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Can we break the covalent bonds of water molecules $\ce{H2O}$ using resonance frequencies? What is the wavelegth of the water's molecule? Can we create a vibration like this and use it to separate hydrogen from oxygen?

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Yes this is possible. Your question does not state the source of the frequency, but in this internet article they have used laser light.

I am not sure at what frequency you need to irradiate water to break the O-H bond, but I would speculate that a good frequency would be close to the IR stretching frequencies of the O-H bond in water.

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    $\begingroup$ I think a better frequency would be one that excites electrons … $\endgroup$
    – Jan
    Dec 30, 2015 at 22:53
  • $\begingroup$ You'll need to get above the ground electronic state, as @Jan notes. And I think the OP needs to chime in with respect to the part about separating hydrogen and oxygen: do you mean as charged species, radicals, diatomic gases, or what? $\endgroup$ Dec 31, 2015 at 0:52
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    $\begingroup$ @Jan. That was also my initial guess, but as soon as you start exciting the electronic levels, the geometry of the molecule gets distorted and you are no longer 'pumping' at the right frequency to break the bond. I don't think it is possible then to break a specific bond. That's why my suggestion was to slowly 'pump' the vibrational levels until the bond breaks. In other words, you would like to stay as close to ground state chemistry. I haven't found the article though where the procedure is given. $\endgroup$
    – Ivo Filot
    Dec 31, 2015 at 13:23
  • $\begingroup$ In the article, they excite surface Si-H bonds. I suspect that being on a surface really helps prevent transfer of energy to other motions by collision. In liquid H2O, I suspect you would just heat the solution rather than break bonds very often, though maybe there's a laser that could deliver energy fast enough to overcome this. $\endgroup$
    – Andrew
    Aug 6, 2019 at 12:03
  • $\begingroup$ The reference is a press-release without details provided, so I highly suspect there is a lot of gotchas that might considerably change the meaning. I particular, I want to point that molecular vibrations are unharmonic and at higher energy levels the vibration levels (and associated frequencies) deviate from expressions for harmonic oscillator. $\endgroup$
    – permeakra
    Mar 10, 2021 at 16:01
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Yes, but not through direct excitation into a dissociated state. This is explained in Ref. 1:

Unfortunately, measuring D0 by direct photoexcitation of H2O from its vibrational ground state to the dissociation threshold is prohibited by the negligibly small intensity of such an overtone transition.

Instead the authors accomplished the measurement by exciting the molecule through a sequence of rovibrational states:

We have performed a direct measurement of one of the most fundamental thermochemical values: the O-H bond energy in water. Using a triple-resonance laser excitation scheme, we excite the molecule through a series of vibrational overtone transitions to access directly the onset of the dissociative continuum. The dissociation energy obtained from our experiments, $\pu{41145.94 ± 0.15 cm−1}$, is ∼30 times more accurate than the currently accepted value and has important implications for other thermochemical quantities linked to the bond energy of water.

Please see the cited reference (behind paywall) for more information.

References

  1. Pavlo Maksyutenko, Thomas R. Rizzo, and Oleg V. Boyarkina). A direct measurement of the dissociation energy of water. J. Chem. Phys. 125, 181101 (2006)
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