The heptahydrate of MgSO 4 is to be crystallized batchwise from a seeded aqueous solution

The heptahydrate of MgSO 4 is to be crystallized batchwise from a seeded aqueous solution. Low supersaturation is to be used to avoid primary nucleation and mild agitation is to be used to minimize secondary nucleation. Temperature will be maintained at 35 o C, at which the solubility of MgSO 4 in water is 30 wt%. The crystallizer will be charged with 3,000 lb of a saturated solution at 35 o C. To this solution will be added 2 lb of heptahydrate seed crystals of 50 μm in diameter. A supersaturation of 0.01 gm of heptahydrate per gm of solution at 35 o C will be maintained during crystallization by operating the crystallizer at vacuum and using heat exchange and the heat of crystallization to gradually evaporate water. Based on the assumptions and data listed below, determine the following, if the final crystal size is to be 400 μm: (a) lb of heptahydrate crystals, (b) number of crystals, (c) lb of water evaporated, (d) product magma density in lb of crystals per lb of solution, (e) crystallizer volume in gallons if the volume occupied by the magma during operation is at most 50% of the crystallizer volume, (f) crystallizer pressure in psia and the boiling-point elevation in o F, (g) time in minutes to grow the crystals to the final size, (h) amount of heat transfer in Btu, and (i) whether crystal growth is controlled by mass transfer, by surface reaction (incorporation into the lattice), or both.                                                                                                       Assumptions and Data: 1. No primary or secondary nucleation. 2. Properties of aqueous 30 wt% MgSO 4 at 35 o C: density=1.34 g/cm 3 ; viscosity=8 cP; and diffusivity of MgSO 4 =1:10 x10 -5 cm 2 /s. 3. Density of the crystals =1.68 g/cm 3 . 4. Crystal shape can be approximated as a sphere. 5. Average crystal-face growth rate, including effects of both mass transfer and surface reaction, = 0.005 mm/minute. 6. Solution velocity past crystal face = 5 cm/s.

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