Question

0.3 g of acetic acid (Molar mass = 60 g mol\(^{-1}\)) dissolved in 30 g of benzene shows a depression in freezing point equal to 0.45°C. Calculate the percentage association of acid if it forms a dimer in the solution.
(Given: \( K_f \) for benzene = 5.12 K kg mol\(^{-1}\))

Hint:

Remember, depression in freezing point is directly related to the number of particles in solution. If association occurs, the number of particles is reduced, affecting the freezing point.

Answer 1

The freezing point depression (\(\Delta T_f\)) is calculated using the formula: \[ \Delta T_f = \frac{K_f \cdot m}{w} \]. Here, \(m\) represents the molality of the solution, and \(w\) is the molar mass of the solute. The provided data includes: \[ \Delta T_f = 0.45^\circ C, \, K_f = 5.12 \, \text{K kg mol}^{-1}, \, \text{and mass of acetic acid} = 0.3 \, \text{g}. \] By applying the formula and determining the molality, the degree of association can be ascertained. If dimerization of acetic acid is assumed, the apparent molar mass escalates, thereby influencing the freezing point depression. Calculations for the percentage association indicate that the acid forms a dimer with an approximate degree of association of 60%.