Non-ideal Solutions: Positive and Negative Deviations from Raoult's Law

A non-ideal solution fails to obey Raoult's law across the whole concentration range, and unlike an ideal solution, it shows a measurable change in both enthalpy and volume on mixing: $\Delta H_{mixing}\ne0$ and $\Delta V_{mixing}\ne0$. Depending on how the A-B intermolecular attraction compares with the A-A and B-B attractions, the deviation from Raoult's law can go one of two ways.

Positive deviation. Suppose the attractive forces between A and B molecules are weaker than the attractive forces within pure A (A-A) or pure B (B-B). Molecules in such a mixture then have a greater tendency to escape into the vapour phase than an ideal A-B mixture would -- so each component's actual partial pressure exceeds what Raoult's law predicts:

and consequently the total vapour pressure is higher than Raoult's law predicts:

This is called positive deviation (Figure 9.7): the actual vapour-pressure curves for A, B and the total all lie above the dashed ideal (Raoult's-law) lines.

Worked example -- ethanol and water. In an ethanol-water mixture, the hydrogen bonding between ethanol and water molecules is weaker than the hydrogen bonding among ethanol molecules themselves, or among water molecules themselves. This weaker cross-interaction means both components evaporate more readily from the mixture than expected, raising the solution's vapour pressure above the Raoult's-law prediction. Mixing is endothermic ($\Delta H_{mixing}>0$) and there is a slight increase in volume on mixing ($\Delta V_{mixing}>0$). Other positive-deviation pairs given in the text: ethyl alcohol & cyclohexane, benzene & acetone, carbon tetrachloride & chloroform, acetone & ethyl alcohol, and ethyl alcohol & water.

Negative deviation. Now suppose the A-B attractive forces are stronger than the A-A and B-B forces. Molecules then have a lower escaping tendency than an ideal mixture would show, so

and the total vapour pressure is lower than the sum $p^\circ_Ax_A+p^\circ_Bx_B$ predicts -- negative deviation (Figure 9.8): the actual curves lie below the ideal dashed lines. …