transport. Since the particle is pure drug, the appropriate expression for the rate of mass transfer is: m=kmA[drugC] where the density of the drug is a constant (drus=1200kg/m3) and C=50kg/m3. The drug particles are assumed to be cylindrical tablets with the mass transfer coefficient given as km=b/R where b=8109m2/s and R is the radius of the cylindrical tablet. A) Write down the transient mass balance describing the change in radius of the cylindrical particle as a function of time. You can assume that the length of the tablet stays constant and that there is no drug dissolution from the ends of the tablet. B) Derive an analytical expression for the particle radius as a function of time. C) How long will it take for the drug particles to disappear if the initial radius of the tablet is 0.005m ? D) Repeat the calculations in parts B and C if the drug is able to dissolve from the ends of the tablet (i.e., if A=Acymuer+Aendu ) assuming that L=5R where L is the length of the cylinder. E) Why does it take longer for the drug tablet to dissolve in Part D? 2. Back-Extraction of Penicillin The penicillin purification process typically involves both an extraction into amyl acetate followed by a back-extraction into water - this allows one to remove non-polar as well as polar impurities. The back-extraction looks the same as a regular extractor except that the penicillin enters the extractor in the organic phase and it is recovered in the water. The pH is adjusted between these steps to change the value of the Henry's law constant (due to the protonation of the acid group in the penicillin molecule), with H1=20 (for the extraction step) and H2=0.03 (for the back-extraction step). A. Derive expressions for the concentration and overall recovery of penicillin in the water leaving the second extractor as a function of the amyl acetate flow rate. Assume that the water flow rate in the back-extraction step is 1/2 the value of the inlet feed water. B. Determine the maximum penicillin recovery for this process (with the amyl acetate flow rate as the variable) for qw=20L/min in the first extractor. C. Comment on the physical basis for this maximum - why does the penicillin recovery go through a maximum as one increases the amyl acetate flow rate? transport. Since the particle is pure drug, the appropriate expression for the rate of mass transfer is: m=kmA[drugC] where the density of the drug is a constant (drus=1200kg/m3) and C=50kg/m3. The drug particles are assumed to be cylindrical tablets with the mass transfer coefficient given as km=b/R where b=8109m2/s and R is the radius of the cylindrical tablet. A) Write down the transient mass balance describing the change in radius of the cylindrical particle as a function of time. You can assume that the length of the tablet stays constant and that there is no drug dissolution from the ends of the tablet. B) Derive an analytical expression for the particle radius as a function of time. C) How long will it take for the drug particles to disappear if the initial radius of the tablet is 0.005m ? D) Repeat the calculations in parts B and C if the drug is able to dissolve from the ends of the tablet (i.e., if A=Acymuer+Aendu ) assuming that L=5R where L is the length of the cylinder. E) Why does it take longer for the drug tablet to dissolve in Part D? 2. Back-Extraction of Penicillin The penicillin purification process typically involves both an extraction into amyl acetate followed by a back-extraction into water - this allows one to remove non-polar as well as polar impurities. The back-extraction looks the same as a regular extractor except that the penicillin enters the extractor in the organic phase and it is recovered in the water. The pH is adjusted between these steps to change the value of the Henry's law constant (due to the protonation of the acid group in the penicillin molecule), with H1=20 (for the extraction step) and H2=0.03 (for the back-extraction step). A. Derive expressions for the concentration and overall recovery of penicillin in the water leaving the second extractor as a function of the amyl acetate flow rate. Assume that the water flow rate in the back-extraction step is 1/2 the value of the inlet feed water. B. Determine the maximum penicillin recovery for this process (with the amyl acetate flow rate as the variable) for qw=20L/min in the first extractor. C. Comment on the physical basis for this maximum - why does the penicillin recovery go through a maximum as one increases the amyl acetate flow rate
