Question

What are positive and negative deviation with respect to ideal binary mixtures?

Answer 1

Ideal solutions are such that `2epsilon_(AB) = epsilon_(A A) + epsilon_(BB)`, i.e. their intermolecular forces are exactly the same. Nonideal solutions can either have positive or negative deviation away from ideal mixed volumes.

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For ideal binary mixtures, let us suppose both components are at least somewhat volatile 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).
• There may be no preference of `A` or `B` to interact with either `A` or `B` over the other (ideal solution).

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.