Cell EMF Calculator

The electromotive force of a galvanic cell is the open-circuit potential difference between its two half-cells, measured when no current flows so that no energy is lost to internal resistance or kinetic barriers. Because every half-cell is tabulated as a reduction potential against the standard hydrogen electrode, the cell value is simply the cathode potential minus the anode potential; the subtraction works because the anode half-reaction is being run in reverse. Tabulated potentials span about 5.9 V, from Li+/Li at -3.04 V through Zn2+/Zn at -0.76 V, Cu2+/Cu at +0.34 V, and Ag+/Ag at +0.80 V up to F2/F- at +2.87 V, so a Daniell zinc-copper cell yields 1.10 V, while water itself caps practical aqueous cells near 1.23 V before electrolysis competes. The link to thermodynamics is dG = -nFE, with n the electrons transferred in the balanced equation and F = 96485 C/mol, so 1.10 V across two electrons corresponds to about -212 kJ/mol. Setting E to zero at equilibrium gives ln(K) = nFE0/RT, which is why modest voltages imply enormous equilibrium constants: 1.10 V with n = 2 corresponds to K near 1e37. The Nernst correction E = E0 - (RT/nF) ln(Q) contributes 59.16/n mV per decade of Q at 25 degrees C. Two limitations matter: standard potentials assume unit activity rather than unit concentration, so real solutions need activity coefficients, and this EMF is the thermodynamic maximum, ignoring overpotential, junction potentials, and IR drop in any cell delivering current.

The field began with a dispute. Luigi Galvani reported in the 1780s that dissected frog legs twitched when touched by dissimilar metals and attributed the effect to animal electricity; Alessandro Volta argued the metals themselves were the source and in 1800 settled the question by building the voltaic pile from stacked zinc and silver discs separated by brine-soaked cloth, the first sustained source of electric current. John Frederic Daniell improved on it in 1836 with a two-compartment zinc-copper cell whose porous barrier prevented the polarization that plagued the pile, and his design became the reference battery of early telegraphy. The quantitative framework came from thermodynamics later in the century. Josiah Willard Gibbs developed free energy in the 1870s, giving meaning to the maximum electrical work a reaction can perform, and Walther Nernst published in 1889 the logarithmic concentration dependence of electrode potential that bears his name; he received the Nobel Prize in Chemistry for 1920. Michael Faraday's earlier electrolysis work had already fixed the constant relating charge to moles of electrons. Sign conventions remained inconsistent between European and American practice until the 1953 IUPAC meeting in Stockholm settled on reduction potentials, which is the convention used in the tables this calculation depends on.