Problem set #3CHE499 TRANSPORT MODELING Spring 2008Problem set #31. 1Consider the anaerobic fermentation of glucose to ethanol by yeast. Glucose (C6H12O6) isconverted into yeast, ethanol (C2H5OH), the byproduct glycerol (C3H8O3), carbon dioxide, andwater. An empirical chemical formula for yeast can be taken as CH1.74N0.2O0.45. We can describethe fermentation by the following reaction:C6H12O6 + aNH3  b CH1.74N0.2O0.45 + c C2H5OH + d C3H8O3 + e CO2 + f H2ODetermine the stoichiometric coefficients of the above reaction if 0.21 moles of glycerol wereformed for each mole of ethanol produced and 0.13 moles of water were formed for each mole ofglycerol.2. 1Consider the anaerobic fermentation of glucose to ethanol by yeast in a batch reactor.C6H12O6 + 0.0462 NH3  0.2309 CH1.74N0.2O0.45 + 1.6840 C2H5OH + 0.2021 C3H8O3 + 1.7948 CO2 + 0.0162 H2OThe growth of yeast cell mass concentration Cc can be described by the Monod relationshipdtdCc = Cc =  maxsscsCKCCIn this equation, Cs is the substrate or glucose concentration with an initial value Cs0 = 100 g/Land the Monod constants are Ks = 1.5 g/L and  max = 0.15 hr-1. The initial yeast cellconcentration after inoculation of the fermentor is 0.2 g/L. Plot the concentration in thefermentor of the yeast cells Cc, glucose Cs, ethanol Cet, and glycerol Cgly. You can plot the yeastcell concentration as a function of time by varying Cc from 0.2 to 3.2 g/L and evaluating thecorresponding time t.3. 2Air at 400 kPa and 400 K passes through a turbine. The turbine is well-insulated. The airleaves the turbine at 125 kPa. Find the maximum amount of work that can be obtained from theturbine and the exit temperature of the air leaving the turbine. Assume air is an ideal gas with aCp = 3.5 R (Gas constant).4. Consider the slow adiabatic expansion of a closed volume of gas for which Cp = 3.5 R. If theinitial gas temperature is 825 K, and the ratio of the final pressure to the initial pressure is 1/3,what is the change in enthalpy of the gas, the change in internal energy, the heat transferred Q,and the work W? Assume a basis of 1 mole of gas.1 Fournier, R. L., “Basic Transport Phenomena in Biomedical Engineering”, Taylor & Francis, 2007, p. 22.2 Fournier, R. L., “Basic Transport Phenomena in Biomedical Engineering”, Taylor & Francis, 2007, p. 865. 1Consider the anaerobic fermentation of glucose to ethanol by yeast in a CSTR.C6H12O6 + 0.0462 NH3  0.2309 CH1.74N0.2O0.45 + 1.6840 C2H5OH + 0.2021 C3H8O3 + 1.7948 CO2 + 0.0162 H2OThe growth of yeast cell mass concentration Cc can be described by the Monod relationshipdtdCc = Cc =  maxsscsCKCCIn this equation, Cs is the substrate or glucose concentration and the Monod constants are Ks = 1.5 g/L and  max = 0.15 hr-1. The feed stream to the fermentor contains no yeast cells, ethanol, or glycol. The concentration of glucose in the feed stream is 100 g/L. The fermentor has a volume of 2000 L and the feed flow rate F to the fermentor is 100 L/hr. Calculate the exiting concentrations of the yeast cells Cc, glucose Cs, ethanol Cet, and glycerol Cgly.6. 1The renal dialysis machine or artificial kidney can be used to treat patients with uremia orrenal failure. During kidney dialysis blood flows through a system of tubes composed of amembrane permeable only to the smaller solutes but not the plasma proteins. On the outside ofthe dialysis tubes is a dialyzing fluid that contains the same concentration of solutes as theplasma, except for the metabolic waste products. As a result, metabolic waste products diffusefrom the blood into the dialysis fluid due to the concentration (or more exactly chemicalpotential) gradient for these substances from the blood to the dialysis fluid. Blood is usuallytaken from an artery at a high pressure, passed through the dialysis machine, and then returned toa vein at a lower pressure. At some time during the dialyis of a patient in kidney failure, theaeterial and veuous blood conditions are as follows:Arterial blood Venous bloodFlow rate, ml/minUrea concentration, mg/ml2002.11951.2a) Calculate the rate at which urea and water are being removed from the blood.b) If the dialyzing fluid enters at the rate of 1500 ml/min and the exiting dialyzing solution(dialysate) leaves at about the same rate, calculate the concentration of urea in thedialysate.c) Suppose we want to reduce the patient’s urea level from an initial value of 2.7 mg/ml to afinal value of 1.1 mg/ml. If the total distribution volume is 40 liters and the average rateof urea removal is that calculated in part (a), how long must the patient be dialyzed?(Neglect the loss in total blood volume due to the removal of water in the dialyzer.) 7. 3At 50oC the vapor pressure of A and B as pure liquids are 268 and 236.2 mmHg, respectively.At this temperature, calculate the total pressure and the composition of the vapor, which is inequilibrium with the liquid containing a mole fraction of A of 0.25.3 Fournier, R. L., “Basic Transport Phenomena in Biomedical Engineering”, Taylor & Francis, 2007, p.