What is Nernst equation?

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What is Nernst equation?

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Answer 1 · 2018-04-10T20:08:43

The Nernst equation describes the change in the cell potential at nonstandard conditions.

And it is:

$E_(cell) = E_(cell)^@ - (RT)/(nF)lnQ$

where:

$E_(cell)$ is the cell potential in $"V"$ at nonstandard conditions.

$E_(cell)^@$ is the standard cell potential in $"V"$ , i.e. at $25^@ "C"$ and $"1 bar"$ .

$R = "8.314472 V"cdot"C/mol"cdot"K"$ is the universal gas constant.

$T$ is the temperature in $"K"$ .

$n$ is the mols of electrons per atom, i.e. $"mol e"^(-)"/mol atom"$ .

$F = "96485 C/mol e"^(-)$ is the Faraday constant.

$Q$ is the usual reaction quotient (i.e. the "not-yet-equilibrium" constant).

This can be derived by knowing how $DeltaG$ relates to $E$ .

$DeltaG = -nFE_(cell)$
$DeltaG^@ = -nFE_(cell)^@$

From this, and knowing that $DeltaG = DeltaG^@ + RTlnQ$ ,

$-nFE_(cell) = -nFE_(cell)^@ + RTlnQ$

Dividing through by $-nF$ ,

$barul|stackrel(" ")(" "E_(cell) = E_(cell)^@ - (RT)/(nF)lnQ" ")|$

And just like $DeltaG = 0$ at equilibrium, $E_(cell) = 0$ at equilibrium, so that

$E_(cell)^@ = (RT)/(nF)lnK$

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What is Nernst equation?

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