Equation of Nernst

In electrochemistry, the equation of Nernst gives the tension of balance (E) of the electrode compared to the potential standard (E⁰) of the couple redox concerned. It has direction only so one redox cell is present in solution (the equation of Nernst thus does not apply to the mixed potential ) and only if the two species of this couple are present.

$E\; =\; E^0\; -\; \backslash \; frac\; \{RT\}\; \{nF\}\; \backslash \; ln\; \backslash \; frac\; \{a\_\; \{\backslash \; mbox\; \{red\}\}\}\; \{a\_\; \{\backslash \; mbox\; \{OX\}\}\}$ $\backslash \; Leftrightarrow\; E\; =\; E^0\; +\; \backslash \; left\; (\backslash \; frac\; \{RT\}\; \{nF\}\; \backslash \; right)\; \backslash \; ln\; \backslash \; frac\; \{a\_\; \{\backslash \; mbox\; \{OX\}\}\}\; \{a\_\; \{\backslash \; mbox\; \{red\}\}\}$

However, with room temperature (25°C = 298,15 K), one with the following relation:

$\backslash \; frac\; \{R\; \backslash ,\; T\}\; \{F\}\; \backslash ,\; \backslash ,\; ln\; 10\; \backslash \; approx\; 0,059$

This is why, for little which one also compares the chemical activities to the concentrations, one often finds the relation following:

$E\; =\; E^0\; -\; \backslash \; frac\; \{0,059\}\; \{N\}\; \backslash \; log\; \backslash \; frac\; \{\}\; \{\}$ with 25 °C $\backslash \; Leftrightarrow\; E\; =\; E^0\; +\; \backslash \; frac\; \{0,059\}\; \{N\}\; \backslash \; log\; \backslash \; frac\; \{\}\; \{\}$ with 25 °C

• R is the Constante perfect gases, equal to 8,314570 J.K^-1.mol^-1

• T the Température in Kelvin
• has the chemical activity of oxidant and of the reducer (generally equal to the concentration)
• F is the Constante of Faraday, equal to 96.485 C.mol^-1 = 1 F
• N is the number of electrons transferred in the half-reaction
• '' concentration from oxidant (or rather of " all that is side of the oxydant" , in particular the possible H⁺ protons, since this formula is often used to calculate pH of a solution)
• '' concentration of the reducer (or rather of " all that is side of the réducteur" , in particular the possible H⁺ protons)

History

The equation of Nernst refers to the German chemist Walther Nernst which was the first to formulate it.

Notice

One introduces sometimes the term: $f\; =\; \backslash \; frac\; \{F\}\; \{R\; \backslash ,\; T\}\; \backslash ,\; \backslash !$. The equation of Nernst is rewritten then in the form: $E\; =\; E^0\; -\; \{(nf)\}^\; \{-\; 1\}\; \backslash \; ln\; \backslash \; frac\; \{a\_\; \{\backslash \; mbox\; \{red\}\}\}\; \{a\_\; \{\backslash \; mbox\; \{OX\}\}\}$

It will be also noted that this same term F can be also written in the form: $f\; =\; \backslash \; frac\; \{N\_a\; E\}\; \{N\_a\; k\_B\; T\}\; =\; \backslash \; frac\; \{E\}\; \{k\_B\; T\}$ where N_a is the Nombre of Avogadro, E the electron charge. and k_B the Boltzmann constant.

Other bonds

• Equation of Nernst (electrophysiology), the equation of Nernst applied to the case of the difference in concentration ionic on both sides of the biological membranes.

• Equation of Goldman-Hodgkin-Katz in voltage, generalization of the equation of Nernst in the case of a membrane containing several conductances.

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