π Nernst Equation Calculator
Real cell potentials, not just standard ones.
How to Use This Calculator
Enter the standard potential, electron count, reaction quotient Q, and temperature. You get the actual cell potential and spontaneity.
The Nernst Equation
At 25 Β°C: E = EΒ° - (0.0592 / n) log10 Q
The logarithmic term means a tenfold concentration change shifts E by 0.0592/n volts at room temperature. pH meters exploit this: a glass electrode's voltage tracks hydrogen ion activity logarithmically.
Worked Example
Daniell cell, EΒ° = 1.10 V, n = 2, Q = 10 at 25 C: E = 1.10 - (0.0592/2)(1) = 1.10 - 0.0296 = 1.070 V. Products building up slightly lowers the voltage.
Batteries and the Nernst Equation
A fresh alkaline battery reads 1.5 V but drops as it discharges because products accumulate and reactants deplete, shifting Q and lowering E exactly as Nernst predicts. Rechargeable batteries reverse this by forcing current backward. The steep voltage drop at the end of discharge happens because Q changes fastest when reactants nearly run out, which is why devices die suddenly rather than fading gradually.
pH Meters Use Nernst Too
A glass pH electrode develops a voltage proportional to log[H+], shifting 59.2 mV per pH unit at 25 C. The meter converts this voltage to a pH reading using the Nernst equation internally. This is why pH meters need temperature compensation: the millivolts-per-pH slope changes with temperature.
Corrosion as a Nernst Problem
Rusting is an electrochemical cell where iron oxidizes at one spot and oxygen reduces at another, with water as the salt bridge. Different oxygen concentrations create different potentials via Nernst, driving current through the metal. This is why rust pits form under paint chips: the chemistry differs between covered and exposed metal.
Concentration Cells
A concentration cell has identical electrodes but different ion concentrations on each side, so EΒ° is zero and all voltage comes from the Nernst term. These cells generate power purely from the drive toward equal concentration. They are elegant demonstrations that chemical potential differences, not just different metals, create voltage.
Frequently Asked Questions
What is the Nernst equation?
E = EΒ° - (RT/nF) ln Q adjusts the standard cell potential for actual concentrations. As products build up, the driving force drops. At 25 C it simplifies to E = EΒ° - (0.0592/n) log Q.
When is a battery dead according to Nernst?
When Q reaches K, E hits zero. The reaction has reached equilibrium and no longer pushes electrons. Recharging forces Q back down by driving the reaction in reverse.
What is Q in the Nernst equation?
The reaction quotient: products over reactants, each raised to its coefficient, omitting solids. For Zn + Cu2+ to Zn2+ + Cu, Q = [Zn2+]/[Cu2+].
How does temperature affect cell potential?
Higher temperature magnifies the concentration term (RT/nF grows), so nonstandard concentrations shift E more. Standard potentials themselves also drift slightly with temperature.
Can E be negative?
Yes, meaning the reaction as written is non-spontaneous and needs input energy. Electrolysis cells run at negative E by definition; you drive them with an external voltage.