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Biochem+Eng+Hmks - PROBLEM SET 1& 2*QUESTIONS ONLY ‐...

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Unformatted text preview: PROBLEM SET 1 & 2 *QUESTIONS ONLY ‐ DUE: MONDAY, SEPTEMBER 13, 2010 DEFINING SYSTEMS *Question 1: a) Define the terms: mass flow rate, volumetric flow rate, density, mass fraction b) What is conserved in a chemical reaction? c) Define closed, open and isolated systems. d) What is the material balance equation for an individual chemical species “A” in an open system? Which terms become zero if you have: a closed system, no reaction, or steady‐state? MASS BALANCES *Question 2: Filtere d The kidneys carry out a separation process where blood enters Blood at a rate of 1200 mL/min and is split into two streams: filtered blood and urine. We are specifically interested in the details of VF = ? the separation of urea and a drug circulating in the patient’s Cu rea, F = ? Blood Cdrug, F = 90 uM blood by the patient. What is known is given in the figure. Find Kidney VB = 1200 mL/min the unknown quantities in the filtered blood and urine streams. Cu rea, B = 10 mg/dL Urine Find the unknown quantities in the filtered blood and urine Cdrug, B = 100 uM streams. Assume density of all streams is the same as water = 1 VU = 1.5 mL/min Curea, U = 500 mg/dL kg/L. Note that 1 uM = 1 micromole per liter. Cdrug, U = ? *Question 3: B A You are preparing a mixture of methanol (MeOH) by combining two solutions of MeOH. More specifically, you are adding 200 g of 150 g 200 g xM, B = 0.700 xM, A = 0.400 solution A and 150 g of solution B. The mass fraction of MeOH in A is 0.4 and the mass fraction of MeOH in B is 0.7. What is the mass C fraction MeOH in the final mixture C (see figure)? *Question 4: You have designed a centrifuge system to Supernatant (S) separate cells from a solution. A mixture of water and cells enters the centrifuge system at a Ccells , S = 0 rate 1000 L/h and contains 500 mg cells/L. You Feed (F) can assume that the density is that of water (1 Centrifuge g/cm3). The inlet stream or feed (F), is separated VF = 1000 L/h to a cell‐free supernatant (S), and a pellet (P) ρF= 1.0 g/cm3 Pellet (P) consisting of a solution containing water and Ccells , F = 500 mg cells/L X cells, P = 0.5 cells. The mass fraction of cells in the pellet is Xwater, P = 1‐ Xcells , P = 0.5 0.5. Using the data in the figure, calculate the mass flow rates mP (g/hr) and mS (g/hr). Question 5: Corn‐steep liquor contains 2.5 wt% dextrose (i.e. the mass fraction of dextrose is 2.5/100 = 0.025) and 50 wt% water; the rest of the liquor stream is solids. Beet molasses contain 50 wt% sucrose, 1.0 wt% dextrose, and 18 wt% water; the rest of the molasses stream contains solids. Beet molasses is mixed with corn‐steep liquor and water in a mixing tank to produce a dilute sugar mixture. The exit stream contains 2.0 wt% dextrose and 12.6 wt% sucrose, and is ready to be fed into a fermentation unit. a) Draw a diagram of the system and label entering and exiting streams. b) What are the mass fractions of dextrose, sucrose, solids, and water in the exit stream? c) What is the ratio of the mass flow rate of the water stream to the mass flow rate of the corn‐steep liquor stream? Question 6: An adult takes about 12 breaths per minute, inhaling roughly 500 mL of air with each breath. The molar composition of the inspired and expired gases are as follows: Species Inspired gas (%) Expired (%) O2 20.6 15.1 0.0 3.7 CO2 N2 77.4 75.0 H2O 2.0 6.2 Assume that the temperature of the air in and air out are the same. Also, note that nitrogen is not transported into or out of the blood in the lungs, so the amount of N2in = amount of N2out a) Draw a diagram of the lung system and the streams in and out of it. b) Calculate the volumes of O2, CO2, and H2O transferred from the pulmonary gases to the blood or vice versa (specify which) per minute. MULTI‐COMPARTMENT MASS BALANCES Question 7: A membrane system is used to filter waste products from the bloodstream (see Figure). The blood can be thought of as being comprised of “waste” and “all other blood constituents.” The membrane can extract 30.0 mg/min of pure waste (stream W) without removing any blood. The unfiltered entering bloodstream (stream U) contains 0.17% waste, and the mass flow rate of the entering bloodstream is 25 g/min. After exiting the membrane, the blood is A U Mixer split into two streams: one (stream R) is recycled to join with the unfiltered blood stream before entering the membrane and one (stream F) leaves W the system as filtered blood. The recycle mass flow Membrane R rate (stream R) is known to be twice that of the Unit filtered mass flow rate (stream F). Calculate the mass flow rate and the wt% of waste in streams A, B F B, F, and R. Hint: the splitter does not change the Splitter composition of the stream that it separates. PROBLEM SET 3 *QUESTIONS ONLY ‐ DUE: MONDAY, SEPTEMBER 20, 2010 MASS BALANCES WITH CHEMICAL REACTIONS *Question 8: Consider an idealized model of glucose uptake and reaction by skeletal muscle: C6H12O6 + 6O2 ‐> 6CO2 + 6H2O The average uptake rate of glucose = 36 ug , 10 6 cells ⋅ h the average uptake rate of oxygen = 10 and the excretion rate of CO2 = 13 ug , 106 cells ⋅ h ug . 106 cells ⋅ h Find (A) the limiting reagent, (B) the % excess, and (C) the % conversion. Relevant information: Species Molecular Weight (g/mol) Glucose 180.2 Oxygen 32.0 44.0 CO2 H2O 18.0 Question 9: The vitamin company you work for produces alanine. Alanine is produced in a reactor in a continuous process. There are two separate inlet streams that contain glutamine (100 mol/min) and pyruvic acid (50 mol/min), respectively. The ratio of the molar flow rate of pyruvic acid in the outlet stream to that in the inlet stream is 0.6. The reaction is: C5H10N2O3 (glutamine) + C3H4O3 (pyruvic acid) ‐> C5H7NO4 (alpha‐ketoglutamic acid) + C3H7NO2 (alanine) a) What is the reaction rate, R, of glutamine? Pyruvic acid? Find the limiting reagent. What are the fractional conversions of glutamine and pyruvic acid? b) Find the outlet molar flow rates of alanine, alpha‐ketoglutamic acid, and any excess reactants. Question 10: Acetobacter aceti bacteria convert ethanol to acetic acid (vinegar) under aerobic (i.e. with oxygen) conditions. A continuous fermentation process for acetic acid production is C2H 5OH Off‐gas shown in the Figure. The conversion reaction is as follows: C2H5OH (ethanol) + O2 ‐> CH3COOH (acetic acid) + H2O The feed stream containing ethanol enters the reactor at a rate of 1.0 kg/hr. Also, air bubbles into the reactor at a rate of 40.0 L/min. An exit off‐gas stream as well as the liquid product stream containing acetic acid and water leave the reactor. Assume reaction goes to completion. Reactor a) What is the reaction rate for this reaction? What is the limiting reactant? What are the fractional conversions of C2H5OH and O2? b) Determine the outlet flow rates of the elements C, H, O in the acetic acid product CH 3COOH Air stream. Also determine the outlet mass flow rates of all compounds in the liquid H 2O product stream and the volumetric flow rates of all compounds in the off‐gas stream. MASS BALANCES WITH RECYCLING *Question 11: You want to build a simple metabolic model of fat absorption and metabolism in the body. 1) Use the information to draw a compartment model that describes what happens to the fat in the body: a. The gut absorbs only 70% of the fat present in the food. b. All the fat absorbed into the gut goes straight to the liver via the portal circulation. There, 20% of the absorbed fat is removed by the liver and the rest travels to the rest of the body via the systemic circulation. c. Since part of the systemic circulation in fact goes back to the liver, some of the fat that was not removed by the liver in step 2 above will come back to the liver and not go to the other tissues. Assume that 10% of that amount comes back to the liver. Hint: build a system consisting of two subsystems, the gut and the liver. 2) What is the fraction of the initial fat in the food is delivered to the rest of the body (excluding the liver)? PROBLEM SET 4 *QUESTIONS ONLY ‐ DUE: MONDAY, SEPTEMBER 27, 2010 REACTION RATE LAWS *Question 12: Consider the reaction A B taking place in a closed system. At t=0 the initial concentration of A is 3.5 mol/L and no B is present. After 1 hour, the concentration of A is down to 1.4 mol/L. 1) Assume that the reaction is 0th order. Answer the following: a. Derive an expression for the concentration of A as a function of time. b. What is the value of k (including the units)? c. Calculate the half‐time at t=0. Show all derivations! 2) Now instead assume that the reaction is 1st order, with the same concentrations of A initially and at 1 hour. Answer the same questions as in part (1). ENZYME‐CATALYZED REACTIONS *Question 13: Enzyme‐catalyzed reactions usually follow Michaelis‐Menten kinetics. It is common to rewrite the basic form of the rate equation dP = VMAX [S] dt KM + [S] into a “linearized” form 1/v as a function of 1/[S] where v = dP/dt. a) Derive the linearized form described above. b) What do the slope and vertical intercept mean? PROBLEM SET 5 *QUESTIONS ONLY ‐ DUE: FRIDAY, OCTOBER 1, 2010 PHARMACOKINETICS *Question 14: Kidneys are vital organs that keep the chemical balance of blood and remove toxic waste from blood. Typically kidneys process about 1.0 liter of blood and filter out 0.08 liter of waste and extra water every hour, and the remainder 0.92 liter of purified blood goes back to the body. We have been monitoring the removal of two toxic wastes from the blood to urine. The table bellow show the volume fraction of toxic wastes in blood before (call this the feed) and after (call this the product) passing through the kidneys. Volume fraction in feed Volume fraction in product i.e. blood before i.e. blood after (%) (%) Waste A 10.4 8.7 Waste B 7.5 6.5 Water 82.1 84.8 a. Calculate the volumetric flow rates (l/hr) of waste streams A and B in the blood and the urine b. Calculate the transfer rate (l/hr) of waste A from blood to urine. Assume steady state c. (Skip) d. Due to the injection of a drug the volume fraction of waste B in the feed changes over time as X(B, feed)=9.2 + 2e‐2t, whereas in the product the volume fraction of B changes with time as X(B, product)=10+1.5e‐2t. You may assume that the volume flow rates of feed and product do not change. What is rate of waste B removal? Question 15: A patient enters the emergency room (E.R.) and needs an infusion of acetaminophen to achieve a steady‐state concentration of 5.0 mg/L in his bloodstream. The volume of distribution of acetaminophen is 63 L. Acetaminophen can be considered to be eliminated entirely by metabolism in the liver, with a first‐order elimination rate constant ke = 0.35 h‐1. a) Find the infusion rate of acetaminophen in mg/min. The patient returns home, but eventually the pain returns. Therefore, the patient takes a 500 mg pill of acetaminophen. Acetaminophen is absorbed by the GI tract via a first order process with a rate constant ka = 2.2 h‐1. b) At what time is the maximum acetaminophen concentration reached and what is the maximum concentration? Assume that the initial concentration of acetaminophen is zero. c) If the patient has liver disease, causing a reduction in the elimination kinetics, sketch what will be the effect on the concentration vs. time profile and explain your answer: a. For the infusion case of part (a) b. For the pill absorption case of part (b) d) Acetaminophen freely crosses the blood‐brain barrier. How does the concentration vs. time profile in the brain compare with that in the bloodstream? ...
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