Nernst Equation Calculator
Compute nernst equation using validated scientific equations. See step-by-step derivations, unit analysis, and reference values.
Formula
E = E0 - (RT / nF) * ln(Q)
The Nernst equation adjusts the standard cell potential (E0) for non-standard conditions. R is the gas constant (8.314 J/mol K), T is temperature (K), n is electrons transferred, F is Faraday's constant (96,485 C/mol), and Q is the reaction quotient of products over reactants.
Worked Examples
Example 1: Zinc-Copper Cell at Non-Standard Concentrations
Problem: Calculate the cell potential for Zn/Cu cell (E0 = 1.10 V, n = 2) when [Zn2+] = 0.1 M and [Cu2+] = 1.0 M at 25 C.
Solution: Q = [Zn2+]/[Cu2+] = 0.1/1.0 = 0.1\nE = 1.10 - (0.02569/2) ln(0.1)\nE = 1.10 - (0.01285)(-2.3026)\nE = 1.10 + 0.0296 = 1.1296 V
Result: E = 1.130 V (higher than E0 due to Q < 1)
Example 2: Concentration Cell
Problem: Find the potential of a Cu/Cu2+ concentration cell with [Cu2+] = 0.01 M on one side and 1.0 M on the other (E0 = 0, n = 2).
Solution: Q = [Cu2+ dilute]/[Cu2+ conc] = 0.01/1.0 = 0.01\nE = 0 - (0.02569/2) ln(0.01)\nE = -(0.01285)(-4.6052)\nE = 0.0592 V
Result: E = 0.0592 V from concentration difference alone
Frequently Asked Questions
What is the Nernst equation?
The Nernst equation relates the cell potential of an electrochemical cell to the standard electrode potential and the activities (or concentrations) of the chemical species involved. It is expressed as E = E0 - (RT/nF) ln(Q), where E is the cell potential under non-standard conditions, E0 is the standard cell potential, R is the gas constant (8.314 J/mol K), T is temperature in Kelvin, n is the number of moles of electrons transferred, F is Faraday's constant (96,485 C/mol), and Q is the reaction quotient. At 25 degrees Celsius, this simplifies to E = E0 - (0.02569/n) ln(Q) or equivalently E = E0 - (0.05916/n) log10(Q). The equation was developed by Walther Nernst in 1889.
What is the relationship between the Nernst equation and equilibrium?
At equilibrium, the cell potential E equals zero and the reaction quotient Q equals the equilibrium constant K. Substituting these into the Nernst equation gives 0 = E0 - (RT/nF) ln(K), which rearranges to E0 = (RT/nF) ln(K) or equivalently K = exp(nFE0/RT). This powerful relationship connects electrochemistry to chemical equilibrium. A large positive E0 corresponds to a very large K, meaning the reaction strongly favors products. At 25 degrees Celsius, each 0.0592 V of standard potential corresponds to a factor of 10 in the equilibrium constant per electron transferred. For example, a cell with E0 = 1.10 V and n = 2 has K approximately equal to 10 to the 37th power.
How is the Nernst equation used in pH measurements?
The pH meter is one of the most common practical applications of the Nernst equation. A glass electrode develops a potential that depends on the hydrogen ion concentration difference across a thin glass membrane. The potential follows the Nernst equation: E = E0 + (RT/F) ln([H+]) = E0 - (RT/F) times 2.303 times pH. At 25 degrees Celsius, this gives a sensitivity of approximately 59.16 mV per pH unit. This is why pH meters must be temperature-compensated, as the Nernst factor RT/F changes with temperature. The reference electrode provides a stable potential against which the indicator electrode potential is measured, allowing accurate determination of the solution pH.
What are the limitations of the Nernst equation?
The Nernst equation has several limitations that affect its accuracy in certain conditions. It uses concentrations as approximations for activities, which is only valid in dilute solutions. For concentrated solutions, true thermodynamic activities must be used, requiring activity coefficients from models like Debye-Huckel. The equation assumes the reaction is reversible and at quasi-equilibrium, which may not hold at high current densities where kinetic overpotentials become significant. Temperature dependence is accounted for through the RT/nF factor, but the standard potential E0 itself varies with temperature, and the equation does not capture this. For gas-phase reactions, partial pressures rather than concentrations should be used in the reaction quotient.
Is Nernst Equation Calculator free to use?
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How do I get the most accurate result?
Enter values as precisely as possible using the correct units for each field. Check that you have selected the right unit (e.g. kilograms vs pounds, meters vs feet) before calculating. Rounding inputs early can reduce output precision.