During electrolysis $\pu{0.02 mol}$ of metal $\ce{X}$ is deposited on cathode when $\pu{0.12 mol}$ of electrons are passed through molten chloride of $\ce{X}.$ What is the formula of the chloride?

I have tried solving it and my answer is $\ce{XCl6}$ which is incorrect. The correct answer given is $\ce{XCl3}.$

In the explanation the book says that $\pu{0.06 mol}$ of electrons have flown to cathode and goes on to divide the amount of electrons at cathode by the amount of metal $\ce{X}$ $(0.06/0.02),$ so it's $3$ which means $1$ atom of $\ce{X}$ gains $3$ electrons, giving it $+3$ charge.

What I do not get is what about the other $\pu{0.06 mol}$ of electrons. Isn't metal $\ce{X}$ supposed to gain all of the $\pu{0.12 mole}$ of electrons? Shouldn't cathode have the total $\pu{0.12 mol}$ of electrons?

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    $\begingroup$ I think your interpretation is more reasonable than the apparent answer, tricky or not. Can you post the name of the book? $\endgroup$ – Buck Thorn May 25 '19 at 9:32

The suppose total and half reaction are:

$$\begin{align} \ce{2 MCl_n &-> 2 M(s) + $n$ Cl2} \\ \ce{M^n+ + $n$ e- &-> M(s)} \\ \ce{2 Cl- &-> Cl2 + 2 e-}\\ \end{align}$$

The question is rather tricky.

Note that I am addressing the supposed question in hand, not the electrochemical evaluation.

In some sense, if we consider large scale motion, no electrons passed through the electrolyte, they just got on one side in and on the other side out.

In usual sense, there is 3:1 electron:halogenide molar ratio for $\ce{MCl3},$ therefore result would we $\pu{0.06 mol}.$

But in yet other sense, if we consider nanoscale motion, the $\pu{0.06 mol}$ of electrons passed through the electrolyte at the anode, and the same amount through the electrolyte at the cathode, therefore in total $\pu{0.12 mol}.$

By other words, $\pu{0.12 mol}$ is total molar amount of electrons involved in net electrochemical reaction, passing through the electrolyte between electroactive substances and electrodes.

I would say, the question is either intentionally tricky either badly formulated.

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  • $\begingroup$ That's absurd, right? The net flux of electrons through the material is zero. The same number of electrons goes in through one electrode as comes out through the other, otherwise you end up with a charged substance. I can't see the justification for doubling the number of electrons. $\endgroup$ – Buck Thorn May 25 '19 at 9:14
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    $\begingroup$ You may not got my meaning. :-) $\endgroup$ – Poutnik May 25 '19 at 9:19
  • $\begingroup$ I did not say the 2 senses are only possible senses. And we cannot know what the author meant. Note also we do not speak about charge, but electron molar amount. No electrons passed. Some got in and some got out. $\endgroup$ – Poutnik May 25 '19 at 9:28
  • $\begingroup$ Ok let me think about it some more :-) $\endgroup$ – Buck Thorn May 25 '19 at 9:28
  • $\begingroup$ I suggest writing the half reactions that would be associated with this process. $\endgroup$ – Buck Thorn May 25 '19 at 9:32

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