According to Guggemos, Slavicek and Kresin, about 5-6!. This is one of those simple ideas, which is probably quite tough to do experimentally. It involved blasting water vapour through a pinhole, adding HCl and measuring the dipole-moment induced deflection by an electric field. They found “evidence for a noticeable rise in the dipole moment occurring at n≈5–6“.
Modelling the structures takes little time. So here are some ωB97XD/6-311++G(2d,2p) gas phase models. I state at the outset that these are not dynamic-stochastic models, averaged over many conformations, but a static picture of individual poses. As usual, click on individual images to obtain an interactive 3D model (Java required).‡
n=1. Dipole moment 3.7D
n=2. Dipole moment 2.4D. Note how the O…H bond becomes shorter.
n=3. Dipole moment 2.5D. Note how the key O..H bond is contracting rapidly, as are the other H-bond interactions. This is the cyclic polarisation effect, where each bond influences the others. We are starting to approach the formation of H3O+ and Cl-!
n=4. Dipole moment 2.3 D, We have two ways to add the next water molecule, firstly to try to stabilise the H3O+. Nope.
n=4, Dipole moment 1.1 D. Better by solvating the Cl-! The proton originally attached to the Cl is now starting its transfer to the water to form that hydronium cation, but the dipole moment is not yet large.
n=5. Dipole moment 4.7D. The ionisation is almost complete and the dipole moment is on the increase.
n=6. The dipole moment is up to 8.2D and the three H-O bonds of the hydronium cation are almost all equal in length.
A cautionary observation though. The isomer below for n=6 is lower in energy by ΔG -1.2 kcal/mol, and its dipole moment is only 2.5D! The charges (summed onto heavy atoms) show the chloride to have -0.88 and the hydronium cation +0.88, so it is a true ion-pair, despite its dipole moment.
So these calculations do indeed appear to confirm that 5-6 water molecules are required to ionise HCl. But it does raise the interesting issue that even for n=6, there are poses for the assembly which have low dipole moments. Clearly of course the observed dipole moment is a dynamic average over many conformations of similar energy but the prediction that some of these may have low dipole moments should be noted.
‡ If you right-click in the 3D model area, you can bring down a list of vibrational modes for each complex from the first item of the pop-up menu that appears (labelled model). You might wish to e.g. explore how the H-Cl stretch vibration changes as the ionisation increases.
- N. Guggemos, P. Slavíček, and V.V. Kresin, "Electric Dipole Moments of Nanosolvated Acid Molecules in Water Clusters", Phys. Rev. Lett., vol. 114, 2015. http://dx.doi.org/10.1103/PhysRevLett.114.043401
- Henry S Rzepa., and Henry S Rzepa., "H 3 Cl 1 O 1", 2015. http://dx.doi.org/10.14469/ch/189758
- Henry S Rzepa., and Henry S Rzepa., "H 5 Cl 1 O 2", 2015. http://dx.doi.org/10.14469/ch/189760
- Henry S Rzepa., and Henry S Rzepa., "H 7 Cl 1 O 3", 2015. http://dx.doi.org/10.14469/ch/189759
- Henry S Rzepa., and Henry S Rzepa., "H 9 Cl 1 O 4", 2015. http://dx.doi.org/10.14469/ch/189763
- Henry S Rzepa., and Henry S Rzepa., "H 11 Cl 1 O 5", 2015. http://dx.doi.org/10.14469/ch/189756
- Henry S Rzepa., and Henry S Rzepa., "H 13 Cl 1 O 6", 2015. http://dx.doi.org/10.14469/ch/189761
- Henry S Rzepa., and Henry S Rzepa., "H 13 Cl 1 O 6", 2015. http://dx.doi.org/10.14469/ch/189764
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