CHE 304 (Spring 2010)
__________________
LAST NAME, FIRST
Problem set #4
(1) Run Kinetic Challenge II (http://www.engin.umich.edu/~cre/icm/cre.html)
You will find the program Kinetic Challenge II in the CHE 304 distribution folder, then
Kinetics, then Kinetic2, then click on Kinetic Challenge II.exe. Turn in the last page of the
program with performance number.
(2)1
(a) Taking H2 as your basis of calculation, construct a complete stoichiometric table for the
following reaction
0.5N2 + 1.5H2  NH3
The reaction is isobaric, isothermal flow system with equimolar feeds of N2 and H2.
(b) If the entering total pressure is 16.4 atm and the entering temperature is 1727oC, calculate
the concentrations of ammonia and hydrogen when the conversion of H2 is 60%.
(c) If you took N2 as your basis of calculation, could 60% conversion of N2 be achieved?
Ans:
a)
H2
N2
NH3
A
B
C
Inlet
0.5
0.5
0
Total
1
b) CH2 = 0.025 mol/L, CNH3 = 0.025 mol/L
c) Maximum conversion X = 1/3
1
Fogler, H. S., Elements of Chemical Reaction Engineering, Prentice Hall, 1999
Oulet
0.5(1  X)
0.5(1  X/3)
X/3
1  X/3
(3)1 The gas-phase reaction 2A + 4B  2C is first-order in A and first-order in B is to be carried
out isothermally in a plug-flow reactor. The entering volumetric flow rate is 2.5 L/min, and the
feed is equimolar in A and B. The entering temperature and pressure are 727oC and 10 atm,
respectively. The specific reaction rate at this temperature is 4 L/molmin and the activation
energy is 15,000 cal/mol.
(a) What is the volumetric flow rate when the conversion of A is 25%?
(b) What is the rate of reaction at the entrance to the reactor.
(c) What is the rate of reaction when the conversion of A is 40%?
(d) What is the concentration of A at the entrance to the reactor?
(e) What is the concentration of A at 40% conversion of A?
(f) What is the value of the specific reaction rate at 1227oC.
Ans:
a)
b)
c)
d)
e)
f)
1.875 L/min
 rA = 1.48510-2 mol/Lmin
 rA = 4.9510-3 mol/Lmin
CA0 = 0.0609 mol/L
CA = 0.0609 mol/L
k = 49.53 L/molmin
(4)1 Calculate the equilibrium conversion and concentrations for each of the following reactions.
(a) The liquid-phase reaction
A+BC
with CA0 = CB0 = 2 mol/L and Keq =
CCe
= 10 L/mol.
C AeC Be
(b) The gas-phase reaction
A  3C
carried out in a flow reactor with no pressure drop. Pure A enters at a temperature of 400oK
and 10 atm. At this temperature Keq = 0.25 mol2/L2.
(c) The gas phase reaction in part (b) carried out in a constant-volume batch reactor.
(d) The gas phase reaction in part (b) carried out in a constant-pressure batch reactor.
Ans:
a) Xe = 0.8; CAe = 0.4 mol/L, CBe = 0.4 mol/L, CCe = 1.6 mol/L
b) Xe = 0.58; CA = 0.0593 mol/L, CB = 0.246 mol/L
c) Xe = 0.392; CA = 0.186 mol/L, CB = 0.359 mol/L
d) Xe = 0.58; CA = 0.0593 mol/L, CB = 0.246 mol/L
(5) (P5-31) The irreversible isomerization
AB
was carried out in a batch reactor and the following concentration-time data were obtained:
t(min)
CA(mol/L)
0
4.0
3
2.89
5
2.25
8
1.45
10
1.0
12
0.65
15
0.25
17.5
0.07
a) Determine the reaction order, , and the specific reaction rate, k using differential method of
rate analysis. Fit your data by a fourth order polynomial.
b) Assume a rate law of the form
 rA = kCA
Integrate the equation for the combined mole balance and rate law and then use Matlab function
fminsearch to determine  and k.
Ans:
%
t=[0 3 5 8 10 12 15 17.5];
C=[4.0 2.89 2.25 1.45 1.0 0.65 0.25 0.07];
np=length(t);
co=polyfit(t,C,4)
dCdt=4*co(1)*t.^3+3*co(2)*t.^2+2*co(3)*t+co(4);
x=log(C);
y=log(-dCdt);
c1=polyfit(x,y,1);
slope = c1(1); k=exp(c1(2));
fprintf('Reaction order = %g, k = %8.3f\n',slope,k)
xp=[x(1) x(np)];
yp=polyval(c1,xp);
plot(x,y,'o',xp,yp);grid on
xlabel('log(C), log(mol/L)')
ylabel('log(dC/dt),log(mol/L.min)')
>> p5d3
co =
Columns 1 through 4
0.0000 -0.0001 0.0112 -0.4031
Column 5
4.0002
Reaction order = 0.529766, k = 0.197 mol0.5/L1.5min
-0.5
log(dC/dt),log(mol/L.min)
-1
-1.5
-2
-2.5
-3
-3.5
-3
b)
-2.5

-2
CA = C 1A0  (1   )kt
-1.5
-1
-0.5
log(C), log(mol/L)

1 /(1 )
global t C
t=[0 3 5 8 10 12 15 17.5];
C=[4.0 2.89 2.25 1.45 1.0 0.65 0.25 0.07];
clf
p=fminsearch('f5d3b',[.9 .9]);
tp=0:18;
a=p(1);k=p(2);
a1=1-a;
Cal=(C(1)^a1-a1*k*tp).^(1/a1);
plot(tp,Cal,t,C,'o')
grid on
xlabel('t(min)');ylabel('C(mol/L)')
legend('Fitted','Data')
fprintf('alfa = %8.3f, k = %8.4f\n',a,k)
Cal=(C(1)^a1-a1*k*t).^(1/a1);
S=sum((C-Cal).^2);
Cave=mean(C);
St=sum((C-Cave).^2);
r=sqrt(1-S/St);
fprintf('correlation coefficient = %8.4f\n',r)
-----------------------------------------------------------------function y=f5d3b(p)
0
0.5
1
1.5
global t C
a=p(1);k=p(2);
a1=1-a;
Cal=(C(1)^a1-a1*k*t).^(1/a1);
y=sum((C-Cal).^2);
----------------------------------------------------------------->> p5d3b
alfa = 0.503, k = 0.1991 mol0.5/L1.5min
correlation coefficient = 1.0000
(6) Instead of expanding T cells in a batch reactor, you decide to expand
them in a CSTR. The fastest you can expand cells in a CSTR is when the
growth rate of the cells (k) is exactly equal to one over the residence time of
the reactor (1/). Assume that you are growing cells in a 1 L CSTR, with a
volumetric flow rate of feed and exit at 0.0294L/h, and that cell growth, rT=
kCT, where k=0.0294 h-1. The steady state concentration of T cells is 109
cells/L. If, at some point in time, a bacterial contaminant gets introduced in
the feed stream at a concentration of 10 cells/L, and the bacteria grows at a
rate of 0.46 h-1, how long will it be before the concentration of bacteria in
the reactor (and in the outlet stream with the T cells) is 106 cells/L. At a
certain concentration, the bacteria not only would pose a health risk to the
patient to whom the T cells could be returned, but they might also secrete
toxins and compete for nutrients, thus killing off the healthy T cell
population.
Ans: 32.96 h
(7)2 We have a process that reacts 67% CH4 in O2 at 10 atm to form syngas (HRx =  8.5
kcal/mol CH4). Note: syngas consists of CO and H2.
(a) Estimate the adiabatic reactor temperature at completion if we produce 100% syngas with
a feed temperature of 400oC. Assume Cp = 7 cal/moloK.
(b) Estimate the adiabatic reactor temperature if we suddenly begin producing 100% total
combustion products (HRx =  192 kcal/mol).
(c) What do we have to be concerned with regarding reactor construction materials and
pressure relief capabilities to design for this possibility.
Ans:
a) 805oC
b) 4971oC
c) Temperature and Pressure will be much higher if combustion occurs. Need special
material and pressure relief.
(8) 2You have a summer job with a company that is interested in building a plant to manufacture
the painkiller ibuprofen [2-(p-isobutylphenyl) propionic acid, C13H18O2] using a new reaction
2
Schmidt, L.D., The Engineering of Chemical Reactions, Oxford, 2004, pg. 83 (p. 2.11)
scheme. Your assignment is to collect some data on one of the reactions, as a first step in
designing a full-scale reactor. In one experiment, you mix 134 g isobutylbenzene (IBB, C10H14)
with 134 g acetic anhydride (AAn, C4H6O3) in a laboratory-scale batch reactor, adjust the
temperature, and wait 1 hour. At the end of the hour you stop the reaction, collect all the material
in the pot, and send it for chemical analysis. The report come back that the pot contains IBB,
acetic anhydride, isobutylacetophenone (IBA, C12H16O) and acetic acid (AAc, CH3COOH).
Unfortunately, someone spilled coffee on the report and all you can read is the amount of
isobutylbenxene: 1.6 g. Your boss is upset-he needs the data right away. Can you determine the
amounts of IBB, AAn, and IBA from the available information for your boss?
Ans:
134 g IBB
134 g AAn
Reactor
x g AAc
y g AAn
z g IBA
1.6 g IBB
(mw = 60)
(mw = 102)
(mw = 176)
(mw = 134)
The three unknowns x, y, and z can be solved from the balances of three element C, H, and O.
x = 59.28 g, y = 33.22 g, and x = 173.90 g
2
Murphy, R. M., “Introduction to Chemical Processes Principles, Analysis, Synthesis”, McGraw Hill, 2007, p. 96