Is it possible to derive the density of water by looking at its molecular structure? Is there a theoretical formula that describe the dependence with temperature?
Thanks for the help!
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$\begingroup$ No, but there are molecular dynamics simulations. However, it is difficult to get the temperatures for phase transitions. $\endgroup$– user137289Oct 23, 2019 at 19:07
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2 Answers
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The exact and/or universal formula doesn't exist. But there are density predictions possible for defined classes of chemical compounds. Those methods are based only on predictions, so the result may vary from the reality. To create such a prediction you have to collect and analyse the physical/chemical properties of large quantity of compounds, basing on the structure, polarity, molecular mass, etc.
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I might have a qualitative picture which has some naive, quantitative implications. I'm not sure how accurate the results would be.
In the Bohr model of the atom, we basically have the electron orbiting the proton at a position where the kinetic energy matches the potential energy and the angular momentum of the electron is an integer multiple of $\hbar$.
Water is a polar molecule that can be roughly modeled as a perfect dipole.
By analogy with the atomic system, what does it look like when two dipoles "orbit" each other? What does it mean when their kinetic energy matches their potential energy? Is it necessary to take into account quantization of the angular momentum?
Further complicating things, different degrees of freedom play a role at different temperatures. There's three translation directions, three possible directions of oscillation then some rotational degrees of freedom at higher temperatures.
The dipole moment of water probable remains constant regardless of temperature, the internal atomic excitations cancelling out on average. This suggests that the change of the dielectric constant of water with temperature has some implications regarding geometric considerations of the water molecules, including density.
