What should the molar concentrations of benzoic acid and sodium benzoate be in a solution that is buffered at a pH of 4.55 and has a freezing point of -2.0 °C? (Assume complete dissociation of sodium benzoate and a density of 1.01 g/mL for the solution.)

A buffer solution is a system that resists changes in pH upon the addition of small amounts of acid or base. It typically consists of a weak acid and its conjugate base, which in this case are benzoic acid and sodium benzoate. The Henderson-Hasselbalch equation can be used to calculate the ratio of these components needed to achieve a specific pH.

The Henderson-Hasselbalch equation relates the pH of a buffer solution to the concentrations of its acid and conjugate base. It is expressed as pH = pKa + log([A-]/[HA]), where pKa is the acid dissociation constant. This equation allows for the determination of the required molar concentrations of benzoic acid and sodium benzoate to achieve the desired pH of 4.55.

Freezing point depression is a colligative property that describes how the freezing point of a solvent decreases when a solute is added. The extent of freezing point depression can be calculated using the formula ΔTf = i * Kf * m, where ΔTf is the change in freezing point, Kf is the freezing point depression constant, and m is the molality of the solution. This concept is essential for understanding how the concentrations of benzoic acid and sodium benzoate affect the solution's freezing point.