Explain why solution volume expands when we have positive deviation?

For ideal binary mixtures, let us suppose both components are liquids.

When two liquids #A# and #B# combine, there is a competition between #A A# or #BB# interactions, and #AB# interactions:

• Liquid #A# may prefer to interact more with liquid #B# than with liquid #A# (negative deviation).
• Liquid #A# may prefer to interact with liquid #A# more than with liquid #B# (positive deviation).

We can examine this relationship by considering the energies #epsilon# of #A A#, #BB#, and #AB# interactions.

NEGATIVE DEVIATION LEADS TO VOLUME CONTRACTION

With negative deviation:

#\mathbf(2epsilon_(AB) < epsilon_(A A) + epsilon_(BB))#

You can see the vapor pressure vs. mole fraction curve dip below the ideal/Raoult's Law lines, hence negative deviation.

Here, #A# prefers to interact with #B# and #B# prefers to interact with #A# because the #AB# interactions are less repulsive. So, liquid #A# mixes favorably with liquid #B#.

Therefore, after mixing, the most likely average distance of molecule #A# from molecule #B# is closer together than it would be from molecule #A#. This means the volume of the solution contracts after mixing, relative to the ideal solution.

That means #A# and #B# are difficult to make vaporize overall because the molecules #A# and #B# are well-attracted together.

POSITIVE DEVIATION LEADS TO VOLUME EXPANSION

On the other hand, with positive deviation:

#\mathbf(2epsilon_(AB) > epsilon_(A A) + epsilon_(BB))#

You can see the vapor pressure vs. mole fraction curve bulge above the ideal/Raoult's Law lines, hence positive deviation.

Here, #A# prefers to interact with #A# and #B# prefers to interact with #B# because the #AB# interactions are more repulsive. So, liquid #A# mixes poorly with liquid #B#.

Therefore, after mixing, the most likely average distance of molecule #A# from molecule #B# is farther away than it would be from molecule #A#. This means the volume of the solution expands after mixing, relative to the ideal solution.

That means #A# and #B# interact unfavorably, and are easy to make vaporize overall because the molecules #A# and #B# are poorly-attracted together.

Therefore, the volume of the solution expands when:

• The interaction of substance #A# and #B# shows positive deviation away from ideal behavior, i.e. #2epsilon_(AB) > epsilon_(A A) + epsilon_(BB)#.
• #A# and #B# are thoroughly mixed together to make a solution.