4.0 mL of a weak monoprotic acid ( HA ) is dissolved in water to make 1 L of solution. The density of the pure acid is 1.25 g mL ⁻¹ and its molar mass is 50 g mol ⁻¹ . If the depression in freezing point of the solution is 0.2232^ C , the acid dissociation constant ( K_a ) of the weak acid is: (Assume the solution is dilute and density of water is 1 g mL ⁻¹ , K_f for water = 1.86 K kg mol ⁻¹ )

Step-by-step solution

Mass of the weak acid HA = Volume Density = 4.0 mL 1.25 g mL ⁻¹ = 5.0 g . Moles of HA = 5.0 g 50 g mol ⁻¹ = 0.1 mol . Since the solution is dilute, the volume of the solution ( 1 L ) is approximately equal to the volume of the solvent, and the mass of the solvent is approximately 1 kg . Thus, molality m 0.1 mol kg ⁻¹ and molarity C 0.1 M . Using the depression in freezing point formula: T_f = i K_f m 0.2232 = i 1.86 0.1 i = 0.2232 0.186 = 1.2 For a weak monoprotic acid, the Van't Hoff factor i = 1 + . 1 + = 1.2 = 0