A 10.0 wt% aqueous solution of sodium chloride is fed to an evaporative crystallizer operated under a partial vacuum. Evaporation of water concentrates the remaining solution beyond its saturation point at the crystallizer temperature and causes crystallization of NaC1. The crystallizer product is a slurry of solute crystals suspended in a saturated solution at 80°C. The unit is to produce 1000 kg NaC1(s)/h. The solubility of NaC1 in water is given by Figure 6.5-1.

(a) Derive expressions for the required rate of evaporation of water (kg/b) and the mass flow rate of solution in the exit slurry in terms of the mass flow rate of the feed stream to the crystallize!. 

Determine the minimum possible feed rate (explain why it is the minimum rate) and the corresponding values of the evaporation rate and exit solution flow rate.

(b) The pump that conveys the exit slurry from the crystallizer to a downstream filter cannot handle material containing more than 40 wt% solids. Determine the maximum feed rate to the crystallizer and the corresponding evaporation rate.