An aqueous solution containing 35 wt% MgSO₄ is fed to an evaporative crystallizer operating at 50°F. The vapor generated is 20% by mass of the feed. The solution, which contains 23 wt% MgSO₄, and the crystals suspended in it are in equilibrium. 

(a) Based on the information in Table 6.5-1, what is the composition of the crystalline product? 

(b) For a crystal production rate of 1000 kg/h, estimate (i) the required feed and vapor flow rates in kg/h, and (ii) the rate at which MgSO₄ could be recovered from the crystals if all the water is removed from them by drying. 

Table 6.5-1

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TABLE 6.5-1 Hydrated MgS04 Salts Form Name Wt% MgSO4 Conditions MgSO4 Anhydrous magnesium sulfate 100.0 > 100°C MgSO4-H20 Magnesium sulfate monohydrate 87.0 67 to 100°C MGSO4-6H20 Magnesium sulfate hexahydrate 52.7 48 to 67°C MgSO4-7H,O Magnesium sulfate heptahydrate 48.8 2 to 48°C MGSO4 12H2O Magnesium sulfate dodecahydrate 35.8 -4 to 2°C