Nernst's Equation

Template:Navbox - conversion of substances and energy in the cell }}

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

Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\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 the_X (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

$E_{X}={\frac {61}{n}}\cdot \log {\frac {[\mathrm {X} ]_{e}}{[\mathrm {X} ]_{i}}}$

E_X = 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 the_X 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.

References

Related articles

• Electrode Processes/Electrochemical Potential
• Extracellular fluid | Intracellular fluid
• Goldmann equation

External links

• Nernst equation (English wikipedia)
• Nernst equation (English wikipedia)

Source

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