Calculate the molality and van't Hoff factor (i) for the...

Calculate the molality and van't Hoff factor $(i)$ for the following aqueous solutions:
(a) 1.00 mass $\% \mathrm{NaCl}$, freezing point $=-0.593^{\circ} \mathrm{C}$
(b) 0.500 mass $\% \mathrm{CH}_{3} \mathrm{COOH}$, freezing point $=-0.159^{\circ} \mathrm{C}$

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Key Concepts

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, unlike molarity, it does not change with temperature since it is based on the mass of the solvent rather than the volume of the solution.

Van't Hoff Factor

The van't Hoff factor is a measure of the number of particles a solute produces when it dissolves in a solvent. It is used in colligative property equations to account for the effects of ionization or dissociation; for example, complete dissociation of an ionic compound ideally produces a number of particles equal to the sum of its ions.

Colligative Properties - Freezing Point Depression

Freezing point depression is a colligative property that describes the lowering of a solvent's freezing point upon the addition of a solute. The relationship is given by the equation ?T_f = i·K_f·m, where ?T_f is the change in freezing point, i is the van't Hoff factor, K_f is the freezing point depression constant, and m is the molality of the solution. This concept is essential for understanding how solutes affect the physical properties of solvents independently of their chemical identity.

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