Complex Systems
5.7 PROBLEMS FOR CHAPTER 5
5-1 Consider a reacting system in which species B and C are formed from reactant A. HOW
could you determine from rudimentary experimental information whether the kinetics scheme should be represented by
v0“OF 0 “O-T V
5.7 Problems for Chapter 5 109 (i) A + B + C
or (ii) A -+ B, A-+C or (iii) A + B + C
5-2 Suppose the reaction in Example 5-4 was studied in a CSTR operated at steady-state, and the results given below were obtained. Calculate the values of kf and k,, and hence write the rate law. Assume T to be the same, constant density, and no D in the feed.
flh 1 2 3 4
100 CAIC~~ 76.5 65.9 57.9 53.3
5-3 The liquid-phase hydrolysis of methyl acetate (A) to acetic acid and methyl alcohol is a re- versible reaction (with rate constants kf and k,, as in equation 5.3-3). Results of an experiment carried out at a particular (constant) temperature in a BR in terms of the fraction hydrolyzed (f~) measured at various times (t), with CA0 = 0.05 mol L-t (no products present initially), are as follows (Coulson et al., 1982, p. 616):
tls 0 1350 3060 5340 7740 00
f* 0 0.21 0.43 0.60 0.73 0.90
(a) Write the chemical equation representing the reaction.
(b) Obtain a rate law for this reaction, including values of the rate constants. State any as- sumption(s) made.
5-4 In an experiment (Williams, 1996) to evaluate a catalyst for the selective oxidation of propene (CsH6) to various products, 1 g of catalyst was placed in a plug-flow reactor operated at 450°C and 1 bar. The feed consisted of propene and air (21 mole % 02,79% NZ (inert)). GC analysis of the inlet and outlet gas gave the following results, the outlet being on a water-free basis (Hz0 is formed in the oxidation):
Substance
propene
(C3H6)oxygen
(02)nitrogen (N2, inert) acrolein (C3H40) propene oxide (CsHsO) acetaldehyde (CzH40) carbon dioxide
Inlet mole % 10.0 18.9 71.1 0 0 0 0
Outlet mole %
?
? 78.3 3.17 0.40 0.59 7.91
(a) If the feed rate of C3H6 is FQQ~ =1 mm01 min-‘, at what rate do (i) CsH6. (ii) 02, and (iii) Hz0 leave the reactor?
(b) What is j&, the fractional conversion of CsHh?
(c) What is the selectivity or fractional yield of each of acrolein, propene oxide, and acetalde- hyde with respect to propene?
(d) What is the rate of reaction expressed as (i) (-TQQ); (ii) rc,n,o (in mm01 min-’ (g cat)-‘)? Assume that the reactor acts as a differential reactor (Section 3.4.1.3.1).
5-5 Repeat Example 5-6 for a CSTR with V = 15 L and 4 = 1.5 L min-‘.
5-6 Suppose the liquid-phase decomposition of A takes place according to the following kinetics scheme with rate laws as indicated:
A -+ B +E;rn = k,cA
Reaction is carried out isothermally in a batch reactor with only A present initially at a con-
CentdOn CA0 = 4 mol L-’ in an inert SOlvent. At t = 1200 s, CA = 1.20 mO1 L-’ and en = 0.84 mol L-l. Calculate (a) the values of kl and k2 (specify the units), and (b) the values of cu and cE at t = 1200 s.
5-7 For reaction according to the kinetics scheme
A+ B + C;rn = klCA
A + D; q, = k*CA
data are as follows:
Assuming that only A is present at t = 0, and that reaction occurs at constant Tin a constant- volume batch reactor, calculate xnt. kl and k2.
5-8 The following data are for the kinetics scheme:
A -*B+C;rn = k,CA
A -+ D; rn = k2CA
Assuming that reaction occurs in a constant-volume batch reactor at a fixed temperature, and that at time zero only A and B are present, calculate (not necessarily in the order listed): (a) kl and k,; (b) CA0 and cnO at time zero; (c) cu at 40 min; (d) ca at 20 min.
5-9 Suppose a substance B decomposes to two sets of products according to the kinetics scheme B-P1 + . . . .h kl = Al exp(-&t/RT)
B %P, + . . . ; k2 = A2 exp(-E&RT)
such that the rate laws for both steps are of the same form (e.g., same order). What is the overall activation energy, EA, for the decomposition of B, in terms of the Arrhenius parameters for the individual steps? (Giralt and Missen, 1974.)
5.7 Problems for Chapter 5 111 (a) Consider EA to be defined by EJ, = RT2d In kldT, where k is the overall rate constant.
(b) Consider EA to be defined by k = A exp( -EiIRT), where A is the overall pre-exponential factor.
(c) If there is any difference between EL and Ei, how are they related?
5-10 For the kinetics scheme A 3 B -% C, each step being first-order, for reaction occurring in a constant-volume batch reactor (only A present initially),
(a) At what time, 2, in terms of kl and k2, are CA and cn equal (other than t + to), and what is the condition for this to happen?
(b) What is the value oft,,, when kl = k2?
(c) Show that cn has an inflection point at 2t,,,.
(d) Calculate kl t,,, and CB,,,~~/CA~ for each of the cases (i) K = kzlkl = 10, (ii) K = 1, and (iii) K = 0.1.
(e) From the results in (d), describe how t,,, and CB,&CA~ change with decreasing K.
5-11 The following liquid-phase reactions take place in a CSTR operating at steady state.
2A + B +C; rc = klci A + B + 2D; ro = 2k2cAcg
The inlet concentration of A is 2.50 mol L-l. The outlet concentrations of A and C are respec- tively 0.45 mol L-l and 0.75 mol L-l. Assuming that there is no B, C, or D in the feed, and that the space time (7) is 1250 s, calculate:
(a) The outlet concentrations of B and D; and (b) kl and k2.
5-12 The following data are for the kinetics scheme:
A + B + C+E;(-Yn) = klCACB; kl = ?
A + C -+ D + E; rn = k2cAcc; k2 = 3.0 X 10m3 L mol-’ rnin-’
tlmin Concentration/m01 L-’
CA CB cc CD CE
0 5.0 0.040 ? 0 0
23 - 0.020 ? - -
M - 0 0 0.060 ?
Assuming that the reactions occur at constant Tin a constant-volume batch reactor, calculate:
(a) The concentration of C at time zero and the concentration of E at time m;
(b) The second-order rate constant kl; and (c) The concentration of C at time 23 min.
5-13 Consider a liquid-phase reaction taking place in a CSTR according to the following kinetics scheme:
A + B + C; rn = klCA
A + C + 2D; rn = 2k2CACc
The inlet concentration of A is CA0 = 3 mol L-l, and there is no B, C, or D in the feed. If, for a space time r = 10 min, the outlet concentrations of A and B are CA = 1.25 and cn = 1.50 mol L-’ at steady-state, calculate the values of (a) kl, (b) k2, (c) CC, and (d) co (not necessarily in the order listed). Include the units of kl and k2 in your answer.
5-14 For reaction according to the kinetics scheme
A + B + C+D;% = kicAcB A + C + 2E; r-E = 2kzcAcc data are as follows:
Assuming that reaction occurs at constant T in a constant-volume batch reactor, calculate kl, cc at t, and kg state the units of kl and k2.
5-15 The decomposition of NzOs in the gas phase to N204 and 02 is complicated by the subsequent decomposition of N204 to NO2 (presence indicated by brown color) in a rapidly established equilibrium. The reacting system can then be modeled by the kinetics scheme
N205(A)%N204(B) + ;Oz(C) N204 =Kp 2 N02(D)
Some data obtained in an experiment at 45°C in a constant-volume BR are as follows (Daniels and Johnston, 1921):
where the partial pressures PA, . . . are also in kPa.
(a) Confirm that the kinetics scheme corresponds to the stoichiometry.
(b) Calculate the values indicated by ?, if Kp = 0.558 bar.
(c) If the decomposition of N205 is first-order, calculate the value of kA.
5-16 The following data (I, in bar) were obtained for the oxidation of methane over a supported molybdena catalyst in a PFR at a particular T (Mauti, 1994). The products are CO2, HCHO, and H20.
tlms
0 0.25 0
8 0.249 0.00075
12 0.2485 0.00108
15 0.248125 0.001219
24 0.247 0.00177
34 0.24575 0.00221
50 0.24375 0.002313
100 0.2375 0.00225
PCH4 PH C H O PC02
0 0.00025 0.00042 0.000656 0.00123 0.00204 0.003938 0.01025
5.7 Problems for Chapter 5 113 Construct a suitable reaction network for this system, and estimate the values of the rate con- stants involved (assume a first-order rate law for each reaction).
5-17 In pulp and paper processing, anthraquinone (AQ) accelerates the delignification of wood and improves liquor selectivity. The kinetics of the liquid-phase oxidation of anthracene (AN) to AQ with NO2 in acetic acid as solvent has been studied by Rodriguez and Tijero (1989) in a semibatch reactor (batch with respect to the liquid phase), under conditions such that the kinetics of the overall gas-liquid process is controlled by the rate of the liquid-phase reaction.
This reaction proceeds through the formation of the intermediate compound anthrone (ANT):
C14H10 (AN) F C14Hg0 (ANT)TCt4Hs02 (AQ)
The following results (as read from a graph) were obtained for an experiment at 95°C in which cAN,o = 0.0337 mol L-l.
tlmin
0 10 20 30 40 50 60 70 80 90
CAN CANT CAQ
0.0337 0
0.0229 0.0104 0.0144 0.0157 0.0092 0.0181 0.0058 0.0169 0.0040 0.0155 0.0030 0.0130 0.0015 0.0114 0.0008 0.0088 0.0006 0.0060 mol L-l
0 0.0008 0.0039 0.0066 0.0114 0.0144 0.0178 0.0209 0.0240 0.0270
If each step in the series network is first-order, determine values of the rate constants ki and kz in s-l.
5-18 Duo et al. (1992) studied the kinetics of reaction of NO, NH3 and (excess) 02 in connection with a process to reduce NO, emissions. They used an isothermal PFR, and reported measured ratios CNO/CNO,~ and CNH~/CNH,,~ for each of several residence times, t. For T = 1142 K, ad inlet concentrations cN0, o =5.15X 10m3, CNH~,~ = 8.45~ 10m3, and CO~,~ = 0.405 mol rnm3, they obtained results as follows (as read from graphs):
tls: 0.039 0.051 0.060 0.076 0.102 0.151 0.227
cNOIcN0.o : 0.756 0.699 0.658 0.590 0.521 0.435 0.315
CNH&NH3.0: 0.710 0.721 0.679 0.607 0.579 0.476 0.381 (a) If the other species involved are N2 and H20, determine a permissible set of chemical
equations to represent the system stoichiometry.
(b) Construct a reaction network consistent with the results in (a), explaining the basis and interpretation.
(c) Calculate the value of the rate constant for each step in (b), assuming (i) constant density;
(ii) constant co,; (iii) each step is irreversible and of order indicated by the form of the step. Comment on the validity of assumptions (i) and (ii).
5-19 Vaidyanathan and Doraiswamy (1968) studied the kinetics of the gas-phase partial oxidation of benzene (C6H6, B) to maleic anhydride (C4Hz.03, M) with air in an integral PFR containing
a catalyst of VzOs - Moos on silica gel. In a series of experiments, they varied the space time r = W/F, where W is the weight of catalyst and F is the total molar flow rate of gas (T in (g cat) h mol-‘), and analyzed for M and CO2 (C) in the outlet stream. (W/F is analogous to the space time V/q, in equation 2.3-2.) For one series at 350°C and an inlet ratio (FJFB), = 140, they reported the following results, with partial pressure p in atm:
r = WIF l@PB 103PM 102Pc
0 1.83 0 0
61 1.60 1.36 0.87
99 1.49 1.87 1.30
131 1.42 2.20 1.58
173 1.34 2.71 1.82
199 1.32 2.86 1.93
230 1.30 3.10 1.97
313 1.23 3.48 2.24
102PH,0 0 0.57 0.84 1.01 1.18 1.25 1.30 1.47 In the following, state any assumptions made and comment on their validity.
(a) Since there are six species involved, determine, from a stoichiometric analysis, how many of the partial pressures (pi) are independent for given (T, P), that is, the smallest number from which all the others may be calculated. Confirm by:alculation for W/F = 313.
(b) For W/F = 313, calculate (i) fa; (ii) Ym and Ycm; (iii) Sm and Sc,n.
(c) From the data in the table, determine whether CdHz03(M) and CO2 are primary or sec- ondary products.
(d) From the data given and results above, construct a reaction network, together with corre- sponding rate laws, and determine values of the rate constants.
(e) The authors used a three-step reaction network to represent all their experimental data (only partial results are given above):
c&j(B) + 402 -+ QH20s(M) + 2Coz + 2H20; rl = klpB CJH203 + 302 + 4CO2 + H20; I.2 = k2p~
C.5H6 + go2 + 6CO2 + 3H@;rs = k3pB
Values of the rate constants at 350°C reported are: ki = 1.141 X 10m3; k2 = 2.468 X 10m3;
ks = 0.396 X 10m3 mol h-’ (g cat)-‘.
(i) Obtain expressions for pa and PM as functions of T.
(ii) Calculate the five quantities in (b) and compare the two sets of results.
(iii) Does this kinetics model predict a maximum in M? If so, calculate values of T,,,~~
and pM,max .
(iv) Are there features of this kinetics model that are not reflected in the (partial) data given in the table above? (Compare with results from (c) and (d).)