I watched an extremely engaging video "Why does ice float in water?" by George Zaidan and Charles Morton, https://www.youtube.com/watch?v=UukRgqzk-KE. In particular, video says "Below 4oC kinetic energy of water molecules falls below the energy of hydrogen bonds. So hydrogen bonds form much more frequently then they break". I decided to verify this statement, and on my way to do so I found energy of hydrogen bonds: "6-30 kJ/mol" according to this source http://book.bionumbers.org/what-is-the-energy-of-a-hydrogen-bond/. However I was unable to find a way to calculate kinetic energy of water molecules. Your help on this matter would be highly appreciated.
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asked Jul 13, 2016 at 16:52
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1 Answer
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It looks like they calculated the average thermal energy of water molecules, which by classical equipartition theorem is $3RT/2$ kJ mol$^{-1}$. This works out at approx 4 kJ mol$^{-1}$ at 40 C. This amount of energy includes translational, vibrational and rotational energy.
The vibrational quanta are large in water and almost all molecules will have only zero point vibrational energy. Rotational quanta are smaller and many will be excited at these temperatures. The smallest rotational quantum value for water is approx 0.2 kJ mol$^{-1}$ the next 6 times larger and the next 12 times (increasing as $J(J+1)$ for quantum number J) so a few rotational levels will be populated. Energy will flow between translation and rotations as random collisions occur between molecules of water. A full calculation involves using the partition functions. Calculating these and their contribution to heat capacity is treated in most undergraduate phys. chem. textbooks.
