Lowering of vapour pressure by solutes

Raoult’s law states that, for an ideal solution of volatile substances, the partial pressure exerted by each component in the gas above the solution is equal to the vapour pressure of the pure component multiplied by its mole fraction in the liquid mixture. The total vapour pressure of the solution is then given by the sum of these individual contributions, which is consistent with Dalton’s law of partial pressures.For a simple case of a two-component solution at room temperature, the total vapour pressure is the sum of the two pure component vapour pressures, each weighted by their mole fraction in the liquid. If one of the components is non-volatile, then it contributes nothing to the vapour above the solution. In this situation the vapour pressure of the solution is simply the vapour pressure of the pure volatile component multiplied by its mole fraction in the liquid.The reduction in vapour pressure compared with the pure liquid is therefore directly proportional to the mole fraction of the non-volatile solute. This means that adding a solute effectively dilutes the volatile solvent, lowering its vapour pressure in proportion to the fraction of solute present.For example, at 20 °C the vapour pressure of pure water is about 23 mbar. If a non-volatile solute is added, the vapour pressure decreases in a linear fashion with increasing solute mole fraction. When plotted against mole fraction, this produces a straight line that intercepts the y-axis at 23 mbar, with a slope of about −23.4 mbar. However, if the vapour pressure is replotted against solute weight percent, the relationship looks very different: instead of a straight line, the curve shows a sharp downturn at high solute concentrations, with the most precipitous drop occurring above roughly 80 wt%.For freeze-drying, the lowering of vapour pressure has important practical consequences. The presence of solutes in a frozen matrix reduces the effective vapour pressure of water compared with that of pure ice. As a result, the driving force for sublimation is diminished, which slows the rate of drying. In addition, because the vapour pressure depression is proportional to solute concentration, regions within the product that are richer in solute will dry more slowly than regions that are more dilute.This effect also underlies the concept of collapse temperature (). As ice is removed during primary drying, the unfrozen solute phase becomes more concentrated. The reduction in vapour pressure alters the balance between sublimation, glass transition behaviour, and structural stability. If the product temperature rises above the collapse temperature while vapour pressure is still depressed by concentrated solute, the dried structure can lose its rigidity and collapse.