Electromotive Force Calculator

Cathode minus anode, and a Daniell cell comes out at 1.10 V exactly as the tables promise.

Cathode half-reaction

Anode half-reaction

Reaction quotient Q

Temperature

Clear

Standard cell potential0.4577 VAg+ + e- -> Ag minus Cu2+ + 2e- -> Cu

Cell potential0.4577 Vat Q = 1 and 25 °C

Electrons transferred2

Nernst slope at this temperature59.159 mV per decadedivided by n, so 29.58 mV here

Standard free energy change-88.3227 kJ/mol

Equilibrium constant2.97483 × 10¹⁵

A positive standard potential means this cell runs on its own: the free energy change is negative and the equilibrium constant is greater than one. All three say the same thing.

The formula

E = E0 - (2.303 RT / nF) log10(Q) ; dG = -nFE

The 0.0592 you were told to memorise

At 25 degrees the prefactor 2.303 RT/F works out at 0.05916 V, which is why textbooks write the Nernst equation with that constant baked in. It is not a fundamental number — it is temperature-dependent, and at body temperature it is already 0.0615. This page recomputes it rather than assuming room temperature.

A decade per 59 millivolts

For a one-electron transfer, every tenfold change in the reaction quotient moves the cell potential by 59 mV. That is the entire basis of the pH meter: a glass electrode is a concentration cell, and one pH unit is one decade in hydrogen ion activity, so the meter reads 59 mV per pH unit and the scale is linear by construction.

Potential and free energy

A cell potential is a free energy per unit of charge. Multiplying by nF converts one to the other, and the sign flips because a spontaneous cell does work on its surroundings. A positive EMF and a negative free energy change are the same statement.

Models, and where they stop

Slater's rules, the Kapustinskii equation and Pauling's ionic-character expression are all empirical fits, not derivations. They were built to reproduce measured numbers with arithmetic simple enough to do by hand, and they succeed at that within perhaps five or ten per cent. Where a page here quotes one, it says which — a figure from a fitted rule and a figure from a Born-Haber cycle are not the same kind of thing, even when they agree.