Nernst's Battery

Plate 96 speaks for itself: “Potassium alone would charge each cell to −89 millivolts.”

The Physics

Ion concentration differences across a cell membrane store energy. The Nernst equation gives the voltage at which a single ion's diffusion is balanced by the electric field.

E = (RT / zF) ln([out] / [in])

• E: equilibrium potential, V
• R: gas constant 8.314 J mol⁻¹ K⁻¹
• T: temperature, K
• z: ion charge number, dimensionless
• F: Faraday constant 96 485 C mol⁻¹
• [out], [in]: concentrations, mol m⁻³ (quoted in mM)

At 310 K, RT/F = 26.7 mV. K⁺ 5/140 mM: −89 mV. Na⁺ 145/12 mM: +67 mV.

Honest caveat: Real resting potentials (about −70 mV) sit between these because the membrane passes several ions.

Sources

• W. Nernst, Z. Phys. Chem. 4, 129 (1889).
• B. Hille, Ion Channels of Excitable Membranes, 3rd ed. (2001).

On the poster

Plate 096, “Nernst's Battery”: the pixel-art plate with its slogan “Potassium alone would charge each cell to −89 millivolts.”, the key equation and the facts panel shown above. Pixelated Physics. Physics. Personified.