Question

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.)

Short answer

Total concentration is 1.36 mol; freezing point is -2.53°C.

Step-by-step solution

Determine Moles Dissociated and Undissociated

Initially, there are 1.00 mol of trichloroacetic acid. Since 36% dissociates, the moles dissociated are \(0.36 \times 1.00 = 0.36\) mol, and the moles remaining undissociated are \(1.00 - 0.36 = 0.64\) mol.

Calculate Total Moles of Solute Particles

The dissociation produces \(0.36\) mol of \(\mathrm{H}^{+}\) and \(0.36\) mol of \(\mathrm{CCl}_3\mathrm{CO}_2^-\). Together with the undissociated \(0.64\) mol of \(\mathrm{CCl}_3\mathrm{CO}_2\mathrm{H}\), the total moles of solute particles are \(0.36 + 0.36 + 0.64 = 1.36\) mol.

Use Freezing Point Depression Formula

The freezing point depression formula is \(\Delta T_f = i \times K_f \times m\), where \(i\) is the van 't Hoff factor (number of solute particles, which is 1.36 mol), \(K_f = 1.86^{\circ} \mathrm{C/mol\ kg}\), and \(m = 1\) mol/kg. Therefore, \(\Delta T_f = 1.36 \times 1.86 = 2.5296^{\circ} \mathrm{C}\).

Calculate New Freezing Point

Subtract the freezing point depression from the normal freezing point of water (0°C): \(0 - 2.53 = -2.53^{\circ} \mathrm{C}\).

Key concepts

Trichloroacetic Acid

Trichloroacetic acid, with the chemical formula \(\mathrm{CCl}_3\mathrm{CO}_2\mathrm{H}\), is an organic compound known for its strong acidic properties due to the presence of three chlorine atoms. These chlorine atoms increase the electron-withdrawing power of the molecule, thereby enhancing the release of \(\mathrm{H}^+\) ions in aqueous solutions. This compound is only partially dissociated in water. This means that not all of the trichloroacetic acid molecules separate into ions. In this context, 36% of the added trichloroacetic acid dissociates. Partial dissociation reduces the total ionic strength of the solution compared to a fully dissociated compound, affecting the physical properties of the solution. Moreover, understanding partial dissociation is crucial because it impacts the calculation of properties like osmotic pressure, boiling point elevation, and, especially, freezing point depression in solutions.

Freezing Point Depression

The freezing point depression is a colligative property, which means it is dependent on the number of solute particles in a solution, not their identity. When a solute is added to a solvent, the freezing point of the resulting solution is lower than that of the pure solvent. This is because solute particles disrupt the formation of a solid lattice, making it harder to freeze the solution.In our exercise, the dissociation of trichloroacetic acid introduces 1.36 moles of solute particles per kilogram of water. We apply the freezing point depression formula \(\Delta T_f = i \times K_f \times m\), where:

• \(i\) is the van 't Hoff factor, representing the total moles of particles
• \(K_f\) is the freezing point depression constant (\(1.86^{\circ} \mathrm{C/mol\ kg}\) for water)
• \(m\) is the molality of the solution, which is 1 mol/kg in this case

This results in a freezing point depression of \(-2.53^{\circ} \mathrm{C}\), indicating how much lower the freezing point is than that of pure water.

Aqueous Solutions

Aqueous solutions are solutions where water is the solvent. Water’s unique properties make it an excellent medium for dissolving various substances, including acids, bases, and salts. The interaction between solute particles and water molecules plays a significant role in determining the behavior of an aqueous solution. In the case of trichloroacetic acid, it dissociates partially in water. The solution consists of a balance between dissociated ions (\(\mathrm{H}^{+}\) and \(\mathrm{CCl}_3\mathrm{CO}_2^-\)) and undissociated molecules of \(\mathrm{CCl}_3\mathrm{CO}_2\mathrm{H}\). Aqueous solutions are particularly interesting in studying colligative properties, as seen with freezing point depression. The partial dissociation of solutes like trichloroacetic acid alters solution properties, influencing phenomena observed in day-to-day life, such as anti-freezing mechanisms and water purification.