A sample of HgCl weighing 9.41 g is dissolved in 32.75 g of...

A sample of HgCl_ weighing 9.41 g is dissolved in 32.75 g of ethanol, C $_{2} \mathrm{H}_{5} \mathrm{OH}$ ( $K_{\mathrm{b}}=1.20^{\circ} \mathrm{C} / \mathrm{m}$ ). The boiling point elevation of the solution is $1.27^{\circ} \mathrm{C} .$ Is $\mathrm{HgCl}_{2}$ an electrolyte in ethanol? Show your calculations.

Key Concepts

Electrolyte Behavior

Electrolyte behavior refers to the ability of a compound to ionize when dissolved in a solvent. An electrolyte dissociates into ions, increasing the number of particles in the solution and altering colligative properties such as boiling point elevation. Analysis of the van’t Hoff factor can indicate whether a substance behaves as an electrolyte in a given solvent.

Colligative Properties

Colligative properties are characteristics of a solution that depend solely on the number of solute particles relative to the solvent, not on the chemical identity of the solute. These properties include boiling point elevation, freezing point depression, vapor pressure lowering, and osmotic pressure. They provide a way to study the effects of solute concentration on the physical properties of solutions.

Boiling Point Elevation

Boiling point elevation is a colligative property that occurs when the vapor pressure of the solvent is lowered by the presence of a non-volatile solute, causing the boiling point to increase. The extent of the change is given by the equation ?T = i × K_b × m, where ?T is the change in boiling point, i is the van’t Hoff factor, K_b is the ebullioscopic 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 particularly useful in colligative property calculations because it is independent of temperature, unlike molarity, which depends on the volume of the solution that can change with temperature.

van’t Hoff Factor

The van’t Hoff factor (i) quantifies the number of particles into which a solute dissociates in solution. For non-electrolytes that do not dissociate, i is equal to 1, while for electrolytes that dissociate into ions, i is greater than 1. Thus, it is crucial in determining the actual number of solute particles affecting the colligative properties.

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