Nernst equation

BOX 5.1

NERNST EQUATION

The equilibrium potential is determined by (1) the concentration of the ion inside and outside the cell, (2) the temperature of the solution, (3) the valence of the ion, and (4) the amount of work required to separate a given quantity of charge. The equation that describes the equilibrium potential was formulated by a German physical chemist named Walter Nernst in 1888:
E_ion = RT/zF · ln([ion]_o/[ion]_i)
Here, E_ion is the membrane potential at which the ionic species is at equilibrium, R is the gas constant [8.315 J per Kelvin per mole (J K⁻¹ mol⁻¹)], T is the temperature in Kelvins (T_Kelvin = 273.16 + T_Celcius), F is Faraday’s constant [96,485 coulombs per mole (C mol⁻¹)], z is the valence of the ion, and [ion]_o and [ion]_i are the concentrations of the ion outside and inside the cell, respectively. For a monovalent, positively charged ion (cation) at room temperature (20°C), substituting the appropriate numbers and converting natural log (ln) into log base 10 (log₁₀) result in
E_ion = 58.2 log₁₀([ion]₀/[ion]_i)
at a body temperature of 37°C, the Nernst equation is
E_ion = 61.5log₁₀([ion]₀/[ion]_i).
David A. McCormick