Different volatilities in ideal solutions?

  • #1
Suppose ##A## and ##B## are two liquids, and intermolecular forces between molecules of ##A## are of magnitude ##f_{AA}## and between molecules of ##B##, ##f_{BB}##. If ##f_{AA}>f_{BB}##, then the pure liquid ##A## is volatile than ##BB##, i.e., the tendencies that the molecules have to leave liquid phase to the gas phase depends on the intermolecular forces between them.

Say we mix ##A## and ##B## to make a solution. From my understanding, such a solution is said to be ideal, if the tendencies that the molecules of ##A## and ##B## have to leave the solution to the gas phase remain unchanged upon mixing.

Now certainly, once the liquids are mixed, molecules of ##A## will interact with those of ##B##, and new intermolecular interactions will form between them; let us say of magnitude ##f_{AB}##.

If the tendency of molecules of ##A## to leave the liquid must remain unchanged, the new interactions it forms with molecules of ##B## must be of the same magnitude as ##f_{AA}##, so ##f_{AA}=f_{AB}##, or the tendency should change. Similarly, for the tendency of molecules of ##B## to leave the solution to not change, ##f_{BB}=f_{AB}##.

But then ##f_{AA}=f_{BB}##, so the liquids must have the same volatilities. Is this so? Have I misunderstood anything?
 

Answers and Replies

  • #2
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If the tendency of molecules of ##A## to leave the liquid must remain unchanged, the new interactions it forms with molecules of ##B## must be of the same magnitude as ##f_{AA}##, so ##f_{AA}=f_{AB}##, or the tendency should change. Similarly, for the tendency of molecules of ##B## to leave the solution to not change, ##f_{BB}=f_{AB}##.

But then ##f_{AA}=f_{BB}##, so the liquids must have the same volatilities. Is this so? Have I misunderstood anything?
Yes, you misunderstood something
The situation ##f_{AA}=f_{BB}=f_{AB}## is one option to have ideal solution, but not the only one.
Consider four molecules - two A and two B molecules.
When the pairs change, they form two pairs of AB.
Therefore, it is sufficient that
##f_{AA}+f_{BB}=2*f_{AB}##
 

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