correction term shows how much the concentration effect shifts the potential. Temperature amplifies this correction — at higher temperatures, concentration effects have a larger impact on the cell voltage.
Inputs
Results
E = 1.10 − (8.314 × 298.15)/(2 × 96485) × ln(0.01) = 1.10 − (0.01285)(−4.605) = 1.10 + 0.0592 = 1.1592 V. With Q = 0.01, the cell potential increases by ~59 mV because reactant concentrations are high relative to products.
Inputs
Results
E = 0.46 − (8.314 × 298.15)/(2 × 96485) × ln(500000) = 0.46 − 0.01285 × 13.12 = 0.46 − 0.1687 = 0.2913 V. The large Q significantly reduces the cell potential as the system approaches equilibrium.
The Nernst equation (E = E° − (RT/nF)ln Q) calculates the electrochemical cell potential under non-standard conditions. It accounts for the effect of ion concentrations and temperature on the voltage of an electrochemical cell.
Q is the ratio of product activities to reactant activities, each raised to their stoichiometric coefficients. For the reaction aA + bB → cC + dD, Q = [C]^c[D]^d / [A]^a[B]^b. Pure solids and liquids have activity = 1.
When Q = K, the cell potential E = 0 and no net reaction occurs. The cell is at thermodynamic equilibrium. This gives the important relationship: E° = (RT/nF)ln K, linking standard potentials to equilibrium constants.
At exactly 25°C (298.15 K), (RT/F)ln(10) = (8.314 × 298.15 / 96485) × 2.303 = 0.05916 V. Converting from natural log to log₁₀ and evaluating at standard temperature gives this convenient constant.
A pH electrode measures hydrogen ion activity. The Nernst equation predicts a 59.16 mV change per pH unit at 25°C (since n = 1 for H⁺/H₂). This is the basis for potentiometric pH measurement.
Yes. The full Nernst equation uses temperature T explicitly. However, E° itself may change with temperature. For accurate high-temperature calculations, you need E° at the relevant temperature or use thermodynamic data to correct it.
The Nernst equation calculates membrane potentials in neurons and cells. The equilibrium potential for an ion across a membrane depends on the concentration ratio on both sides. For example, the potassium equilibrium potential is approximately −90 mV in typical neurons.
As a battery discharges, reactants are consumed and products accumulate, increasing Q. This causes the cell voltage to drop according to the Nernst equation, which is why batteries show declining voltage over their discharge cycle.
R must be in J/(mol·K), T in kelvin, F in C/mol, and E in volts. The reaction quotient Q is dimensionless (uses activities). When using concentrations as approximations for activities, they should be in mol/L relative to the standard state of 1 M.
In concentration cells, E° = 0 because both electrodes are identical. The entire potential comes from the Nernst correction: E = (RT/nF)ln(C₁/C₂), driven solely by the concentration difference between the two half-cells.
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