Nernst's Equation

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

$$ E_X = \frac{R \cdot T}{ν \cdot F} \cdot \ln \frac{[\mathrm{X}]_e}{[\mathrm{X}]_i}$$


 * 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+ andundefined Na+, +2 for Ca2+, −1 for Cl−, etc.)undefined
 * 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

$$ E_X = \frac{61}{n} \cdot \log \frac{[\mathrm{X}]_e}{[\mathrm{X}]_i}$$


 * 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:


 * [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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