An aqueous solution of a certain organic compound has a...

An aqueous solution of a certain organic compound has a density of $1.063 \mathrm{g} / \mathrm{mL},$ an osmotic pressure of 12.16 $\mathrm{atm}$ at $25.0^{\circ} \mathrm{C},$ and a freezing point of $-1.03^{\circ} \mathrm{C}$ . The compound is known not to dissociate in water. What is the molar mass of the compound?

Key Concepts

Colligative Properties

Colligative properties are characteristics of solutions that depend solely on the ratio of solute to solvent particles, rather than the chemical nature of the solute. Examples include freezing point depression, boiling point elevation, vapor pressure lowering, and osmotic pressure. These properties allow for the calculation of solute concentration and molar mass from measurable changes in solution behavior.

Osmotic Pressure

Osmotic pressure is a colligative property that results from a solvent moving across a semipermeable membrane from a region of lower solute concentration to one of higher solute concentration. It is directly proportional to the molar concentration of the solute (using the van 't Hoff equation, ? = MRT), allowing for the determination of solute molarity when the pressure, temperature, and gas constant are known.

Freezing Point Depression

Freezing point depression occurs when a solute is dissolved in a solvent, resulting in a lower freezing temperature of the solution compared to the pure solvent. This effect is quantified by the equation ?Tf = Kf · m, where Kf is the cryoscopic constant of the solvent and m is the molality of the solution. Measuring the drop in freezing point can provide insight into the solute concentration and, consequently, its molar mass.

Conversion Between Concentration Units (Molarity and Molality)

Understanding the conversion between molarity (moles of solute per liter of solution) and molality (moles of solute per kilogram of solvent) is essential when using colligative properties. Solution density is often used to relate these two concentration units, facilitating the calculation of molar mass by comparing the measured colligative effects with the mass of the solvent present.

Molar Mass Determination

Molar mass represents the mass of one mole of a substance and can be determined experimentally by relating the mass of the dissolved solute to the number of moles present. When colligative properties provide a measure of concentration (via osmotic pressure or freezing point depression), they can be combined with the known mass of the solute to calculate its molar mass.

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