Question

At -13.5C (a common temperature for household freezers), what is the maximum mass of sucralose (C12H19Cl3O8) you can add to 3.00 kg of pure water and still have the solution freeze? Assume that sucralose is a molecular solid and does not ionize when it dissolves in water. Kf values are:

Constants for freezing-point depression and boiling-point elevation calculations at 1 atm:

Solvent	Formula	Kf value* (°C/m)	Normal freezing point (°C)	Kb value (°C/m)	Normal boiling point (°C)
water	H2O	1.86	0.00	0.512	100.00
benzene	C6H6	5.12	5.49	2.53	80.1
cyclohexane	C6H12	20.8	6.59	2.92	80.7
ethanol	C2H6O	1.99	–117.3	1.22	78.4
carbon tetrachloride	CCl4	29.8	–22.9	5.03	76.8
camphor	C10H16O	37.8	176

Answer 1

Ans. Given: Freezing point of the solution = - 13.5⁰C.

Freezing point of a solution is the minimum temperature at which is transits from liquid to solid phase.

So, we need to prepare a sucralose solution that has a melting point of -13.5⁰C.

Let the number of moles of sucralose required = n mol

Molality of resultant solution = Moles of sucralose / Mass of solvent or water in kg

                                                = n mol / 3.0 kg

                                                = (n/ 3.0) mol/ kg                             ; [1 mol/ kg = 1 m]

                                                = (n/ 3.0) m

Now, using                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 = 1.86⁰C / m

                        m = molality of the solution

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

= 0.0⁰C – (- 13.5⁰C) = 13.5⁰C

Putting the values in equation 1-

            13.5⁰C = 1 x (1.86⁰C / m) x (n/ 3.0) m

            Or, (13.5 x 3.0) / 1.86 = n

            Or, n = 21.77

Therefore, required amount of sucralose = n mol = 21.77 mol

# Mass of sucralose required = Required moles of sucralose x Molar mass of sucralose

                                                = 21.77 mol x (397.63616 g/ mol)

                                                = 8656.54 g

Thus, required mass of sucralose = 8656.54 g