If the desired production rate in the crystallizer of Example 27.5 is 4.200 kg/h of MgS₄·7H₂O, the volume of liquid in the crystallizer is 7.7 m³, and the nucleation rate is 2.7 x 10⁹ nuclei/m³·h, what is the predominant crystal size? What would it be if the nucleation rate were 2.0 x 10⁸ nuclei/m³·h? (assume a=1.)

Example 27.5

A continuous vacuum crystallizer is fed with a 31 percent MgSO₄ solution. The equilibrium temperature of the magma in the crystallizer is 86°F (30°C), and the boiling point elevation of the solution is 2°F (1.11°C). A product magma containing 5 tons (4,536 kg) of MgSO₄·7H.O per hour is obtained. The volume ratio of solid to magma is 0.15; the densities of the crystals and mother liquor are 105 and 82.5 lb/nt³. respectively. What are the temperature of the feed, the feed rate, and the rate of evaporation?