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I suspect that initially, scientists believed that the acid ion was $\ce{H^+}$ since $\ce{H2}$ is released through electrolysis, right? But what experiment was done to change the standpoint to assume that it is instead the $\ce{H3O^+}$ ion?

Or perhaps there's both $\ce{H^+}$ and $\ce{H3O^+}$ ions?

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According to Wikipedia, the actual structure of hydronium was discovered using infrared spectroscopy.

It should be noted that $\ce{H+}$ notation is still useful for reaction balancing, since it's much easier to count atoms in $\ce{H+}$ instead of $\ce{H3O+}$, even if the former ion may not really exist.

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Actually, the initial theories before Lewis suggested that $\ce{H+}$ is the cause of acidity. However, it soon turned up that an ion as small as the nucleus of hydrogen (you may simply call it a proton) can't be created in low energy reactions due to its high polarising power. So, $\ce{H+}$ is though the cause of acidic nature in aqueous solutions, $\ce{H+}$ never exists as $\ce{H+}$ but as $\ce{H3O+}$, $\ce{H9O4+}$, etc. It is because the proton is heavily hydrated. Though we are not very sure of what is the actual hydrated form, we usually refer it to as $\ce{H3O+}$ or $\ce{H+ (aq)}$.

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    $\begingroup$ It's not that we don't know what the hydrated form is, but there simply is no definite form, but a highly dynamic equillibrium between several states. $\endgroup$ – Karl Apr 19 '17 at 16:11
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As stated here, the notion that (pure) water disassociates into some kind of ions is actually very misleading. Instead of thinking of liquid water as existing in separate molecules, it is far better to consider it as a vast network of hydrogen and oxygen atoms, where bonds are not in a binary state of 'formed' or 'broken' only, but have continuously varying strength depending more or less on the distance. It is then easy to understand how a charge imbalance can be very rapidly transferred to another location by just slight shifts in the positions of the atoms in the network. Unfortunately, this process is still called "proton transfer" despite the fact that there is no actual movement of a single proton across a long distance.

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  • $\begingroup$ Of course, for the purpose of analyzing reactions it is sufficient to use the "H3O+" ion since it has pretty much the same properties as the local configuration of the hydrogen and oxygen atoms that are involved in the reaction, namely the slightly positive H and the slightly negative O that can accept up to 1,4 'bonds' (electron pairs) each. $\endgroup$ – user21820 Apr 20 '17 at 14:20

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