What is the Nernst equation?

It gives the potential of an electrochemical cell under non-standard conditions by correcting the standard potential for the reaction quotient and temperature. It subtracts the gas constant times temperature, over electrons times Faraday's constant, times the natural log of the quotient.

Why does a battery's voltage drop as it discharges?

As a battery discharges, products build up and reactants are consumed, raising the reaction quotient above one. The Nernst equation then subtracts a larger term from the standard potential, so the cell voltage falls. This calculator shows that effect.

What is the 0.0592 figure?

At 25 degrees Celsius, the gas constant times temperature over Faraday's constant, converted to base-ten logarithms, comes to about 0.0592 volts. So the Nernst equation simplifies to subtracting 0.0592 over the number of electrons, times the log of the quotient, the slope per tenfold change in Q.

Nernst Equation Calculator

This calculator applies the Nernst equation to find the potential of an electrochemical cell or electrode under non-standard conditions. Standard electrode potentials are quoted for a specific set of conditions, with all species at unit concentration or pressure, but real cells rarely sit at those conditions. The Nernst equation corrects the standard potential for the actual concentrations, temperature and reaction quotient, telling you the true voltage a cell will deliver as it operates and its reactants are consumed. It is fundamental to electrochemistry, underpinning batteries, fuel cells, corrosion, pH measurement and biological membrane potentials. This tool computes it. You enter the standard cell or electrode potential, the number of electrons transferred in the reaction, the reaction quotient, which compares the activities of products and reactants, and the temperature, and the calculator returns the actual potential, the standard potential for reference, the term that adjusts it, and the Nernst slope. The results update as you type. Use it for chemistry study, for understanding how a battery's voltage changes as it discharges, or for electrochemistry problems. The equation subtracts from the standard potential a term equal to the gas constant times the temperature, divided by the electrons transferred times Faraday's constant, multiplied by the natural logarithm of the reaction quotient. At 25 degrees Celsius this simplifies to subtracting about 0.0592 over the number of electrons, times the base-ten logarithm of the quotient. A reaction quotient above one, meaning products dominate, lowers the potential, while a quotient below one raises it, which is exactly why a battery's voltage falls as it discharges and products build up. The calculation uses Faraday's constant of 96,485 coulombs per mole and the gas constant of 8.314 joules per mole per kelvin.

Standard potential E° (V)

Electrons (n)

Reaction quotient Q

Temperature (K)

1.0704 V

cell potential

Standard potential1.10 V

Adjustment-0.0296 V

Slope per decade0.0296 V

Nernst: E = E° - (RT/nF) ln Q, with R = 8.314, F = 96485. At 25°C the slope per decade is 0.0592/n. Q above 1 lowers E; below 1 raises it.

How it works

The Nernst equation subtracts from the standard potential a correction term: the gas constant times the temperature, divided by the number of electrons times Faraday's constant, multiplied by the natural logarithm of the reaction quotient. A reaction quotient greater than one lowers the potential as products accumulate, while one less than one raises it.

Worked example

For a cell with a standard potential of 1.10 volts transferring 2 electrons, at 298.15 kelvin with a reaction quotient of 10, the correction is the gas constant times temperature over 2 times Faraday's constant, times the natural log of 10, about 0.0296 volts. The actual potential is 1.10 minus 0.0296, about 1.0704 volts.

Related calculators

Gibbs Free Energy: spontaneity.
Equilibrium Constant: reaction quotient.
pH Calculator: pH and pOH.
Coulomb's Law: charge force.

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