Dissolve sugar in water and the water evaporates a little more slowly. Vapor Pressure and Boiling explained where vapor pressure comes from; mole fraction measures how much of the surface the solvent still holds.
Key idea
For a nonvolatile solute (one that doesn't evaporate), the solution's vapor pressure is $$P_\text{solution} = \chi_\text{solvent}\,P^\circ_\text{solvent},$$ where $P^\circ$ is the pure solvent's vapor pressure. The lowering is $\Delta P = \chi_\text{solute}\,P^\circ$. For ionic solutes, count every ion as a particle.
Why it works
Solvent molecules escape from the surface; solute particles at the surface take up some of that space but never escape. If 10% of the particles are solute, only 90% of the surface is solvent, so the escaping rate, and the vapor pressure, drops to 90% of the pure solvent's. Condensation adjusts to match, so the new equilibrium pressure is $\chi_\text{solvent}P^\circ$. The identity of the solute doesn't matter, only the number of its particles: a colligative property ("depending on the collection").
Worked example: Sugar water
A solution contains $1.00\ \text{mol}$ of glucose in $9.00\ \text{mol}$ of water at $25^\circ\text{C}$, where pure water's vapor pressure is $23.8\ \text{mmHg}$. Find the solution's vapor pressure.
- $\chi_\text{water} = \dfrac{9.00}{9.00 + 1.00} = 0.900$.
- $P = 0.900 \times 23.8 = 21.4\ \text{mmHg}$.
Answer: $21.4\ \text{mmHg}$ (lowered by 2.4).
Worked example: From masses
$50.0\ \text{g}$ of sucrose ($342.3\ \text{g/mol}$) is dissolved in $250.0\ \text{g}$ of water at $30^\circ\text{C}$ ($P^\circ = 31.8\ \text{mmHg}$). By how much is the vapor pressure lowered?
- Moles: sucrose $50.0/342.3 = 0.1461$; water $250.0/18.02 = 13.87$.
- $$\chi_\text{sucrose} = \dfrac{0.1461}{0.1461 + 13.87} = 0.01042$$
- $\Delta P = 0.01042 \times 31.8 = 0.331\ \text{mmHg}$.
Answer: $0.331\ \text{mmHg}$
Worked example: An ionic solute
$0.500\ \text{mol}$ of NaCl is dissolved in $10.0\ \text{mol}$ of water at $25^\circ\text{C}$ ($P^\circ = 23.8\ \text{mmHg}$). Estimate the vapor pressure, treating the salt as fully split into ions.
- NaCl gives 2 ions: $1.00\ \text{mol}$ of solute particles.
- $\chi_\text{water} = \dfrac{10.0}{10.0 + 1.00} = 0.909$.
- $P = 0.909 \times 23.8 = 21.6\ \text{mmHg}$.
Answer: About $21.6\ \text{mmHg}$.
If the solute is volatile too, as in a mixture of two liquids, each one contributes its own share: $P_\text{total} = \chi_A P^\circ_A + \chi_B P^\circ_B$. The vapor is then richer in the more volatile liquid, which is the principle behind distillation.
Common mistake
Using the solute's mole fraction where the solvent's belongs: "$P = 0.100 \times 23.8 = 2.38$ mmHg." That would mean a little sugar wipes out 90% of the vapor pressure. Check: a dilute solution's vapor pressure should be only a little below the pure solvent's; $\chi_\text{solvent}$ is the number close to 1.