Thyroxine, an important hormone that controls the rate of...

Thyroxine, an important hormone that controls the rate of metabolism in the body, can be isolated from the thyroid gland. When $0.455 \mathrm{g}$ thyroxine is dissolved in $10.0 \mathrm{g}$ benzene, the freezing point of the solution is depressed by $0.300^{\circ} \mathrm{C}$. What is the molar mass of thyroxine? See Table $10-5$

Key Concepts

Colligative Properties

Colligative properties are characteristics of solutions that depend solely on the number of solute particles present, rather than their identity. This concept is fundamental when studying phenomena like boiling point elevation and freezing point depression, where the addition of a solute changes the physical properties of the solvent by interrupting its intermolecular forces.

Freezing Point Depression

Freezing point depression is a colligative property that describes the lowering of a solvent's freezing temperature when a solute is dissolved in it. The change in freezing point is directly proportional to the molal concentration of the solute and is calculated using the equation ?Tf = Kf × m, where ?Tf is the drop in temperature, Kf is the cryoscopic constant of the solvent, and m is the molality.

Molality

Molality is a unit of concentration defined as the number of moles of solute per kilogram of solvent. It is particularly useful in calculations involving colligative properties because it remains independent of temperature, unlike molarity which can change with thermal expansion or contraction.

Cryoscopic Constant

The cryoscopic constant, denoted as Kf, is a property of a specific solvent that quantifies the depression in freezing point per molal concentration of a solute. This constant allows for the direct correlation between the amount of solute dissolved and the resultant change in the physical freezing behavior of the host solvent.

Molar Mass Determination

Determining the molar mass of a substance using colligative properties involves experimentally measuring how a known mass of solute affects a property of the solvent, such as the freezing point. By combining measured values with the appropriate constants and concentration units, one can back-calculate the number of moles of the solute, and hence determine its molar mass.

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