Magnesium sulfate has a number of uses, some of which are related to the ability of the anhydrate form to remove water from air and others based on the high solubility of the heptahydrate (MgSO₄∙7H₂O) form, also known as Epsomsalt. The densities of the anhydrate and heptahydrate crystalline forms are 2.66 and 1.68 g/mL, respectively.

Suppose you wish to form a 20.0 wt% MgSO₄ aqueous solution by simply pouring crystals of one of the forms into a tank of water while the temperature is held constant at 30°C. The specific gravity of the 20.0 wt% solution at 30°C is 1.22. Answer the following questions for both forms of the MgSO₄ crystals:

(a) What volume of water should be in the tank before crystals are added if the final product is to be 1000 kg of the 20 wt% solution?

(b) Suppose the tank diameter is 0.30 m. What is the height of liquid in the tank before the crystals are added?

(c) What is the height of the water in the tank after addition of the crystals but before they begin to dissolve?

(d) What is the height of liquid in the tank after all the MgSO₄ has dissolved?