Suppose we have a supersaturated solution that is isolated from the environment. Some of the solutes condense into a crystal in the solution. Is it possible for the solution to get cooler during this process?

If so, why doesn't it violate the second law?

  • $\begingroup$ And why would it get cooler? Start there. $\endgroup$ – Jon Custer Feb 8 '16 at 2:29
  • $\begingroup$ Sorry, I don't understand your comment. I want to know whether this is possible. Has it ever been observed? How does your comment help me understand that? $\endgroup$ – Mark Eichenlaub Feb 8 '16 at 2:33
  • $\begingroup$ Compare the free energies of the two states. Since it is supersaturated, the solution would prefer (that is, have a lower free energy) if crystals formed - it is thermodynamically favored. Once crystals begin to form, where does that excess free energy go? (Hint - in supercooled liquid->solid transformations this is called recalescence). $\endgroup$ – Jon Custer Feb 8 '16 at 16:28
  • $\begingroup$ Seriously, I'm not in need of a lesson on thermodynamics; I'm a physics PhD student. I just want to know if this ever happens. It is claimed that it does on page 584 here (www3.nd.edu/~powers/ame.20231/wright1970.pdf) but the reference it gives doesn't seem to corroborate it, that I can determine. $\endgroup$ – Mark Eichenlaub Feb 8 '16 at 16:58

The system sodium sulfate (Na2SO4) / sodium sulfate decahydrate (Na2SO4 * 10 H2O) / Water might be an example.

  • Dissolving Na2SO4 in water is exothermic due to hydration.
  • Dissolving Na2SO4 * 10 H2O is endothermic (entropy effect).

Below 32.384°C Na2SO4 * 10 H2O crystallizes from aqueous solution, above 32.384°C water free Na2SO4.

The solubility of sodium sulphate shows the following unusual shape with a maximum at 32.384°C.

enter image description here

If you would now prepare a saturated solution of sodium sulphate at 32.384°C, and would then be able increase the temperature without precipitation of Na2SO4, you would get a supersaturated solution of sodium sulphate.

Putting a seed crystal of Na2SO4 into it should result in crystallization with the solution getting cooler during this process.

Note that the crystallization frees water molecules that were previously bonded through hydration. This will lead to an increase of entropy.

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  • $\begingroup$ That's a sneaky system. I particularly like the entropy increase via crystallization. I hope it works. :-) $\endgroup$ – Jason Patterson Feb 8 '16 at 22:50

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