E1. An alternate method for doing anti-solvent crystallization to crystallize relatively large molecules is to use constant volume diafiltration (Section 19.5.3).

Repeat Example 17-15 except use constant volume diafiltration at \(25^{\circ} \mathrm{C}\) to keep the total volume at \(100 \mathrm{~L}\) while the acetone concentration is reduced from \(100 \mathrm{vol} \%\) to \(80 \mathrm{vol} \%\). Assume the membrane is selected so that Rlovastatin \(=1\), Racetone \(=0\), and \(\mathrm{R}\) water \(=0\). Do not assume that volumes add.

a. How many \(\mathrm{kg}\) of water and how many \(\mathrm{kg}\) of acetone are in the final solution?

b. How many \(L\) of water are added?

c. How many \(\mathrm{kg}\) of acetone exit and how many \(\mathrm{kg}\) of water exit?

d. How many \(\mathrm{kg}\) of lovastatin crystallize and what is the yield?

E2. We have \(150 \mathrm{~kg}\) of a saturated solution of \(\mathrm{MgSO}_{4}\) at \(30^{\circ} \mathrm{C}\). We add enough methanol to have a \(20 \mathrm{wt} \%\) methanol solvent solution. How many \(\mathrm{kg}\) of anhydrous \(\mathrm{MgSO}_{4}\) precipitate and how many \(\mathrm{kg}\) of methanol is added? Data: Figure \(17-23\) (use the data point at \(0 \mathrm{wt} \%\) methanol, not the solid curve marked E). The y axis gives the moles of anhydrous salt dissolved/1000 moles solvent. The stable crystal form at \(30^{\circ} \mathrm{C}\) is \(\mathrm{MgSO}_{4} \cdot 7 \mathrm{H}_{2} \mathrm{O}\). MW anhydrous \(\mathrm{MgSO}_{4}=120.36\). \(\mathrm{MW}\) methanol \(=32.04\). \(\mathrm{MW}\) water \(=18.016\).