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I am told that

$$Q = nF$$

where $Q$ is the quantity of current, $n$ is the amount of electrons and $F$ is Faraday's constant. Since Faraday's constant is the charge carried by 1 mol of electrons, multiplying it by the amount of electrons to give the total charge makes perfect sense. But why does dividing $Q$ by $nF$ gives the amount of substance? Won't the answer just be 1 for all possible values?

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For a general electrolytic reaction,

$$\ce{M^{n+} + $n$ e^- -> M}$$

where $n$ moles of electrons are consumed in depositing 1 mole of substance ($n$ is also known as $n$-factor). So, for $x$ moles of substance, $nx$ moles of electrons would be consumed. Therefore,

$$Q = nxF,$$

dividing by $nF$ on both sides, we have

$$\frac{Q}{nF} = x,$$

which is the amount of substance.

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  • $\begingroup$ Ah, that makes perfect sense. Thank you! $\endgroup$ – Tetsu Dau Sep 4 at 5:52
  • $\begingroup$ @rv7 Please visit this page, this page and this one on how to format your future posts better with MathJax and Markdown. $\endgroup$ – andselisk Sep 4 at 7:55
  • $\begingroup$ @TetsuDau: you're welcome. $\endgroup$ – rv7 Sep 4 at 8:03
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    $\begingroup$ @andselisk: Thanks for the links. I'll take care of that next time. $\endgroup$ – rv7 Sep 4 at 8:05
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    $\begingroup$ Often, $z$ is used for the stoichiometric factor, and $n$ for the amount of substance, so it becomes $n = \frac{Q}{z F}$, see e.g. bipm.org/utils/en/pdf/SIApp2_mol_en.pdf @rv7 $\endgroup$ – Karsten Theis Sep 4 at 9:59

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