0.5 molal aqueous solution of a weak acid (HX) is 20 % ionized. If K_f for water is 1.86 K kg mol ⁻¹ Calculate the lowering in freezing point of the solution.

Step-by-step solution

The ionization of the weak acid HX is given by: HX H ^+ + X ^- The van't Hoff factor i is calculated as: i = 1 + Given that the acid is 20 % ionized, = 0.2 . i = 1 + 0.2 = 1.2 The lowering in freezing point T_f is given by: T_f = i K_f m Substituting the given values: T_f = 1.2 1.86 0.5 T_f = 1.116 K 1.12 K Answer: 1.12 K