Question

A solution is made by dissolving 0.571 mol of nonelectrolyte solute in 815 g of benzene. Calculate the freezing point, Tf, and boiling point, Tb, of the solution.

Answer 1

Ans. Molarity of solution = Moles of solute / Mass of solvent in kg

                                                = 0.571 mol / 0.815 kg                                ; [1 kg = 10³ g]

                                                = 0.700 mol/kg

                                                = 0.700 m                                                      ; [1 m = 1 mol/kg]

#A. Now, freezing point depression, dT_f is given by-

            dT_f = i K_f m               - equation 1

            where, i = Van’t Hoff factor. [i = 1 for non-electrolyte solute].

                        K_f = molal freezing point depression constant of solvent = 5.12⁰C / m

                        m = molality of the solution

                        dT_f = Freezing point of pure solvent – Freezing point of solution

                        Freezing point of pure solvent, benzene = 5.5⁰C

Putting the values in equation 1-

            dT_f = 1 x (5.12⁰C / m) x 0.700 m = 3.58⁰C

Now,

            Freezing point of solution = Freezing point of pure solvent - dT_f

                                                            = 5.5⁰C – 3.58⁰C

                                                            = 1.92⁰C

Therefore, freezing point of resultant solution = 1.92⁰C

#B. Elevation in boiling point of a solution is given by-

dT_b = i Kb m                        - equation 1

            where, i = Van’t Hoff factor = [i = 1 for non-electrolyte solute].

                        K_b = molal boiling point elevation constant of the solvent = 2.65⁰C/m

                        m = molality of the solution

                        dT_b = Boiling point of solution - Boiling point of pure solvent

                        Boiling point of benzene = 80.1⁰C

Putting the values in equation 1-

            dTb = 1 x (2.65⁰C/m) x 0.700 m = 1.86⁰C

Now,

            Boiling point of solution = Boiling point of pure solvent + dT_b

                                                            = 80.1⁰C + 1.86⁰C

                                                            = 81.96⁰C

Therefore, boiling point of resultant solution = 81.96⁰C