Derive nernst equation for general reaction a A+b B c C+d D - Vidyadip

Question

Derive nernst equation for general reaction $a A+b B \rightarrow c C+d D$

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Answer

$→ aA + bB \xrightarrow{ ne ^{-}} cC + dD
$
Nernst equation can be written as :
$
\begin{aligned}
E _{\text {(cell) }} & = E _{\text {(cell) }}^{\ominus}-\frac{ RT }{ nF } \ln Q \\
& = E _{\text {(cell) }}^{\ominus}-\frac{ RT }{ nF } \ ln \frac{[ C ]^{ c }[ D ]^d}{[A]^{ a }[ B ]^{ b }} \\
& = E _{\text {(cell) }}^0-\frac{0.059}{ n } \ log \frac{[ C ]^c[ D ]^d}{[A]^{ a }[ B ]^{ b }}
\end{aligned}$

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