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Just learnt that $\ce{H+}$ (aq) is equal to $\ce{H3O+}$ and now I know why.

I'm thinking about cell processes that involve $\ce{H+}$ transport. I wonder if that $\ce{H+}$ is $\ce{H3O+}$ too, like mitochondrial electron transport chain.

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    $\begingroup$ $\ce{H3O+}$, written as $\ce{H3O+}$ $\endgroup$
    – Poutnik
    Dec 31, 2021 at 22:46
  • $\begingroup$ Already at the level of composition, $\ce{H^+}$ and $\ce{H3O^+}$ are not equal to each other. In addition, given the high charge density $\ce{H+}$ would carry, $\ce{H3O^+}$ and «higher forms» of hydronium ions are more likely in aqueous solutions. $\endgroup$
    – Buttonwood
    Jan 1, 2022 at 0:46
  • $\begingroup$ This gif might help you understand how $\ce{H+}$ is transferred. $\endgroup$ Jan 1, 2022 at 10:17

2 Answers 2

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$\ce{H+}$ (aq) is equal to $\ce{H3O+}$

It would be more accurate to say $\ce{H+ (aq)}$ is equivalent to $\ce{H3O+ (aq)}$. This acknowledges that the two species have different mass, and that it does not matter how to write them because they are surrounded by plenty of water anyway, and the water reacts with the species, leading to a highly dynamic situation.

I wonder if that $\ce{H+}$ is $\ce{H3O+}$ too, like mitochondrial electron transport chain.

There are several ways how protons are thought to be transported in the electron transport chain:

  1. As part of redox half-reactions like $\ce{2H+ + 2e- + Q -> QH2}$. If this half reaction occurs on one side of the membrane and the reverse occurs on the other side, you get a net transport of 2 protons. The protons travel neither in the form of $\ce{H+}$ or $\ce{H3O+}$, but rather covalently attached to the Q electron carrrier. This is well-established for complex III.

  2. As part of protonation and deprotonation reactions, either involving water or other acids and bases. Complex I has a "water wire" that enables multiple such steps. It also has several amino acid side chains that get protonated and deprotonated. For example, histidine can gain a proton on one side of its ring and donate a second proton on the other side of its ring. In complex IV (cytochrome oxidase), the acid/base reactions are thought to be driven by electron transfer leading to local electrical fields.

  3. Protons can tunnel between proton carriers. This is invoked when the distances between proton carriers are too large to form hydrogen bonds.

You might talk of $\ce{H3O+}$ transfer for mechanism 2) involving water molecules. Otherwise, it makes more sense to use the term proton transfer.

Some sources:

  1. Complex IV https://www.pnas.org/content/95/22/12747
  2. Complex I https://www.biorxiv.org/content/biorxiv/early/2021/04/16/2021.04.16.440187.full.pdf
  3. Complex III https://en.wikipedia.org/wiki/Q_cycle
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First of all, a proton is highly unstable, because it is an ionized H atom. Therefore, it always wants to find a potential well to be stablized (just like electrons want to find a potential well on neuclei; however, note that the two potential wells are inverted due to opposite signs). A proton is often found to bind to lone-pair electrons ":", e.g. the lone pair of a $\ce{H2O}$ molecule, to give $\ce{H3O+}$. Neutralization reaction between HCl and $\ce{NH3}$ in water can be thought of as HCl being dissociated, with the proton leaving the lone pair on $\ce{Cl-}$ and being transferred to the lone pair on water forming $\ce{H3O+}$, and then to $\ce{NH3}$ forming $\ce{NH4+}$. Using gas phase data as a tentative reference, $\ce{H2O}$ and $\ce{NH3}$ have proton affinities of 697 and 854 kJ/mol (see https://en.wikipedia.org/wiki/Proton_affinity_(data_page)). Therefore, eventually proton prefers to bind to $\ce{NH3}$ than $\ce{H2O}$.

However, in water the proton may be shared between two water molecules, which in turn are solvated by a shell of other water molecules. Therefore, it is not accurate to say "$\ce{H+}$(aq) is equal to $\ce{H3O+}$". If you read the Wiki page on Hydronium https://en.wikipedia.org/wiki/Hydronium, you will see the following statement relevant to your question: "Three main structures for the aqueous proton have garnered experimental support: The Eigen cation, which is a tetrahydrate, $\ce{H3O+(H2O)3}$; the Zundel cation, which is a symmetric dihydrate, $\ce{H+(H2O)2}$; and the Stoyanov cation, an expanded Zundel cation, which is a hexahydrate: $\ce{H+(H2O)2(H2O)4}$. Spectroscopic evidence from well-defined IR spectra overwhelmingly supports the Stoyanov cation as the predominant form. For this reason, it has been suggested that wherever possible, the symbol $\ce{H+}$(aq) should be used instead of the hydronium ion."

Next about $\ce{H+}$ transport mechanism, we can look at how protons are transported in proton-exchange membranes (PEMs) such as Nafion. There are essentially three types of mechanisms: Grotthus mechanism, vehicle mechanism, and surface mechanism. The following figure is taken from a book titled "Polymer Science: A Comprehensive Reference - Volume 10 Polymers for a sustainable environment and green energy." Grotthus mechanism involves consecutive hop of proton and turn of water molecules so that the proton being transported migrates between neighboring water molecules. In this case, imagine a team of soccer players standing in a line, which does not have to be straigt line. Each soccer player has two arms each holding one soccer standing for hydrogen atom. Each has two legs standanding for two lone-pair orbitals (two arms and two legs are equal to eight valence electrons and each limb equal to two valence electrons). Then a soccer is passed from one player to another, where each player uses only one of his/her leg to take the ball and then pass to the next one in the line. (Note this picture is simplified - the soccer passed to the next player could be the one on one of the two hands.) During this process, the hop and turn movements are involved. This is how you can understand Grotthus mechanism. In contrast, vehicle mechanism involves a proton-carrying molecule to do all the work instead of relying on a team work. These two mechanisms take place in the aqueous region between Nafion surfaces. A third mechanism called surface mechanism takes place on the surface of Nafion in the boundary region, which takes advantage of the lone pairs on the terminal sulfonic acid units.

With that background said, how protons are transported in cell processes depends on where it takes place, either through the cell membrane or within a cell. You have to be more specific about the question. It can be imagined that due to the presence of water, protons bind to the lone pairs of water molecules, and therefore both Grotthus mechanism and vehicle mechanism are possible. In addition, the surface of some cell structures may have lone pairs as well, which may faciliate the surface mechanism. In any case, protons do not exist by themselves but bind to lone pairs and undergo transport from lone pairs to lone pairs. Note that between the transfer from one lone pair to another lone pair, there should be an energy barrier separating the two potential wells. However, protons are very light and may display some degree of wave character, and therefore, they may undergo quantum tunneling to realize transfer without needing to fully climb up the energy barrier. Hope this helps.

Simplified schematic representation of proton transport in hydrated PEMs. A comparison of the surface mechanism, Grotthuss mechanism,
and vehicle mechanism.

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  • $\begingroup$ First of all, a proton is highly unstable, because it is an ionized H atom. Rather an ionized H atom is highly unstable, because it is a proton. $\endgroup$
    – Poutnik
    Jan 2, 2022 at 7:00
  • $\begingroup$ :-) Just one way to understand it :-) $\endgroup$
    – Josiah_H
    Jan 2, 2022 at 7:57

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