CHE 304 (Spring 2010) ______
LAST NAME, FIRST
Problem set #5
(1) Run Great Race (http://www.engin.umich.edu/~cre/icm/cre.html)
Click on the CHE 304 distribution folder, then copy the Tictac Race folder to your flash drive or H:\ drive. Open this folder and click on the appropriate program name (Great Race.exe). Turn in the last page of the program with performance number.
(2)[1] Consider a cylindrical batch reactor that has one end fitted with a frictionless piston attached to the spring as shown:
The reaction A + B ® 8C with the rate reaction - rA = k1CA2CB is taking place in this type of reactor.
(a) Write the rate law solely as a function of conversion, numerically evaluating all possible symbols.
(b) What is the conversion and rate of reaction when V = 0.25 ft3?
Additional information: Equal moles of A and B are present at t = 0. Initial volume: 0.15 ft3. Value of k1: 1.0 (ft3/lbmol)2×s-1. The relationship between the volume of the reactor and pressure within the reactor is V = (0.1)(P), (V in ft3, P in atm). Temperature of system (considered constant): 140oF. Gas constant: 0.73 ft3×atm/lbmol×oR.
Ans:
a) - rA = k1CA2CB = (1)( 1.712´10-3)3 = 5.02´10-9
b) X = 0.5926; - rA = 7.33´10-11 lbmol/ft3×s
(3)1 The gas phase reaction between chlorine and methane to form carbon tetrachloride and hydrochloric acid is to be carried out at 75oC and 850 kPa in a continuous-flow reactor. The vapor pressure of carbon tetrachloride at 75oC is approximately 95 kPa. Set up a stoichiometric table for this reaction with phase change. Calculate the conversion of methane at which condensation begins. The volumetric flow rate is 0.4 L/s.
Ans:
X = 0.5588
(4)1 The reaction
C2H6(g) + 2Br2(g) ® C2H4Br2(g,l) + 2HBr(g)
is to be carried out at 200oC and 2000 kPa. The vapor pressure of 1,2-dibromoethane at 200oC is 506.5 kPa. The reaction is first order in C2H6 and second order in Br2 with k = 0.01 L6/mol2×min. Calculate the conversion of ethane at which condensation begins. The volumetric flow rate is 0.5 L/s.
Ans:
X = (3)(0.2532) = 0.7597
(5)1 The elementary gas-phase reaction
(CH3)3COOC(CH3)3 ® C2H6 + 2CH3COCH3
is carried out isothermally in a flow reactor with no pressure drop. The specific reaction rate at 50oC is 10-4 min-1 and the activation energy is 85 kJ/mol. Pure di-tert-butyl peroxide enters the reactor at 10 atm and 127oC and a molar flow rate of 2.5 mol/min. Calculate the reactor volume to achieve 90% conversion in:
(a) a CSTR
(b) a PFR
(c) If this reaction is to be carried out at 10 atm and 127oC in a batch mode with 90% conversion, what reactor size and cost would be required to process (2.5 mol/min ´ 60 min/h ´ 24 h/day) 3600 mol of di-tert-butyl peroxide per day? The down time for the batch reactor is 6 hours.
(d) Assume that the reaction is reversible with Keq = 0.025 mol2/L2 and calculate the equilibrium conversion.
Ans:
a) 5597 L b) 1134 L
c) 4721 L d) 0.512
(6) [1]Consider the anaerobic fermentation of glucose to ethanol by yeast. Glucose (C6H12O6) is converted into yeast, ethanol (C2H5OH), the byproduct glycerol (C3H8O3), carbon dioxide, and water. An empirical chemical formula for yeast can be taken as CH1.74N0.2O0.45. We can describe the fermentation by the following reaction:
C6H12O6 + aNH3 ® b CH1.74N0.2O0.45 + c C2H5OH + d C3H8O3 + e CO2 + f H2O
Determine the stoichiometric coefficients of the above reaction if 0.21 moles of glycerol were formed for each mole of ethanol produced and 0.13 moles of water were formed for each mole of glycerol.
Ans:
C6H12O6 + 0.0806 NH3 ® 0.4029 CH1.74N0.2O0.45 + 1.4921 C2H5OH
+ 0.3133 C3H8O3 + 1.6729 CO2 + 0.0407 H2O
(7) The following reaction
C2H4Br2 + 3KI ® C2H4 + 2KBr + KI3
A + 3B ® C + 2D + E
is carried out in a differential reactor. There is no product in the feed. The exiting concentration of ethylene is recorded as a function of temperature and entering concentrations.
T(oK) / 323 / 333 / 343 / 353 / 363 / 363C2H4Br2 (mol/L) / 0.1 / 0.1 / 0.05 / 0.1 / 0.2 / 0.01
KI (mol/L) / 0.1 / 0.1 / 0.1 / 0.05 / 0.01 / 0.01
C2H4 (mol/L) / 0.002 / 0.006 / 0.008 / 0.02 / 0.02 / 0.01
The space time (=V/Q0) for the differential reactor is 2 minutes. If the rate expression for C (ethylene) is given by
RC = 3.65´106exp(- E/(8.314T))CAa CBb
Determine the values of E, a, and b using fminsearch with initial guess E = 40000 J/mol, a = .5, and b = .5.
Ans:
V = = Þ rC = = 0.5CC
global T CA CB rC
T=[323 333 343 353 363 363];
CA=[.1 .1 .05 .1 .2 .01];
CB=[.1 .1 .1 .05 .01 .01];
CC=[.002 .006 .008 .02 .02 .01];
VoQ=0.5;
rC=VoQ*CC;
p=fminsearch('F5d14',[40000 .5 .5]);
E=p(1);a=p(2);b=p(3);
fprintf('E = %g, a = %g, b = %g\n',E,a,b)
function y=F5d14(p)
global T CA CB rC
E=p(1);a=p(2);b=p(3);
rCc=3.65e6*exp(-E./(8.314*T)).*CA.^a.*CB.^b;
y=sum((rC-rCc).^2);
> p4d14Fo
E = 54127.9, a = 0.246206, b = 0.291713
(8) 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 H2O
The growth of yeast cell mass concentration Cc can be described by the Monod relationship
= mCc = m max
In this equation, Cs is the substrate or glucose concentration with an initial value Cs0 = 100 g/L and the Monod constants are Ks = 1.5 g/L and m max = 0.15 hr-1. The initial yeast cell concentration after inoculation of the fermentor is 0.2 g/L. Use Matlab to plot the concentrations in the fermentor of the yeast cells Cc, glucose Cs, ethanol Cet, and glycerol Cgly as functions of time. (Note: You can plot the yeast cell concentration as a function of time by varying Cc from 0.2 to 3.2 g/L and evaluating the corresponding time t).
[1] Fogler, H. S., Elements of Chemical Reaction Engineering, Prentice Hall, 1999
[1] Fournier, R. L., “Basic Transport Phenomena in Biomedical Engineering”, Taylor & Francis, 2007, p. 22.