Consider an aqueous solution containing sodium chloride that...

Consider an aqueous solution containing sodium chloride that has a density of $1.01 \mathrm{g} / \mathrm{mL}$. Assume the solution behaves ideally. The freezing point of this solution at 1.0 atm is $-1.28^{\circ} \mathrm{C}$ Calculate the percent composition of this solution (by mass).

Key Concepts

Percent Composition and Density

Percent composition by mass is a metric that describes the ratio of the mass of the solute to the total mass of the solution, expressed as a percentage. Density, which relates mass to volume, is used to convert between these quantities in solution calculations, enabling the determination of how much solute is present in a given volume of solution.

Dissociation and the Van't Hoff Factor

In solutions involving electrolytes, solute compounds (like salts) dissociate into multiple ions. The van't Hoff factor (i) represents the number of particles produced per formula unit of solute, which is critical when calculating colligative properties since it determines the effective concentration of particles in the solution.

Colligative Properties

These are properties of solutions that depend on the number of solute particles present rather than their specific type. They include phenomena like boiling point elevation, freezing point depression, vapor pressure lowering, and osmotic pressure, and are essential for analyzing how solute addition affects the physical properties of solvents.

Freezing Point Depression

This is the lowering of the freezing point of a solvent when a solute is dissolved in it. The degree of freezing point depression is directly proportional to the molal concentration of the solute particles in the solution and is described by the equation ?Tf = i · Kf · m, where i is the van't Hoff factor, Kf is the cryoscopic constant, and m is the molality.

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 does not change with temperature, allowing for accurate estimation of effects like freezing point depression.

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