A $40\%$ solution of MgSO$4$ at $230\backslash$deg F is cooled, without appreciable evaporation, to $160\backslash$deg F in a batch water$-$cooled crystallizer.

a$.$ How much feed must be processed in order to obtain $300$ lb of crystals?

b$.$ How much heat must be removed from the solution per $300$ lb of crystals?

c$.$ If the solution is cooled to $80$F$,$ what is the type of crystals that will be formed?

d$.$ In the previous problem, how much feed must be processed to obtain $300$ lb of crystals?

e$.$ How much heat must be removed from the solution to obtain $300$ lb of crystals?