Question

The solubility of an active pharmaceutical ingredient Z in water-acetone mixtures has been determined experimentally at 298 K and the resulting data can be expressed as Cs = 0.002(1+ 15 x_A^2.5), where the saturation composition Cs has units of kg of Z per kg of solvent mixture and xA is the mass fraction of acetone in the solvent mixture.

Molar masses: Z: 236 g/mol; acetone: 58.1 g/mol; water: 18.0 g/mol.

PART A: In order to compare experimental data to thermodynamic model calculations, compositions of solutions need to be expressed in mole fractions. Consider saturated solutions at two different solvent compositions: pure acetone and equimolar mixture of water and acetone. Using the solubility data given above, calculate the solute mole fraction in the two respective saturated solutions.

PART B: A saturated solution of Z in acetone was prepared at 298 K. A supersaturated solution was then prepared by mixing 1000 kg of the solution with 2000 kg of water. Using the solubility data given above, calculate the saturation concentration of Z in the resulting mixture and the corresponding relative supersaturation.

PART C: Crystals of Z have cuboid shape with dimensions a × b × c , where a:b:c = 1:1:10, and corresponding linear crystal growth rates Ga = Gb = 1 ?m/min and Gc = 10 ?m/min. A seed crystal of Z with dimensions of 5 × 5 × 50 ?m is introduced into a supersaturated solution. Assuming that a constant solution composition is maintained, calculate how long it takes for the seed crystal to increase its mass to 1000 times of its original value.

PART D: Consider an isothermal seeded batch crystallisation process starting from the supersaturated solution obtained in (b). The batch was seeded with 10 kg of seed crystals of Z with dimensions of 5 × 5 × 50 ?m. Determine the total mass of crystals of Z that was obtained from the given batch when the final relative supersaturation was 1.02.

Answer 1