Vapor Pressure Lowering

The vapor pressure of solution is lower than that of the pure liquid. More correctly, the vapor pressure of solution containing a non-volatile (zero vapor pressure) solute is lower than that of the pure solvent. So if you dissolve sugar into water, the vapor pressure of the solution is lower than that of pure water. There are a number of ways to think about this phenomena but it important to realize that the main effect is a result of entropy.

The higher the entropy of a substance the lower its free energy. If we compare the entropy of a solution to that of a pure solvent, the entropy of the solution will be higher. Therefore, the free energy of the solution will be lower than that of the pure solvent. Lower free energy is more stable. From a thermodynamic standpoint, the solution is more stable than a pure solvent. Because the solution is more stable, fewer molecules are leaving to the gas phase. This lower evaporation rate leads to a lower vapor pressure.

From an ideal solution perspective (ΔHsolution=0) this effect is straight forward to calculate. The vapor pressure of the solution simply depends on the mole fraction of solvent. This idea is know as Raoult's Law. It states

\[P_{\rm solution} = \chi _{solvent} \; P^{\circ}\]

Where \(P^{\circ}\) is the vapor pressure of the pure solvent. What matters is not what the solute is, but how many moles of it there are. The more moles of solute, the lower the mole fraction of solvent, the lower the vapor pressure. Since we often write properties of solution based on the concentration of solute (rather than solvent) this formula can be re-written as a change in vapor pressure as

\[\Delta P = -\chi _{solute} \; P^{\circ}\]

It is important to note that this effect is relatively small. That is because even in very very concentrated solutions, the majority of the mixture is still solvent. Thus the solvent mole fraction is always very close to 100%. The only way to dramatically lower the mole fraction is to examine mixture of two liquids (rather than solids dissolved in liquids).

For vapor pressure lowering the effect also depends on the total concentration of all solutes. However, because the concentration is written as a mole fraction it is difficult to include the vant' Hoff factor i in the formula. This is because the mole fraction is a ratio. In this case the ratio of the moles of solute : the total number of moles. The total number of moles depends on the moles of solute and the moles of solvent. So, for an ionic solute remember to take into account the number ions formed in solution when calculating the moles of solute.

Vapor Pressure

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