A solution of 1.00 g of anhydrous aluminum chloride, AlCl3, in 50.0 g of water freezes at -1.1

step 1 This is question 104 from chapter 13 and we have one gram of in hydrantrous aluminum chloride an

A solution of 1.00 g of anhydrous aluminum chloride, AlCl3,...

A solution of $1.00 \mathrm{~g}$ of anhydrous aluminum chloride, $\mathrm{AlCl}_{3}$, in $50.0 \mathrm{~g}$ of water freezes at $-1.11^{\circ} \mathrm{C}$. Does the molar mass determined from this freezing point agree with that calculated from the formula? Why?

Key Concepts

Molar Mass Determination via Colligative Properties

Determining molar mass using colligative properties involves measuring changes in a physical property, such as the freezing point, upon the addition of a known mass of solute to a solvent. By applying the freezing point depression formula and taking into account dissociation through the van't Hoff factor, one can calculate the molality and, subsequently, the molar mass of the solute. This provides an experimental method to verify chemical formulas and assess the behavior of solutes in solution.

van't Hoff Factor

The van't Hoff factor, denoted as i, accounts for the number of particles into which a solute dissociates in solution. For electrolytes that dissociate into ions, this factor becomes crucial in accurately calculating colligative effects. It helps bridge the gap between the theoretical and practical behavior of solutions in colligative property experiments.

Colligative Properties

Colligative properties are characteristics of solutions that depend solely on the number of solute particles present, not their identity. These properties include freezing point depression, boiling point elevation, vapor pressure lowering, and osmotic pressure, and they are useful in determining molar masses and other solution properties.

Freezing Point Depression

Freezing point depression refers to the lowering of the freezing temperature of a solvent when a non-volatile solute is added. The magnitude of this depression is proportional to the number of solute particles, and it is described by the equation ?Tf = Kf · m · i, where Kf is the cryoscopic constant, m is the molality, and i is the van't Hoff factor.

Molality

Molality is a concentration unit defined as the number of moles of solute per kilogram of solvent. It is particularly useful in studying colligative properties because it does not change with temperature, making it a reliable measure when dealing with freezing point depression and boiling point elevation phenomena.

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