Safrole is contained in oil of sassafras and was once used...

Safrole is contained in oil of sassafras and was once used to flavor root beer. A $2.39-\mathrm{mg}$ sample of safrole was dissolved in $103.0 \mathrm{mg}$ of diphenyl ether. The solution had a melting point of $25.70^{\circ} \mathrm{C}$. Calculate the molecular mass of safrole. The freezing point of pure diphenyl ether is $26.84^{\circ} \mathrm{C}$, and the freezing-pointdepression constant, $K_{f}$, is $8.00^{\circ} \mathrm{C} / m .$

Key Concepts

Molecular Mass Determination via Colligative Properties

This method involves using colligative properties, such as freezing point depression, to calculate the molar mass of a solute. By measuring the change in the freezing point of the solvent upon adding a known mass of solute and using the known freezing point depression constant, one can calculate the molality, the number of moles of the solute, and consequently its molecular mass.

Freezing Point Depression

This is a colligative property where the freezing point of a solvent is lowered by the addition of a solute. The amount by which the freezing point is depressed is directly proportional to the molal concentration of the solute particles. The relation ?Tf = Kf · m is used to quantify this effect where ?Tf is the freezing point depression, Kf is the cryoscopic constant, and m is the molality of the solution.

Molality

Molality is a concentration unit defined as the number of moles of solute per kilogram of solvent. It is independent of temperature, which makes it particularly useful in calculations involving temperature changes, such as freezing point depression. It allows for the determination of the solute's molar concentration in the solvent used.

Colligative Properties

Colligative properties are characteristics of solutions that depend on the number of solute particles rather than their chemical identity. They include freezing point depression, boiling point elevation, vapor pressure lowering, and osmotic pressure. These properties are instrumental in determining variables such as molecular mass through solution behavior.

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