# Gas station without pumps

## 2011 January 2

### Hydronium ions

Filed under: Uncategorized — gasstationwithoutpumps @ 22:54
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On my bike commute one Wednesday morning in November, I was thinking about water, not because I was thirsty, but because of the central role it plays in biology and biochemistry.  I’m mostly self-taught when it comes to physics and chemistry, so there are huge holes in my understanding.  I was realizing this morning that I have no idea what the equilibrium is between hydrogen ions and hydronium ions in water ($H^{+} + H_2O \leftrightharpoons H_3O^{+}$).

Furthermore, I don’t know the shape of a hydronium ion.  Are the three hydrogens on three corners of a tetrahedron or do they redistribute themselves to be as far apart as possible, forming a flat triangle with the oxygen in the  middle?  That question is clearly a quantum mechanical question,but I’m looking for an answer that is a simplification of the wave equation: more a chemist’s view than a physicist’s.  According to Wikipedia (Hydronium—structure),

H3O+ has a trigonal pyramid geometry with the oxygen atom at its apex. The H-O-H bond angle is approximately 113°, and the center of mass is very close to the oxygen atom.

That’s a larger angle than a tetrahedron (109.47 degrees) but smaller than a flat triangle (120 degrees).  I wonder how this structure was determined? Experimentally? by quantum mechanical calculation?

Wikipedia also implies that there are no H+ ions in water, and that they are all hydronium. That is undoubtedly a simplification, but how much of one? The $H^{+}$ could be in several forms ($H_{2k+1}O_k^{+}$ for $k\geq 0$), and the lone proton is probably rare, but I’ve not been able to find a good reference on the distribution of $k$.  The best I’ve been able to find is in Wikipedia (Hydronium—solvation), which explains various models for the delocalization of the proton over several water molecules as a disruption of the hydrogen-bonding network.  This actually makes more sense to me than thinking of hydronium as $H_3O^{+}$.  That is, there doesn’t see to be any particular reason for the proton to be always in association with the same oxygen.

## 1 Comment »

1. Lewis dot structures and VSEPR theory are very useful in determining the shape of simple molecules such as hydronium ion or water. H3O+ has total of 8 electrons, 6 of them in O-H bonds and two of them as a lone pair on central O atom. That means that you have 4 electron pairs around the central oxygen, resulting in the tetrahedral arrangement of these four electron pairs around the central atom. This happens because electron pairs like to be as far away from each other as possible, and tetrahedral arrangement is the one that maximizes the angles between them. One of the electron pairs is a lone pair (pointing in one of the corners of the tetrahedron), so the resulting molecular structure is trigonal pyramidal. Normally, the lone pair takes more space than single bonds, so VSEPR would predict the H-O-H bond angle to be actually smaller than the tetrahedral 109.5 angle. However, the positive charge is equally distributed over the hydrogen atoms, so it is pushing them further apart, thus arriving at angle of approximately 113 degrees. By the way, that angle was determined experimentally via infrared spectroscopy, but you can justify it based on the simple arguments mentioned above.
Also, any decent general chemistry book will have a good description of the Lewis dot structures and VSEPR if you want to learn more.

Comment by anon — 2011 January 3 @ 17:02

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