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Prove that fo...

Question

Prove that for two half reactions having potentials $E_{1}$ and $E_{2}$ which are combined to yield a third half reaction, having a potential $E_{3}$ ,
$E_{3} = \frac{n_{1} E_{1} + n_{2} E_{2}}{n_{3}}$ .

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Solution

$△ G_{3} = △ G_{1} + △ G_{2}$
$- n_{3} F_{3} = - n_{1} F E_{1} - n_{2} F E_{2}$
or $n_{3} E_{3} = n_{1} E_{1} + n_{2} E_{2}$
or $E_{3} = \frac{n_{1} E_{1} + n_{2} E_{2}}{n_{3}}$ .

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