Many compounds are only partially dissociated into ions in aqueous solution. Trichloroacetic acid (CCl₃CO₂H), for instance, is partially dissociated in water according to the equation CCl₃CO₂H (aq) → H⁺ (aq) + CCl₃CO₂⁻ (aq) For a solution prepared by dissolving 1.00 mol of trichloroacetic acid in 1.00 kg of water, 36.0% of the trichloroacetic acid dissociates to form H⁺ and CCl₃CO₂⁻ ions. What is the freezing point of this solution? (The freezing point of 1 kg of water is lowered 1.86 °C for each mole of solute particles.)

Verified step by step guidance

1. Determine the number of moles of trichloroacetic acid that dissociate by multiplying the initial moles (1.00 mol) by the dissociation percentage (36.0%).
2. Calculate the moles of ions produced. Since each mole of trichloroacetic acid produces one mole of H⁺ and one mole of CCl₃CO₂⁻, the total moles of ions is twice the moles of dissociated trichloroacetic acid.
3. Add the moles of undissociated trichloroacetic acid to the total moles of ions to find the total moles of solute particles in the solution.
4. Use the freezing point depression formula, $\mathrm{\Delta }{T}_f=i\cdot K_f\cdot m$, where $i$ is the van't Hoff factor (total moles of particles per mole of solute), $K_f$ is the freezing point depression constant (1.86 °C kg/mol for water), and $m$ is the molality of the solution.
5. Calculate the change in freezing point, $\mathrm{\Delta }{T}_f$, and subtract it from the normal freezing point of water (0 °C) to find the freezing point of the solution.

Key Concepts

Dissociation of Acids

Dissociation refers to the process by which an acid separates into its constituent ions in solution. In the case of trichloroacetic acid, it partially dissociates into hydrogen ions (H⁺) and trichloroacetate ions (CCl₃CO₂⁻). Understanding the extent of dissociation is crucial for calculating the concentration of ions in solution, which directly affects properties like freezing point.

Colligative Properties

Colligative properties are physical properties of solutions that depend on the number of solute particles rather than their identity. Freezing point depression is one such property, where the presence of solute particles lowers the freezing point of a solvent. The formula for calculating the change in freezing point involves the van 't Hoff factor, which accounts for the number of particles produced from the solute's dissociation.

Freezing Point Depression

Freezing point depression quantifies how much the freezing point of a solvent decreases when a solute is added. For every mole of solute particles, the freezing point of water decreases by 1.86 °C. In this scenario, knowing the percentage of dissociation allows us to determine the effective number of solute particles, which is essential for calculating the new freezing point of the solution.