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In the Castner–Kellner process, why is sodium amalgam formed instead of hydrogen gas at the cathode?

If we electrolyse brine solution, then it will liberate hydrogen at cathode, not sodium, because $\ce{Na+}$ has a negative reduction potential while that of $\ce{H+}$ is (by definition) 0. What factor here causes the sodium to get reduced to form an amalgam in spite of the reduction potentials?

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    $\begingroup$ This is actually a nice question, for which I do not have the answer. The brine must be cold and concentrated, from what I have read. And it is even possible to electrolyze ammonium chloride, under similar conditions, to get ammonium amalgam. Upon warming, the latter yields nitrogen and hydrogen gases. $\endgroup$ – Ed V Feb 10 '20 at 14:56
  • $\begingroup$ Now that I think about it, my guess is that the significant overpotential, for hydrogen gas evolution at the Hg cathode, is a big factor. $\endgroup$ – Ed V Feb 10 '20 at 15:02
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    $\begingroup$ You probably want to avoid using all caps in the title, which is probably responsible for the downvotes. Capital letters makes it seem like you're SHOUTING... $\endgroup$ – orthocresol Feb 10 '20 at 15:13
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    $\begingroup$ @M.Farooq, you don't see many questions on MathOverflow with allcaps in the title. It's ok to say that there's a "high tendency for downvoting" (I might even agree with that, though I'm not sure), but IMO more helpful to point out possible reasons so that OP may take note and edit the current question / learn for future ones. [For what it's worth, I didn't downvote this.] $\endgroup$ – orthocresol Feb 10 '20 at 16:04
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    $\begingroup$ @orthocresol, I was talking about a general trend in Chem about downvoting. As I have said it again and again, the problem with downvoting is that we do not know if a high school student is downvoting it or an Einstein. In may schools, esp. in South Asia, block letters are often used by teachers in headings while writing notes or even on the blackboard. $\endgroup$ – M. Farooq Feb 10 '20 at 16:54
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I am not sure if you are familiar with the term "overpotential." With mercury electrode, as a cathode, it takes more negative potential to reduce hydrogen ions to hydrogen gas, rather it is easier for sodium ions to get reduced on a mercury surface and form an amalgam (an alloy of Hg and Na). This is a peculiarity of the mercury electrode.

Mercury cell in chlor-alkali industry

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