Walther Nernst · Zeitschrift für physikalische Chemie 4 (1889): 129–181 · Leipzig
Written as Nernst's habilitation in Wilhelm Ostwald's Leipzig laboratory — the same rooms where van 't Hoff's osmotic theory and Arrhenius's ions were turning physical chemistry into a quantitative science — the memoir asks a deceptively simple question: how large is the electrical force an ion can exert, and on what does it depend?
1 · The osmotic analogy
Nernst takes over van 't Hoff's result that dissolved particles behave like a gas, exerting an osmotic pressure proportional to their concentration, and Arrhenius's claim that in solution a salt is already split into free ions. An ion in solution is therefore like a gas under pressure; differences in that pressure are differences in a tendency to move.
2 · Electrolytic solution pressure (Lösungstension)
To this he adds one new quantity: every metal is supposed to have an “electrolytic solution pressure” P, an intrinsic tendency to shed ions into the solution, leaving electrons behind on the metal. Against it pushes the osmotic pressure p of the ions already dissolved, which tends to drive them back onto the metal. The electrode comes to rest where the two are balanced, and the charge separation built up in reaching that balance is the electrode potential.
3 · The resulting law
Equating the electrical work of moving the ions against the osmotic work of compressing them from one pressure to the other gives a logarithmic law: the potential depends on the logarithm of the concentration (strictly, the ratio of solution pressure to osmotic pressure). In the form used ever since, the electromotive force of a cell is E = E° − (RT/nF) ln Q.
E = (RT / nF) · ln(P / p) → E = E° − (RT / nF) · ln Q ; 2.303 RT/F ≈ 59.2 mV per tenfold concentration ratio at 25 °C.
4 · Concentration cells and consequences
The clearest test is a cell with the same metal in the same salt at two concentrations: the standard term cancels and a voltage appears from the concentration difference alone. From the same law Nernst reads off how cell voltages, solubilities and equilibria depend on concentration — the working equations of electrochemistry.
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The literal picture of a “solution pressure” was later dropped in favour of Gibbs's chemical potential, and dilute concentrations were replaced by activities — but the logarithmic law itself, and the 59 mV-per-decade slope, are exactly as Nernst left them.
Leipzig · 1889