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Activated carbon is less expensive than mercury . They are recyclable . Mercury is toxic. Nowadays activated carbon is being used in supercapacitors,Li-ion battery.

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    $\begingroup$ Reference electrodes for pH measurements are made of silver/silver chloride electrodes. $\endgroup$ – Maurice Sep 4 '20 at 15:14
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    $\begingroup$ Just for curiosity - what do you think is the potential of the activated carbon electrode ? $\endgroup$ – Poutnik Sep 4 '20 at 15:26
  • $\begingroup$ Activated carbon may be relatively quickly contaminated by foreign substances coming from the analyzed solutions. $\endgroup$ – Maurice Sep 4 '20 at 18:35
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    $\begingroup$ Electrodes are made from graphite of glassy carbon, not activated carbon. $\endgroup$ – Mithoron Sep 4 '20 at 21:51
  • $\begingroup$ Struggling to understand the chain of thought present in the question. $\endgroup$ – Jan Sep 9 '20 at 10:19
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Reference electrodes must involve a well defined redox system with reproducible potential.

Mercury is an essential part of the redox system of the calomel reference electrode $\ce{Hg|Hg2Cl2(s)|Cl-}$: $$\ce{2 Hg <=> Hg2^2+ + 2 e-}$$ $$\ce{Hg2^2+ + 2 Cl- <=> Hg2Cl2(s)}$$ and cannot be removed nor replaced, unless you want to use a difference electrode.

A similar, more often used reference electrode is the silver chloride electrode, $\ce{Ag|AgCl(s)|Cl-}$, being safer, simpler and more practical: $$\ce{Ag <=> Ag+ + e-}$$ $$\ce{Ag+ + Cl- <=> AgCl(s)}$$ This electrode can be very compact and is frequently integrated to measurement electrodes, forming a full electrochemical cell, like the pH "glass" electrode.

If a glassy carbon were used, it would be inert electrode material, similarly as platinum in the primary hydrogen reference electrode. It would need a well defined redox system established within the solution.

Note that Li-Ion cells use graphite, not activated carbon, forming lithium graphite intercalate.

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I do give you partial credit for contemplating the employment of a form of a carbon-based electrode!

Here is a related extract from a 2019 review published in Frontiers in Chemistry:

Boron-doped diamond (BDD) electrodes present several notable properties, such as the largest potential window of all electrode materials (especially in anodic potentials), low background and capacitive currents, reduced fouling compared to other electrodes, mechanical robustness, and good stability over time. On the other hand, flow-based systems are known as well-established approaches to minimize reagent consumption and waste generation and with good compromise between sample throughput and analytical performance (mechanization of chemical assays). This review focuses on the use of BDD electrodes for electrochemical detection in flow systems, such as flow injection analysis (FIA), batch injection analysis (BIA), high performance liquid chromatography (HPLC), and capillary electrophoresis (CE). The discussion deals with the historical evolution of BDD, types of electrochemical pre-treatments (cathodically/H-terminated or anodically/O-terminated), cell configurations, and analytical performance. Articles are discussed in chronological order and subdivided according to the type of flow system: FIA, BIA, HPLC, and CE.

This is evidently a technical area of specialization and, yes, doping even your active carbon large surface area electrode may prove interesting.

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