Question

CHAPTER 6 Multiphase Systems(Elementary princilples of Chemical Engineering 4th Ed)

6.88) Serine (Ser, molecular weight=105.1g/mol) is a non-essential amino acid (seeFootnote16) produced by fermentation. As with many other fermentation products, substantial downstream processing is required to meet specifications on product purity. Crystallization from an aqueous solution is useful in meeting those specifications. The following table shows how serine solubility in water varies with temperature:

              

T(°C)	5.0    10.0      15.0     20.0     25.0     30.0     35.0      45.0     50.0
Solubility17 (g Ser/100g H2O)	18.45   22.71   26.88   30.22   35.91 39.40   44.34 50.77   53.76

(a) Prepare a plot of solubility as a function of temperature that can be used for interpolation.

(b) An aqueous solution of serine containing 60 g Ser/100 g H2O is pumped into a batch cooling crystallizer, and the temperature is reduced slowly to 10°C, causing the formation of crystals of the monohydrated salt Ser H2O.Using the given solubility data, estimate the mass of crystals produced per unit mass of feed solution and the fraction of serine fed that is recovered as crystalline product.

(c) The molecular structure of serine makes it much more hydrophilic than other amino acids, and therefore its solubility is about an order of magnitude greater than that of most other amino acids. The addition of methanol to reduce the solubility in the solution has been suggested. Experimental data show that the solubility of Ser as a function of methanol content is given by the correlation S/S₀ =exp(-4.8x_m)where x_m is the mass fraction of methanol in a methanol–water solvent mixture,S₀ (g/g solvent) is serine solubility in water at a given temperature, and S is the solubility in the methanol–water solvent. In an alternative to the processing scheme described in Part(b), sufficient methanol is added to the crystallizer after it has reached 10°C to produce a final solution that has a methanol-to-water mass ratio of 55:45, and the resulting system is allowed to come to equilibrium. Estimate the mass of crystals produced per unit mass of feed solution and the fraction of serine fed that is recovered as crystalline product.

Answer 1

Solution.

a) A plot of solubility as a function of temperature is given below:

b) Using the approximating equation for solubility, S = 0.8005t+14.926, the solubility of Ser at 10 °C is

S(10°C) = 0.8005*10+14.926 = 22.93 g/100 g H₂O.

Therefore, the mass of crystals is 60-22.93 = 37.07 g/100 g H₂O.

The fraction recovered as crystalline product is 37.07/60 = 0.618, or 61.8%.

c) The solubility of Ser in water at 10 °C is 22.93 g/100 g H₂O (from part b), or 0.2293 g/g solvent.

The mass fraction of methanol in a methanol–water solvent mixture is 55/(55+45)=0.55;

The solubility in the methanol–water solvent is

Therefore, the mass of crystals produced per unit mass of feed solution is 0.2293-0.016 = 0.213 g/g solvent.

The fraction of serine fed that is recovered as crystalline product is 0.213/0.2293=0.929, or 92.9 %.