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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 theprogram with performance number.

(2)1

(a) Taking H2as your basis of calculation, construct a complete stoichiometric table for thefollowing reaction

0.5N2+ 1.5H2NH3

The reaction is isobaric, isothermal flow system with equimolar feeds of N 2and H2.

(b) If the entering total pressure is 16.4 atm and the entering temperature is 1727 oC, calculate

the concentrations of ammonia and hydrogen when the conversion of H2is 60%.

(c) If you took N2as your basis of calculation, could 60% conversion of N2be achieved?

Ans:

a)

Inlet Oulet

H2N2

NH3

ABC

Total

0.50.50

1

0.5(1 X)

0.5(1 X/3)

X/3

1 X/3

b)CH2= 0.025 mol/L, CNH3= 0.025 mol/L

c)Maximum conversionX = 1/3

1Fogler, H. S., Elements of Chemical Reaction Engineering, Prentice Hall, 1999

http://www.engin.umich.edu/~cre/icm/cre.htmlhttp://www.engin.umich.edu/~cre/icm/cre.html

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(3)1The 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 thefeed is equimolar in A and B. The entering temperature and pressure are 727 oC 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) 1.875 L/min

b) rA= 1.48510-2mol/Lmin

c) rA= 4.9510-3mol/Lmin

d) CA0= 0.0609 mol/L

e) CA= 0.0609 mol/Lf) k= 49.53 L/molmin

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(4)1Calculate 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=BeAe

Ce

CC

C= 10 L/mol.

(b) The gas-phase reaction

A 3C

carried out in a flow reactor with no pressure drop. Pure A enters at a temperature of 400 oKand 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

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(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) 0 3 5 8 10 12 15 17.5

CA(mol/L) 4.0 2.89 2.25 1.45 1.0 0.65 0.25 0.07

a)Determine the reaction order, , and the specific reaction rate, kusing 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 Matlabfunction

fminsearchto 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 0.5 0.25 0.07];n!=len"th#t$;c=!l&fit#t'C'4$(C(t=4)c#1$)t.*3+3)c#2$)t.*2+2)c#3$)t+c#4$;,=l"#C$;&=l"#-(C(t$;c1=!l&fit#,'&'1$;sl!e = c1#1$; =e,!#c1#2$$;

f!rintf#/eactin r(er = %"' = %8.3fn/'sl!e'$,!=[,#1$ ,#n!$];&!=!l&al#c1',!$;!lt#,'&'//',!'&!$;"ri( n,label#/l"#C$' l"#ml$/$&label#/l"#(C(t$'l"#ml.min$/$

!5(3c = Cl6mns 1 thr6"h 4

0.0000 -0.0001 0.0112 -0.4031

Cl6mn 54.0002eactin r(er = 0.5297' = 0.197 ml0.51.5min

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-3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5-3.5

-3

-2.5

-2

-1.5

-1

-0.5

log(C), log(mol/L)

log(dC/dt),l

og(mol/L.m

in)

b)

CA= [ ] )1/(11 0 )1(

ktCA

"lbal t Ct=[0 3 5 8 10 12 15 17.5];C=[4.0 2.89 2.25 1.45 1.0 0.5 0.25 0.07];clf!=fminsearch#/f5(3b/'[.9 .9]$;t!=018;a=!#1$;=!#2$;a1=1-a;Cal=#C#1$*a1-a1))t!$.*#1a1$;!lt#t!'Cal't'C'//$"ri( n,label#/t#min$/$;&label#/C#ml$/$le"en(#/itte(/'/ata/$f!rintf#/alfa = %8.3f' = %8.4fn/'a'$Cal=#C#1$*a1-a1))t$.*#1a1$;:=s6m##C-Cal$.*2$;Cae=mean#C$;:t=s6m##C-Cae$.*2$;r=srt#1-::t$;f!rintf#/crrelatin cefficient = %8.4fn/'r$------------------------------------------------------------------f6nctin &=f5(3b#!$

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"lbal t Ca=!#1$;=!#2$;a1=1-a;Cal=#C#1$*a1-a1))t$.*#1a1$;&=s6m##C-Cal$.*2$;------------------------------------------------------------------

!5(3b

alfa = 0.503' = 0.1991 ml0.5

1.5

min

crrelatin cefficient = 1.0000

(6) Instead of expanding T cells in a batch reactor, you decide to expandthem in a CSTR. The fastest you can expand cells in a CSTR is when thegrowth rate of the cells (k) is exactly eual to one o!er the residence time

of the reactor ("#). $ssume that you are growing cells in a " % CSTR, with

a !olumetric flow rate of feed and exit at &.&'%#h, and that cell growth,rT* kCT,where k*&.&' h

+". The steady state concentration of T cells is"& cells#%. If, at some point in time, a bacterial contaminant getsintroduced in the feed stream at a concentration of "& cells#%, and thebacteria grows at a rate of &. h+", how long will it be before theconcentration of bacteria in the reactor (and in the outlet stream with the Tcells) is "&cells#%. $t a certain concentration, the bacteria not only wouldpose a health ris- to the patient to whom the T cells could be returned, butthey might also secrete toxins and compete for nutrients, thus -illing off thehealthy T cell population.

Ans:32.96 h

(7)2 We have a process that reacts 67% CH4 in O2at 10 atm to form syngas (H! " #$

&ca'/mo' CH4)$ Note:syngas consists of CO an H2$(a) stimate the aia*atic reactor temperat+re at comp'etion if ,e pro+ce 100% syngas ,ith

a fee temperat+re of 400oC$ -ss+me Cp" 7 ca'/mo'o.$

(b) stimate the aia*atic reactor temperat+re if ,e s+en'y *egin pro+cing 100% tota'

com*+stion pro+cts (H!" 12 &ca'/mo')$

(c) What o ,e have to *e concerne ,ith regaring reactor constr+ction materia's anpress+re re'ief capa*i'ities to esign for this possi*i'ity$

Ans:

a) #0oCb) 471oCc) emperat+re an ress+re ,i'' *e m+ch higher if com*+stion occ+rs$ ee specia'

materia' an press+re re'ief$

2Schmidt, L.D., The Engineering of Chemical Reactions, Oxford, 2004, pg. 83 (p. 2.11)

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