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

Aug 21, 2017

Ideal solutions are such that $2 {\epsilon}_{A B} = {\epsilon}_{A A} + {\epsilon}_{B B}$, i.e. their intermolecular forces are exactly the same. Nonideal solutions can either have positive or negative deviation away from ideal mixed volumes.

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 $B B$ interactions, and $A B$ 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 $A A$, $B B$, and $A B$ interactions.

NEGATIVE DEVIATION LEADS TO VOLUME CONTRACTION

With negative deviation:

$\setminus m a t h b f \left(2 {\epsilon}_{A B} < {\epsilon}_{A A} + {\epsilon}_{B B}\right)$ 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 $A B$ 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:

$\setminus m a t h b f \left(2 {\epsilon}_{A B} > {\epsilon}_{A A} + {\epsilon}_{B B}\right)$ 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 $A B$ 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.