Talk:Electrolysis

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Wiki Education Foundation-supported course assignment[edit]

This article was the subject of a Wiki Education Foundation-supported course assignment, between 19 August 2019 and 6 December 2019. Further details are available on the course page. Student editor(s): Makaylacg, Simeonbauer. Peer reviewers: HeavenlyNova.

Above undated message substituted from Template:Dashboard.wikiedu.org assignment by PrimeBOT (talk) 20:22, 16 January 2022 (UTC)[reply]

Stainless Steels and Anode Consumption[edit]

The use of stainless steel(SS) as an anode should be approached with great caution or best yet, avoided altogether. SS contains chromium. No matter what misinformation you may have read on the internet, SS anodes ARE INDEED consumed. During consumption highly toxic chromates are released into the electrolyte. Hexavalent chromium is extremely toxic and highly carcinogenic. Disposal of this electrolyte into the ground or down the drain is illegal and poses risks of contaminating ground water and city water supplies. Touching this chromate-containing electrolyte must also be avoided by all means.

The main page of this article should be updated to reflect the extreme toxicity the use of SS anodes will introduce into the used electrolyte solution. —Preceding unsigned comment added by 67.186.20.215 (talk) 17:48, 12 October 2008 (UTC)[reply]

The production of chromate from stainless steel anodes can be minimised by limiting the voltage across the cell and/or adding a reducing agent such as sulfite to the electrolyte. Chromium(III) is much less toxic than chromate, and is much less of a problem to dispose of. 2corner (talk) 09:40, 15 October 2008 (UTC)[reply]

Stanley Meyer[edit]

In my opinion, his name should be removed from the experimenters' list, as even if he has made a significant contribution to hydrogen powered cars, which I personally doubt, this is not really electrolysis research.2corner (talk) 10:48, 24 July 2008 (UTC)[reply]

Anode consumption[edit]

In electrolysis the anode is frequently consumed but this is not (never!) written down as part of the chemical reaction. Especially graphit anodes in aluminium electrolysis is oxydised and "bubbles away" as CO2.

Does anyone have information about the reactions that consume the anode and which preserve them? Would this be a valuable part of the article?

84.160.202.86 17:56, 29 Mar 2005 (UTC)

Very valuable.

That's crap. in electroplating the reactions are significantly about the consumption of the anode in the cases where the anode suplies the cations for plating.

Efficiency[edit]

What are some typical efficiencies then? - Omegatron 03:43, Jun 26, 2005 (UTC)

Numbers are all over the place:

  • "real-world efficiencies range from 83% under laboratory conditions to as low as 66% in a typical commercial-scale facility." [1]
  • "Such a high-temperature system has the potential to achieve overall hydrogen production efficiencies in the 45 to 50 percent range, compared to approximately 30 percent for conventional electrolysis." [2]
  • "With output pressures of 0.2 - 0.5 MPa these processes can reach efficiencies, related to the lower heating value of hydrogen, of around 65%." "Operating efficiencies lie in the 50-60% range for the smaller electrolysers and around 65-70% for the larger plants." [3]
  • "Hydrogen production by electrolysis is about 80% efficient considering only the electricity, but the thermal efficiency of producing that electricity ranges from about 34% in light water reactors to 50% in advanced systems, giving overall efficiencies of 25-40%. A significant investment in electrolytic cells is also required. The oxygen by-product also has value." [4]
  • "Some of NHE’s electrolysers have an efficiency of over 80% (high heating value)." "Efficiency factors for PEM electrolysers up to 94% are predicted, but this is only theoretical at this time." "Another type of steam electrolyser is the German “Hot Elly”; this system can reach an efficiency of 92%."[5]
  • "Norsk Hydro Electrolyzers (NHE) is currently one of the world's leading producers of electrolyzers, and they have an efficiency of about 85%." [6]
  • "The best available technology captures 90% of the energy on a HHV basis and 76% on a LHV basis." [7]

There appears to be a discrepancy between the pure efficiency of hydrogen and oxygen production vs input power, and the same with resistive heating of the water included?

  • "Hydrogen production from natural gas commonly employs a process known as steam reforming. ... Most of the hydrogen utilized by the chemical and petroleum industries is generated with steam reforming. Steam reforming reaches efficiencies of 70% - 90%." [8] - Omegatron 23:57, July 30, 2005 (UTC)

"Just a thought... there is a link to a .pdf file on this page and it uses the Adobe Acrbobat icon. I personally hate the Adobe .pdf view and use a different open source type viewer, I would have to see Adobe become synonymous with pdf files. This is just a general thought for all of wikipedia." (my first post, sorry if it's not to code) Ummmcam 03:24, 28 September 2006 (UTC)[reply]

The overview section stating that hydrogen produced by steam reforming has a higher energy output than the electrical energy consumed could be misinterpreted. There should be a simple way to explain that the process of creating steam is also calculated into the overall energy consumed. Only the efficiency of the process of hydrogen output to energy input is raised.I55ere (talk) 15:31, 5 March 2008 (UTC)[reply]

OK, so I'm not a member, but I thought you guys might like to know that the sentence "when considering a power plant that converts the heat of nuclear reactions into hydrogen via electrolysis, the total efficiency is more like 25%–40%", doesn't seem to be confirmed at the reference given. 22:45, 23 April 2008 —Preceding unsigned comment added by 142.150.49.30 (talk)

How does it actually work?[edit]

The separation of ions is not necessary for electrolysis, and does not often occur. For instance, when electroplating using copper sulphate solutions, the blue colour of Cu++ ions is uniformly spread in the solution. In a very long tube, or in a gel electrolyte, as used for eletrophoresis, ion separation is seen. 2corner (talk) 05:39, 28 May 2008 (UTC)[reply]

"At the electrodes, electrons are absorbed or released by the ions, forming concentrations of the desired element or compound. For example, when water is electrolyzed, hydrogen gas (H2) will form at the cathode, and oxygen gas (O2) at the anode."

In the beginning of the article, it says that "The source materials is dissolved in an appropriate solvent, or melted, so that constituent ions are available in the solution", so wouldn't the water be the solvent and the salt or other compound which is added be the material to be separated? I think what is actually happening is that water routinely breaks into H+ and OH. The H+ goes towards the negative electrode, and the OH towards the positive. I think the salt or whatever in this case produces more Hs and OHs? At the negative electrode the H+s meet up and form H2 somehow, and at the positive electrode...  ??? I don't know. It's been a while since I took chemistry. What's actually happening? — Omegatron 16:31, August 29, 2005 (UTC)
Oh here's a description: [9]. I don't really understand it all, though. — Omegatron 16:35, August 29, 2005 (UTC)
Here's a page [10] that describes electrolysis of water without the need for an electrolyte. The water is oxidised at the anode, producing electrons, and reduced at the cathode, consuming electrons. It works without an electrolyte because pure water has a small [11] but non-zero ion concentration (10^-7 mol/L per ion, according to [12]). Adding an electrolyte just speeds everything up. --Heron 17:41, 29 August 2005 (UTC)[reply]

What source materials are typically used to give us the ions?[edit]

The reader, at the beginning of the overview, is presented with the phrase "A source material" - a person who is a non scientist sees an undefined idea here... which can throw off his comprehension. It would be nice to add a clause "A source material, such as a metal or..." Would someone with a hands on familiarity with electrolysis be kind enough to add a couple words there?

Some electrolytes for water could include sodium chloride NaCl(table salt), sodium hydroxide NaOH (lye), Potassium hydroxide KOH(Potash lye), and Bicarbonate of soda NaHCO3 (baking soda). These are easy to acquire and are simple to use. Sodium chloride and bicarbonate of soda are safe for beginners to handle.I55ere (talk) 15:01, 5 March 2008 (UTC)[reply]
..."Sodium chloride and bicarbonate of soda are safe for beginners to handle.I55ere (talk) 15:01, 5 March 2008 (UTC)[reply]
I think table salt is not safe for beginners- I read somewhere that it will release poisonous Chlorine gas. Scary, this would be an easy/common error in novice kitchen chemistry! Is Chlorine really released?Electricmic (talk) 02:41, 14 May 2010 (UTC)[reply]

DC Circuits[edit]

Is electrolysis a type of DC circuit?

--Sean; 24 September 2005

Yes. Most, if not all, electrolysis is done using a DC circuit. --Heron 14:07, 25 September 2005 (UTC)[reply]

  • Quite so. This article doesn't explain very well, and i want to improve it. But basically whether an electrode is +ve or -ve is VERY important as it dictates what chemical reaction will occur at that electrode. Usually these are kept constant (i.e. DC) in order to exploit one of the reactions, for example collecting produced hydrogen. I have built many (large) electrolytic cells in order to fill weather balloons with hyrdogen and detonate them in the air. They produce quite a pleasing bang - especially with some oxygen in there too. Anyway i've built 20L, 60L, and a 200L hyrdogen machine - and would love to talk to the person at the start of this talk page who needed to know more about anode corrosion. Leave a note on my talk page and i'll get into contact with you. Also anyone in Victoria, Australia whos interested in recreational electrolysis (i.e. making and blowing up hyrdogen balloons) give us a yell.

THE KING 04:33, 21 March 2006 (UTC)[reply]

I am currently doing electrolysis of Copper Sulphate. I started using a iron anode (positive) and a copper cathode (negative). The iron anode dissolves into the solution as fast as copper comes out of solution onto the cathode. I then used a Stainless steel anode. This also deteriorated (dissolved) but slowly. Lead Oxide (PbO2) was also used as an anode. The deteriation of PbO2 is even slower. I lost 100g of PbO2 but produced 1kg Copper on the Cathode. In this case the Pb mostly does not go into solution and oxygen comes off the anode to balance things out. I am currently using Iridium Oxide coated Titanium. These anodes do not corrode (better not considering the cost of AU$120 each). The anodes appear to be remaining intact and the solution becomes very acid. Produce about 1kg copper per 5 amps per week. Anodes currently running at between 10 and 15 amps. POWER supplies- I am using the 5V DC terminal of computer power supplies (15 power supplies for 15 anodes) I have 3 cathodes all earthed together. A computer power supply is rated at 20Amps at 5V. Most will go to 25 amps before overload switch cuts in. The anodes are rated at 30 Amps max. Martin Essenberg 03:38, 2 June 2006 (UTC)Martin [why not use copper anode, effectively transferring Cu from anode to material you are plating] —Preceding unsigned comment added by 208.38.9.185 (talk) 03:17, August 25, 2007 (UTC)[reply]

Military use[edit]

Space station is hardly a military installation. I suggest changing the section name to "Other uses". --Michagal 16:06, 9 August 2006 (UTC)[reply]

The author makes the claim that a nuclear submarine could remain underwater indefinately. I disagree; at some point the crewmen will run out of a supply of food, am I not correct? If so, that should be changed. --- Darkstaruav 14:35, 9 December 2006

It says submarine, nothing about the people inside it. Just pointing it out --Jon Fawkes 02:11, 16 May 2007 (UTC)[reply]

Hahaha. In that case any vehicle can stay underwater indefinitely. --tigen
If I push your car into a nice deep lake, it'll stay there indefinitely. That's not the issue. The deal with a nuclear submarine is that its nuclear power plant will produce energy for a very long time without refuelling. (NOT forever - not "indefinitely" - but for many years). If you use it to produce oxygen from hydrolysis of the surrounding seawater, its crew can breathe for as long as the nuclear fuel holds out. If you use the nuclear reactor to electrolyse water, you can burn it with the hydrogen and oxygen to make pure water for drinking without the need for filtering, desalination, chlorinating or anything like that. You also have all the electricity you need for heating, cooling, whatever and plenty of motive power for driving the submarine around without surfacing. That's what they're talking about. They don't LITERALLY mean "indefinitely" - they mean that electricity, oxygen and drinking water aren't the limiting factor. With a good supply of dehydrated food, the submarine can stay underwater for a ridiculously long time...but certainly not forever. From a practical perspective - the sanity of the crew is your biggest limitation. SteveBaker (talk) 21:29, 12 June 2008 (UTC)[reply]
I have read that the fresh water in submarines is low pressure (vacuum) distilled from the sea water, it requires pump energy (electricity or turning shaft) and perhaps heat to start it but the compressed water vapour is used to warm up the sea water when it is running as it condenses. Electrolysis can be used on the pure water to gain Oxygen. The waste brine and Hydrogen will be ejected into the sea. Direct electrolysing of sea water will yield more Chlorine gas than you would want so it is not a practical method of generating pure H2 and O2 and then still having to burn (or fuel cell reform) it to make fresh water.
Idyllic press (talk) 19:54, 7 March 2014 (UTC)[reply]

Damages of electrolysis[edit]

It is known fact that electrolysis damages terminals of DC power supply in humid environments. I think this should be mentioned in the article. Car batteries usually have special insulation device on the positive terminal. Communication equipment uses -48V standard power supply to tackle this issue. --Michagal 16:06, 9 August 2006 (UTC)[reply]

Electrowinning[edit]

Should this article also be merged with electrowinning?

potassium dichromate[edit]

What reaction will occur at anode in the electrolysis of potassium dichromate? What product will be formed???Superdvd 10:53, 26 January 2007 (UTC)[reply]

Dichromate is reduced to chromium(III). Bbi5291 18:48, 23 September 2007 (UTC)[reply]

Reduction normally happens at the cathode, and I believe that dichromate would be reduced to chromium(III) there. At the anode, oxidation normally occurs. The most likely reactions would be oxidation of water to oxygen gas (if using an noble metal electrode such as platinum), or the corrosion of the electrode (if using a base metal electrode such as copper): Pt anode: 2 H2O --> O2 + 2 H+ + 2 electrons ;

Cu anode: Cu --> Cu++ + 2 electrons. 2corner (talk) 09:34, 27 May 2008 (UTC)[reply]

definition?[edit]

I am not certain, but the deffinition, to me, would seem to be a bit inadiquite and lacks detail... anyone agree?

I think that it should include the fact that the compound/element must either be dissolved, melted or the anode/cathode in some cases.

I agree...though with predescending thoughts.[ZHK]

any ideas on this? —The preceding unsigned comment was added by BenHowes (talkcontribs) 16:41, 6 February 2007 (UTC).[reply]

Etymology of the word might be interesting. Does electro lysis mean to cut using electricity?Electricmic (talk) 02:45, 14 May 2010 (UTC)[reply]

Picture?[edit]

I think the article needs a picture... 154.20.151.165 03:54, 23 May 2007 (UTC)[reply]

I changed the spelling in the caption see http://en.wikipedia.org/wiki/August_Wilhelm_von_Hofmann and http://en.wikipedia.org/wiki/Hofmann_voltameter
In the diagram, the electrodes seem a bit low - in our school voltammeter, the electrodes are above the cross piece to keep the gases made separate.
Skihatboatbike (talk) 15:06, 2 April 2008 (UTC)[reply]
I also think it would be a better illustration of an apparatus if the electrodes were raised higher than the cross pipe to maintain the safe separation of the gas products though some commercially sold units have low electrodes that are not a serious problem if the apparatus is vertical.
I believe it would also be a bit more typical if the gas volumes in the two arms were in some other ratio than 1:1, say 2:1 like in a typical water electrolysis experiment.
Idyllic press (talk) 20:47, 7 March 2014 (UTC)[reply]

Replace Copper in First Paragraph[edit]

Copper has a long history of being smelted and used from simple ores. Does anyone have an objection to replacing copper with aluminum? Until fairly recently (1850's) aluminum was more valuable than gold precisely because it requires an electrical current to separate from its ore.--Legomancer 02:00, 1 June 2007 (UTC)[reply]

The Other Electrolysis[edit]

Although science-minded people like us think of the chemical kind of electrolysis first, there's also cosmetic electrolysis, i.e., the hair removal process. Some articles (Rita Hayworth for one) link to this article in reference to the cosmetic procedure, which is pretty strange, as I'm pretty sure Rita's water and other molecules stayed mostly bonded throughout her life. Recommend the creation of a separate article, something like "Electrolysis (cosmetic)", unless someone has a better idea. --Iritscen 19:28, 7 June 2007 (UTC)[reply]

There is already a link to Electrology at the top of the page, but maybe it is not clear from the wording that this is the cosmetic procedure. --PeR 09:43, 8 June 2007 (UTC)[reply]
Ahh, I missed that somehow. Thanks for clarifying, and for fixing the link from Rita's article. --Iritscen 17:20, 6 July 2007 (UTC)[reply]

Copyright infringement / plagiarism; please remedy[edit]

Entire portions of the electrolysis entry were plagiarized from the web site of CR Scientific LLC without providing so much as a link or reference.

I should know. I am the original author of the following. In fact, I spent a great deal of time on the wording:

"In electrolysis, the anode is the positive electrode, meaning it has a deficit of electrons; species in contact with the anode can be stripped of electrons (i.e., they are oxidized). The cathode is the negative electrode, meaning it has a surplus of electrons. Species in contact with the cathode tend to gain electrons (i.e., they are reduced)."

"A higher current flow (amperage) through the cell means it will be passing more electrons through it at any given time. This means a faster rate of reduction at the cathode and a faster rate of oxidation at the anode. This corresponds to a greater number of moles of product. The amount of current that passes depends on the conductance of the electrodes and electrolyte, though it also depends on how much current the power source itself can generate.

Current also makes a difference in that it can shift chemical equilibria by sheer mass action. The processes in an electrolytic cell with just two or three reactants can become very complex. Most of the time it is best to search the literature to see what current density works best for a desired process. For instance, metals plated at a certain current density might form a durable and shiny coating on the substrate, whereas some other current density might form an excessively grainy, dull coating.

A higher potential difference (voltage) applied to the cell means the cathode will have more energy to bring about reduction, and the anode will have more energy to bring about oxidation. Higher potential difference enables the electrolytic cell to oxidize and reduce energetically more "difficult" compounds. This can drastically change what products will form in a given experiment. On a practical level, both current and voltage determine what will form in a cell."


Although it is flattering that someone chose my company's article as a source for a Wikipedia entry, the manner in which it was handled was inappropriate and represents a copyright violation.

I suggest that the article be edited as soon as possible to remedy the infringement; while CR Scientific LLC has no problem with quotations and paraphrasing, plagiarism of our articles is unacceptable.

In the meantime I am going to read over the rest of the article to see if any other phrases have been lifted directly. We have CD archives of our articles going back several years in the event there is any confusion.

Sincerely, Christian Thorsten

CR Scientific LLC —Preceding unsigned comment added by Crsci9 (talkcontribs) 13:26, 25 February 2008 (UTC)[reply]

I have removed the infringing text from the article. Someone should check the article to ensure that it continues to make sense with these paragraphs removed. - Mark 14:43, 25 February 2008 (UTC)[reply]

efficiency of electrolysis[edit]

I may be wrong, but I am pretty sure the definition and usage of the term Lower Calorific Value is wrong, and I have corrected it to what I think is correct. Engineman (talk) 09:17, 9 June 2008 (UTC)[reply]


electrolysis of sewage[edit]

Penn State and Oregon State University both have projects to do this. The advantage of sewage over plain water is that with water you often need to add ions. Sewage already has ions in it, so it is already a good conductor of electricity. Sewage is also something that we already want to reduce in volume, and the removal of the H2 and the accompanying O2 from it accomplishes a size reduction, and produces at least one useful thing. Part of sewage treatment is the process of "dewatering", and the electrolytic producton of hydrogen from sewage does this. Furthermore, if you can condense the water that reoccurs when the Hydrogen has been "burned" you have clean water. John5Russell3Finley (talk) 15:51, 25 January 2009 (UTC)[reply]

Error in E values for electrolysis of water[edit]

In the section Competing half-reactions in solution electrolysis these values for the oxidation and reductions of water are quoted:

   the electrode potential for the reduction producing hydrogen is −0.41 V
   the electrode potential for the oxidation producing oxygen is +0.82 V

I think they are wrong. As they are, they seem to suggest that the electrolysis of water is a spontaneous change, when it clearly is not. The literature quotes the reduction of water to produce hydrogen gas as -0.83 V and the oxidation of water to produce oxygen gas as -1.23 V. Whoever added those values has mixed them up pretty badly.

Before I change them, I hope someone can verify that I am correct in this. rrh02 (talk) 00:55, 06 February 2019 (UTC)[reply]

References to electrochemical cell[edit]

The text that states the processes in the electrochemical cell are the "reverse" of electrolysis are just wrong. If cells were the "reverse process" then ionic solutions would spontaneously generate electricity - this does not happen. The cell has a specific setup and relies on differences in electrode potential. I have tried to clarify this. Clive long (talk) 09:32, 29 January 2009 (UTC)[reply]

reversible - surely they are if you take account of the gaseous components of H2 and Cl2 - for example when hydrogen chloride solutions are electrolysed then the creation of bubbles of hydrogen and oxygen at the cathode and anode create an overpotential- try stopping a cell and then putting a voltmeter across there is a temporary reverse emf - effectively electrolysis has created a short lived "hydrogen" electrode and a "chlorine" electrode which connected externally form a galvanic cell. The effect would persist if H2 and Cl2 were continuously bubbled over the electrodes.--Axiosaurus (talk) 15:22, 20 February 2009 (UTC)[reply]

The incorrect diagram of an electrochemical cell has reappeared at the top of the article. This is not a setup that performs electrolysis and is quite misleading to people who are unfamiliar with electrolysis. I will work to find a royalty free diagram of an electrrolysis cell or draw my own and replace the one that has been reinserted on the page Clive long (talk) 08:19, 5 February 2009 (UTC)[reply]

Problems with section.[edit]

The following section has a few blatant mistakes but more important implies rationals that are false. First off electrolysis a NaCl solution results in Chloralkali process unless electrocatalysts are used that can facilitate the two half reactions involved in splitting hydrogen. Platinum is one such electrocatalyst. Furthmore if a Zn electrode is used the Zn doesn't dissolve it is oxidized from Zn to Zn2+ in because Zn2+ has a more negative reduction potentials than O2. The reason "reactive metal electrodes" aren't used to produce "large quantities of hydrogen" is because the implied alloys are poor electrocatalysts, contamination issues are not a major concern with current technology. I'm not sure where this content came from but it needs to be cited if it returns in any form.--OMCV (talk) 02:49, 29 June 2009 (UTC)[reply]

Electrolysis of water can be observed by passing direct current from a battery or other DC power supply through a cup of water (in practice a salt water solution increases the reaction intensity making it easier to observe). Using metallic electrodes, hydrogen gas will be seen to bubble up at the cathode, and oxygen will bubble at the anode. If metals other than platinum or stainless steel are used as the anode, there is a chance that the oxygen will react with the anode instead of being released as a gas, or that the anode will dissolve. For example, using iron electrodes in a sodium chloride solution electrolyte, iron oxides will be produced at the anode. With zinc electrodes in a sodium chloride electrolyte, the anode will dissolve, producing zinc ions (Zn2+) in the solution, and no oxygen will be formed. When producing large quantities of hydrogen, the use of reactive metal electrodes can significantly contaminate the electrolytic cell - which is why iron electrodes are not usually used for commercial electrolysis. Electrodes made of stainless steel can be used because they will not react with the oxygen.

Electrolyte (Electrochemistry)/electrolysis[edit]

From the Electrochemistry section(in the electrolyte page): "instead, a chemical reaction occurs at the cathode consuming electrons from the anode, and another reaction occurs at the anode producing electrons to be taken up by the cathode."

This apparently seems contradictory to what that is in Process of electrolysis on the electrolysis page, which says:

"Positively-charged ions (cations) move towards the electron-providing (negative) cathode, whereas negatively-charged ions (anions) move towards the positive anode."

The Electrochemistry section states that the cathode consumes electrons [?what does "from the anode" mean?] and the anode produces electrons. However, the electrolysis page states that the cathode provides the electrons, which would mean that the anode takes up the electrons.

Isn't there something wrong? PS I also posted this on the electrolyte talk page since this concerns both pages. 218.186.9.231 (talk) 15:53, 4 March 2010 (UTC)[reply]

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unclear law[edit]

Quote: ...at the electrodes is directly proportional to their equivalent weight.

1. To who's equivalent weight? The electrodes?

2. Is "equivalent weight" a special term from physics or just saying that the mass of released material is proportional to the equivalent weight of the <thing answered in question 1> ?

פשוט pashute ♫ (talk) 14:05, 5 September 2017 (UTC)[reply]

DC is not a requirement[edit]

Direct current is in no way a requirement. Electrolysis is a phenomenon whereby chemical reactions occur due to an electric current. It doesn't matter what form. However, for nearly all practical applications, DC is used. But in fields such as analytical electrochemistry, AC is used (e.g., cyclic voltammetry). This article needs to clearly differentiate between the phenomenon and its exploitation. 71.50.180.112 (talk) 15:49, 26 December 2017 (UTC)[reply]

History of electrolysis[edit]

I'm going to add some more to the history about some other scientists who helped develop the idea, such as Luigi Galvani and Sir Humphrey Davy. Makaylacg (talk) 01:59, 1 November 2019 (UTC)[reply]