Many compounds are only partially dissociated into ions in...

Many compounds are only partially dissociated into ions in aqueous solution. Trichloroacetic acid $\left(\mathrm{CCl}_{3} \mathrm{CO}_{2} \mathrm{H}\right),$ for instance, is partially dissociated in water according to the equation $$ \mathrm{CCl}_{3} \mathrm{CO}_{2} \mathrm{H}(a q) \longrightarrow \mathrm{H}^{+}(a q)+\mathrm{CCl}_{3} \mathrm{CO}_{2}^{-}(a q) $$ For a solution prepared by dissolving $1.00 \mathrm{~mol}$ of trichloroacetic acid in $1.00 \mathrm{~kg}$ of water, $36.0 \%$ of the trichloroacetic acid dissociates to form $\mathrm{H}^{+}$ and $\mathrm{CCl}_{3} \mathrm{CO}_{2}^{-}$ ions. (a) What is the total concentration of dissolved ions and molecules in $1 \mathrm{~kg}$ of water? (b) What is the freezing point of this solution? (The freezing point of $1 \mathrm{~kg}$ of water is lowered $1.86^{\circ} \mathrm{C} / \mathrm{K}$ for each mole of solute particles.)

Many compounds are only partially dissociated into ions in aqueous solution. Trichloroacetic acid $\left(\mathrm{CCl}_{3} \mathrm{CO}_{2} \mathrm{H}\right),$ for instance, is partially dissociated in water according to the equation
$$
\mathrm{CCl}_{3} \mathrm{CO}_{2} \mathrm{H}(a q) \longrightarrow \mathrm{H}^{+}(a q)+\mathrm{CCl}_{3} \mathrm{CO}_{2}^{-}(a q)
$$
For a solution prepared by dissolving $1.00 \mathrm{~mol}$ of trichloroacetic acid in $1.00 \mathrm{~kg}$ of water, $36.0 \%$ of the trichloroacetic acid dissociates to form $\mathrm{H}^{+}$ and $\mathrm{CCl}_{3} \mathrm{CO}_{2}^{-}$ ions.
(a) What is the total concentration of dissolved ions and molecules in $1 \mathrm{~kg}$ of water?
(b) What is the freezing point of this solution? (The freezing point of $1 \mathrm{~kg}$ of water is lowered $1.86^{\circ} \mathrm{C} / \mathrm{K}$ for each mole of solute particles.)

Key Concepts

Colligative Properties

Colligative properties are physical properties of solutions that depend solely on the number of solute particles in a solvent and not on the nature of the chemical species. These properties include freezing point depression, boiling point elevation, vapor pressure lowering, and osmotic pressure, and are crucial in determining how the addition of a solute affects the phase behavior and other thermodynamic properties of the solvent.

Freezing Point Depression

Freezing point depression is a colligative property where the freezing point of a solvent is lowered when a solute is dissolved in it. The magnitude of the depression is directly proportional to the molal concentration of solute particles, and is described by the equation ?Tf = i · Kf · m, where ?Tf is the change in freezing point, Kf is the cryoscopic constant for the solvent, m is the molality, and i is the van’t Hoff factor representing the number of particles produced per formula unit of solute.

Dissociation in Aqueous Solutions

Dissociation in aqueous solutions refers to the process whereby a compound, when dissolved in water, separates into its constituent ions. The extent of this process can vary from complete to partial dissociation. In cases of partial dissociation, only a fraction of the molecular solute disintegrates into ions, altering the total number of particles in solution, which is particularly important when calculating properties that depend on particle count.

van’t Hoff Factor

The van’t Hoff factor (i) quantifies the effect of solute dissociation on colligative properties by indicating the number of particles into which a solute actually dissociates in solution. In situations where dissociation is only partial, the effective van’t Hoff factor is less than the maximum theoretical value, and it is used in calculations such as freezing point depression to accurately account for the number of solute particles present.

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