Calculate the vapor pressure at 20^∘ C of a saturated...

Calculate the vapor pressure at $20^{\circ} \mathrm{C}$ of a saturated solution of the nonvolatile solute, urea, $\mathrm{CO}\left(\mathrm{NH}_{2}\right)_{2},$ in methanol, $\mathrm{CH}_{3} \mathrm{OH}$. The solubility is $17 \mathrm{g}$ urea/ $100 \mathrm{mL}$ methanol. The density of methanol is $0.792 \mathrm{g} / \mathrm{mL}$, and its vapor pressure at $20^{\circ} \mathrm{C}$ is $95.7 \mathrm{mmHg}$.

Key Concepts

Raoult's Law

Raoult's Law states that the vapor pressure of an ideal solution is directly proportional to the mole fraction of the solvent. This means that when a nonvolatile solute is added to a volatile solvent, the vapor pressure of the solution is lower than that of the pure solvent. The law provides a way to calculate the decrease in vapor pressure based on the proportion of solute particles present, which is key to understanding this type of colligative effect.

Colligative Properties

Colligative properties are characteristics of solutions that depend only on the number of solute particles, not their identity. Vapor pressure lowering, boiling point elevation, freezing point depression, and osmotic pressure are all examples of colligative properties. These properties are particularly useful for studying solutions, as they help predict changes in physical behavior when a solute is dissolved in a solvent.

Mole Fraction Calculation

Mole fraction is a way of expressing the concentration of a component in a mixture by dividing the number of moles of that component by the total number of moles of all components present. In the context of vapor pressure lowering, calculating the mole fraction of the solvent is essential because Raoult's Law uses this ratio to determine the vapor pressure of the solution.

Density and Unit Conversion in Solutions

Density is often used to convert between volume and mass when dealing with solutions. This conversion is necessary for calculating the number of moles of a solvent from its volume, which then allows for the determination of the mole fraction. Understanding how density relates to mass and volume is crucial in solving solution concentration and vapor pressure problems.

Nonvolatile Solute Concept

A nonvolatile solute is one that does not appreciably contribute to the vapor phase of a solution. In vapor pressure lowering, only the solvent contributes to the vapor phase, since the nonvolatile solute remains in the liquid phase. This property makes nonvolatile solutes ideal for studying colligative effects such as vapor pressure reduction.

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