L-Serine is an amino acid that often is provided when intravenous feeding solutions are used to maintain the health of a patient. It has a molecular weight of 105, is produced by fermentation and recovered and purified by crystallization at 10°C. Yield is enhanced by adding methanol to the system, thereby reducing serine solubility in aqueous solutions.

An aqueous serine solution containing 30 wt% serine and 70% water is added along with methanol to a batch crystallizer that is allowed to equilibrate at 10°C. The resulting crystals are recovered by filtration; liquid passing through the filter is known as filtrate, and the recovered crystals may be assumed in this problem to be free of adhering filtrate. The crystals contain a mole of water for every mole of serine and are known as a monohydrate. The crystal mass recovered in a particular laboratory run is 500 g, and the filtrate is determined to be 2.4 wt% serine, 48.8% water, and 48.8% methanol.

(a) Draw and label a flowchart for the operation and carry out a degree-of-freedom analysis.

Determine the ratio of mass of methanol added per unit mass of feed.

(b) The laboratory process is to be scaled to produce 750 kg/h of product crystals. Determine the required aqueous serine solution rates of aqueous serine solution and methanol.