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Does intermolecular force of attraction have anything to do with molecules having more energy in their liquid state than their solid state? If not, what is responsible for greater kinetic energy in liquids?

Lime
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    A new degree of freedom occurs in liquids : translation. In the solid state, the only degrees of freedom are rotation and vibration. – Maurice Jun 13 '21 at 16:00
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    @Maurice With unusual exceptions, solids have vibrational freedom only. – theorist Jun 13 '21 at 20:38
  • @theorist On the contrary, the translational kinetic energy of a substance is a function of temperature not state. At a phase transition, for example, the solid and liquid phases, being at the same T, have the same translational kinetic energy. Obviously, in the solid the average displacement of each molecule is much smaller, but there's definitely translation happening. More here: https://chemistry.stackexchange.com/questions/88803/kinetic-energy-of-molecules-in-liquid-state/89011#89011 – Andrew Jun 14 '21 at 11:59
  • @Maurice - see comment above – Andrew Jun 14 '21 at 12:00
  • @Andrew I don't see that. Indeed, back in Jan. I questioned the ans. you linked, and never rec'd an adequate reply. Physically, it doesn't makes sense to me that particles in solids have translational freedom (w/ the exception of free electrons in metals). And the basic models we have for the heat capacities of solids treat them as either collections of harmonic oscillators (Einstein), or as having collective vibrational modes (Debye); i.e., no translational motion is included. See also my ans. here: https://chemistry.stackexchange.com/questions/129290/what-exactly-is-temperature/129366#129366 – theorist Jun 14 '21 at 19:45
  • @Andrew And from a quick search of the literature: "A monoatomic molecule in the gas or liquid phase moves with free motion. Such a movement of a monomolecule is called a translational mode (Fig. 1(i)). By contrast, bonded atoms in a molecule or a solid phase vibrate with other atoms coherently, which is called the vibrational mode." [ https://pubs.rsc.org/en/content/articlelanding/2020/sc/d0sc02605k#cit1 ] – theorist Jun 14 '21 at 19:58
  • @theorist - it does get into semantics a bit, but a vibrational mode in which the center of mass is in motion technically is or contains a translational mode. In a typical solid, these can be modeled as harmonic oscillators in which the restoring force is intermolecular rather than intramolecular. If they become coupled across a larger scale, the result is a phonon, but that coupling isn't required for translation to be happening. – Andrew Jun 14 '21 at 20:16
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    @Andrew Sure, but by that way of thinking rotational motion is also translational, because the atomic centers are are moving through space as the particle rotates. But no one calls that translational. By the same token, no one (at least that I know of) refers to vib. motion as a translational DOF just b/c it includes particle motion. The point is that all modes involve motion, and thus to call all modes translational because of it makes the distinction between translation, rotation, and vibration meaningless. And it is important/useful to distinguish these b/c they are qualitatively different. – theorist Jun 14 '21 at 21:22
  • @theorist -The key point is the movement of the center of mass of the molecule. Movement of atoms in a rotation is not translation if the center of mass remains stationary. The normal vibrational and rotational modes of a molecule are clearly defined as having a stationary center of mass. Any movement of the COM requires activating a translational mode in addition to the vibration. – Andrew Jun 14 '21 at 22:01
  • @Andrew In liquids (or anytime the molecule is subject to external forces), the CM can move as a result of rotations. So you're saying anytime there is vibration or rotation in which the CM moves, that should be considered to have a translational component. Questions: (1) I offered generally-accepted approaches in which the motion of solids is treated as purely vibrational. Can you give me examples of generally-accepted approaches in which the vibrational DOF's in solids are broken up into translational and non-translational components? I've never seen this done. What I'm really asking is... – theorist Jun 15 '21 at 02:59
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    ...for you to show that your anzatz, if you will, is also generally-accepted within the field (as I've done), rather than an outlier view. (2) Can you explain why your anzatz is useful, i.e., why it would give a better model of the properties of solids than the standard ones, in which the partition functions are vibrational only? (3) You wrote "the solid and liquid phases, being at the same T, have the same translational kinetic energy". That would only be the case if the translational states are equally accessible in both. Is that the case, and how would you demonstrate this? – theorist Jun 15 '21 at 03:01
  • Let us continue this discussion in chat. – Andrew Jun 15 '21 at 13:08

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It is a common misconception that molecules in a liquid state categorically have more kinetic energy than molecules in a solid state. This is only true when the liquid is at a higher temperature than the solid, simply because translational kinetic energy is proportional to temperature.

In a molecular solid, the individual molecules cannot move very far, but they can still move, and if their centers of mass are moving at all, they have translational kinetic energy. The kinetic energy in these small motions is proportional to the temperature, just as is the case with the larger motions of molecules in a liquid.

So if a solid and liquid are in equilibrium at the same temperature (the melting point), both phases will have the same amount of kinetic energy (assuming we are not at such a low temperature that quantum effects come into play).

You are correct, however, that molecules in the liquid state have more energy than in the solid state and that intermolecular forces play a role. The difference in energy, though, is in the potential energy rather than the kinetic energy. When bonds form, whether intramolecular or intermolecular, there is a decrease in potential energy. In order to break those bonds, we have to increase the potential energy. When we add energy to convert a solid to a liquid (or a liquid to a gas), that energy goes to increasing the potential energy rather than the kinetic energy.

Andrew
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There's a form of inverse relationship between the strength of intermolecular force of attraction between molecules of a substance and the degree of kinetic energy of the substance. The higher the strength of intermolecular force between the molecules of a substance the lower the kinetic energy(K.E.). The molecules of solid have greater intermolecular force that exist between them compare to the molecules of liquid, and as such they have less kinetic energy (the energy of a body in motion). The the link below explains the concept of kinetic energy https://www.khanacademy.org/science/biology/energy-and-enzymes/the-laws-of-thermodynamics/a/types-of-energy

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