Nernst's Equation

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The Nernst equation is used to calculate the electrochemical equilibrium potential E of any X ion.

Failed to parse (syntax error): {\displaystyle E_X = \frac{R \cdot T}{ν \cdot F} \cdot \ln \frac{[\mathrm{X}]_e}{[\mathrm{X}]_i}}

E X = electrochemical equilibrium potential of theX (V) ion
R = universal gas constant [8,314,472 J/(mol· K)]
T = absolute temperature in K (body temperature 37 °C = 310,15 K)
ν = power of the ion (e.g. + 1 for K+ and Na+, +2 for Ca2+, −1 for Cl, etc.)
F = Faraday's constant (96,485.339 9 C/mol)
ln = natural logarithm
[X]e = extracellular concentration of the X ion
[X]i = intracellular concentration of the X ion


The above form of the equation can be greatly simplified under certain conditions. At a body temperature of 310 K (i.e. 37 °C), the RT/F term is equal to 0.0267 . If we convert the natural logarithm to a decimal one (ln x = 2.3 · log 10 x), multiply the equation1000 (conversion from V to mV),

1000 · RT / F · 2,3 · log x = 1000 · 0,0267 · 2,3 · log x = 61 · log x .

So we get


EX = elektrochemický rovnovážný potenciál iontu X (mV)
n = mocenství iontu (např. + 1 pro K+ a Na+, +2 pro Ca2+, −1 pro Cl apod.)
[X]e = extracelulární koncentrace iontu X
[X]i = intracelulární koncentrace iontu X

The values of the extracellular and intracellular concentration of the electrochemical equilibrium potential of some ions are given in the table below:

Xe (mmol/l) Xi (mmol/l) EX (mV)
Na+ 145 15 +60
K+ 4 150 −96
Ca2+ 2,5 10−4 +134
Cl 100 5 −79
[X]e = extracellular concentration of the X ion
[X]i = intracellular concentration of the X ion
E X = electrochemical equilibrium potential of theX ion (mV)

The equation was formulated by the German chemist Walther Hermann Nernst, who received the Nobel Prize in 1920 for discoveries in the field of physical chemistry.


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Source[edit | edit source]

AMBLER, Zdeněk. Basics of neurology. 6th edition. Prague: Galén, 2006. pp. 171-181. ISBN 80-7262-433-4 .