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.
b. 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. Step 1: Calculate the number of moles of trichloroacetic acid (CCl₃CO₂H) that dissociate. Since 36.0% of the acid dissociates, multiply the initial moles of trichloroacetic acid (1.00 mol) by 0.36 to find the moles of dissociated acid.
2. Step 2: Determine the total number of solute particles in the solution. For every mole of trichloroacetic acid that dissociates, it produces 2 particles (1 H⁺ ion and 1 CCl₃CO₂⁻ ion). Add the moles of dissociated particles to the moles of undissociated trichloroacetic acid (which remains as 1 particle per mole). The total number of solute particles is the sum of these contributions.
3. Step 3: Calculate the molality (m) of the solution. Molality is defined as the number of moles of solute particles per kilogram of solvent. Use the total number of solute particles from Step 2 and divide by the mass of the solvent (1.00 kg of water).
4. Step 4: Use the freezing point depression formula to calculate the change in freezing point (ΔT_f). The formula is ΔT_f = i × K_f × m, where i is the van 't Hoff factor (the number of particles per formula unit, which you calculated in Step 2), K_f is the freezing point depression constant for water (1.86 °C·kg/mol), and m is the molality from Step 3.
5. Step 5: Subtract the freezing point depression (ΔT_f) from the normal freezing point of water (0.00 °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 freezing point depression indicates that for each mole of solute particles, the freezing point decreases by a specific amount, which is essential for solving the given problem.

Freezing Point Depression Calculation

To calculate the freezing point depression, one must determine the total number of solute particles in the solution. For trichloroacetic acid, 36.0% dissociation means that from 1.00 mol of acid, 0.36 mol dissociates into 0.36 mol of H⁺ and 0.36 mol of CCl₃CO₂⁻, resulting in a total of 0.72 mol of particles. This total is then used in the freezing point depression formula to find the new freezing point of the solution.