I.Ill AIIAI ■ ■ .1- . » MA 11 I PA I A I'll! IUI I M! S. R. Logan, I'undamentals ofChemical Kinetics, LongmM, ItlMX (1996). J. H. Espenson, Chemical Kinetics and Reaction Mechanisms, Mc(iraw-llill, New York, I'Ml'i A treatment of statistical methods and their pitfalls in kinetics is given in: A Cornish-Bowden, Analysis of Enzyme Kinetic Data, Oxford University Press, Oxford, I K I')') > R. de Levie, When, why and how to use weighted least-squares, J. Chem. Educ, 63 10 (l')K(i). (ini Rev. Analytic Chem., 30, 59. P. R. Bevington and D. K. Robinson, Data Reduction and Error Analysis for the Physical Sciences, McGraw-Hill, New York, 1992. 3.19 PROBLEMS 3.1 Define the following terms: (a) Conversion (b) Integral method (c) Differential method (d) Direct method (e) Indirect method (f) Powell's method (g) Essen's method (h) Van't Hoff's method (i) Half-life (j) Batch reactor (k) CSTR (I) Plug-flow reactor (m) Residence time (n) Batch method (o) Flow method (p) Stopped-flow method (q) Temperature-Jump method (r) Shock tube (s) Flash photolysis (t) Molecular beam 3.2 What did you learn in this chapter that was new? Had you heard of direct method! before? How about indirect methods? Were you aware of the inaccuracies in Essen's method? What else did you learn that was new? 3.3 Compare integral methods and differential methods for the analysis of rate dala What are the advantages and disadvantages of each method? 3.4 Compare the various experimental methods in Table 3.1. How does each method work? What determines how long it takes to initiate the reaction? 3.5 Find 10 examples of kinetic processes in your home, such as cooking different kinds of meals, washing clothes, you digesting different types of food, or pi.mi growing on your windowsill. (a) What experiments would you do to determine a rate equation for each ol them? What variables would you think were important? (b) Find an approximation to the rate equation for each of the reactions from yoin everyday observations. (c) Pick one of the examples and explain how you would go about determining i direct measurement of the rate equation. Be sure to say specifically whai vmi would do. (d) For the same example, explain how you would go about dctcrmiiiiii)' .m indirect measurement of the rate equation. Be sure to say specificall) WtMl you would do. I ft I In- I).ill 1111- ill li ilium i s I 1,0 yi'ill . In) (alciilalo a rale conslnnl loi I ho decomposition of tritium, Assume a lusl .ml. i reaction, iiii if.u long will ii take foi 99.9991 iii the tritium to disappear? \ nun' thai vmi arc working in the semiconductor industry, IBM imi unnouni i .1 thai the) have a now process to replace aluminum wiih copper in theii chips Voui buss tells you, "Wo need a copper process, too, Gel me one." You look in the literature, and find thai you can deposit copper via the chemical vapoi deposition (( Vl>) reaction: Cu(hl'ac), + H: Cu + III lilac) where hfuc is a hexalluoroacetylacetonate ligand. Your company already makes i \ I i reactors, so this seems like a gooil process for you In bring back I" )..... boss What would you do to measure the kinetics of the process to enable youi company to soil a copper deposition process, loo? Be sure to say wii.it you would do during the experiment, what you would measure, ami how you would analyze mmii data, I N Assume thai you are working in the pharmaceutical industry. Your company |iisl in ini soiling lnterluken-11 and noticed thai ii degrades when n sits in a bottle foi .J..ml I weeks. How would you measure the kinetics of the process' He sine lo i onsider what criteria you would use to decide whether to make direct oi ind..... measurements, qualitatively how you would make the measurements, and how you will analyze your data. i'» \ lusi order polymerization reaction is being run in a batch reactor. A ooiioonlialion ol 0 0(1 / mol/1 iter of monomer is loaded into the reactor, and then a calalysl is added in Initiate the reaction, Experiments show thai the reaction is 1091 complete In l<> minutes, la) ('alculaic the rate constant, ili) i calculate the hall life, (c) How long will n take ini ilio reaction lo bo 9091 complete? uii How uniiiti the lime in (c) change ii you increased the concentration In the rcacloi in 0.16 mol/litei? ii-i Repeal foi a second ordei reaction, t III N-ll, can be made via oxidation of ammonia over a platinum gauze You do an experiment and lind thai you gel 50% conversion of the ammonia with a 0.1 second n Idem e time (t) in the reactoi at kmmi k i .H Estimate the rate constant for the reaction assuming that the reaction Is llrsl ordei in die ammonia pressure and zero order in i ho oxygen pressure (hi Mow long ol a residence time will you need to gel lo 'WA conversion ill iooo kv (0) Now illume dial ihc rcuction is instead second ordei in the ummonll pNMUN idi I .inn,no iho i,iio constant fa the ruction assuming V)% conversion In <> l second Assume n stun liioinoliu teed ill I aim piossiuo 140 anai v; iir i < ii mak i >a i a l'M( illl I M' i.ilile l\l. II' AilihhcMi.il il.it.i lni I k.iiiii>l.- I i.' Time, minutes (concentration, mol/liter Time, minutes < Concentration, mol/liter i Ime, minutes Concentration, mol/litei 30 0.25 60 0.14 90 0.10 (e) What would your conversion be if you used the residence time you calculated in part (b)? (f) Calculate a rate constant that would give you 90% conversion lor part (e). (g) The results in (F) have a lot of industrial significance. People often design their reactors assuming that they have a first-order reaction, and then adjust the temperature of the reactor to get the conversion that they want. Explain how you could change the temperature to increase the rate constant for tin-reaction. (h) Assume that you used your results in (a) to design your reactor, but in fact the reaction is second-order, so the actual conversion is the value you calculate in problem (e). How much would you have to increase the temperature to gel 90% conversion? 3.11 In Example 3.A we fit some data for the growth of Paramecium. (a) Reproduce the results yourself. A suitable spreadsheet is available in the instructions materials. (b) Change the first point. Assume that the measured rate at a Paramecium concentration of 2 is 5.4, not 10.4. How will your results change? (c) Next, compare the fits obtained with the various methods. How do the r2 values compare? How do the variances compare? (d) What do your results in (c) tell you about the influence of errors in data on the various methods to analyze data? (e) Do an F test as in Example 3.B. Are the differences between the two models significant? (f) Try the model in Example 3.C. How well does it work? 3.12 In Example 3.D we used a number of methods to analyze the rate data in Table 3.5. (a) Reproduce the results yourself. A suitable spreadsheet is in the instructions materials. (b) Assume that we have three more points as given in Table P3.12. How will that change your results? (c) How does r2 change? (d) Now assume that you mixed up the point for time = 90 and recorded ,i concentration of 0.05 mol/liter. How will that change your results? (e) According to the Essen plot, which model has the lowest value of r with the one bad point? (f) What do you conclude aboul the utility "i i' u a u.is ol assessing the reliability of kinetic dala'.' |,|] In Example U\ we used Van l Unit's method to analyze llie dala in table < I I in) Set up your own spreadsheet to calculate the conversions from llie dala ibi Verify the numbers in fable I.F.2. (ť) Verily the numbers in Table 3.F.3. Id) Analyze the data using Essen's method. (e) Analyze the data using Powell's method. (I) How do your results differ? i l I In Example ■ HO I (inlil.i. i. where lilac is a hcxafluoroacetylacetonate ligand. The following dala were obtained III.i. II Pressure, lni I I itch Kale, uni/minute Hlacll Pressure, loir Etch Rale, urn/minute I Had I Pressure, loir Etch Rate, um/tninuti 0.25 0.30 0.031 0.055 0.35 0.40 0.081 0.099 0.45 0.50 0.113 o 126 in) lil these data to equation (2.12) to determine the order of the reaction, lb) Sieger and Masel also measured (he temperature dependence ol the i.ilc. and obtained the following data: Temperature, Etch rale. Temperature Etch rate. Temperature 11, h rat K urn/minute K mm/minute K urn/minute 548 0.101 573 0.132 598 I) IK') 563 0.123 583 0.162 613 0,211 Estimate the activation barrier for the reaction, (c) How well do these data lit Perrin's equation? which Mis better, Arrhenlui law oi renin's equation? Id) Does lite activation barrier agree with equation (2.31)? What is the signilu UM | Ol llus icsull? i || V.Mimc thai you have modeled a reaction. A I II > products, and find lhal il Inflows the rale equation with known values of k| and k You do mil know K, and k, so you decide In )•" Into the lub ami measure il Youi dala .n< uivon 111 'able P* Id 142 ANAl YM!. ( ll MAII IIAIA I'll! Mil I M* II i (a) Use linear regression lo esliniale a value nl K,. (///'/;/: Plot r„/|(k,K.,|A|/I I K2[A])] versus [B].) (b) How good is your regression coefficient? (c) Make a plot of the calculated rate versus the predicted rate. How well does the model actually fit the data? Now assume that the reaction follows the rate equation: -I'B = k,K:[A| 1 + K2[A] (k4 + K3[B]) 3.17 k]K2[Al 1 +K2|A| (d) Use linear regression to estimate a value of K3. Hint: Plot rb/ versus |B]. (e) How good is your regression coefficient? (f) Make a plot of the calculated rate versus the predicted rate. How well does the model actually fit the data? (g) Notice that the first model fits the data to two significant figures, even though the regression coefficient is 4 x 10"5. In contrast, the second model has a much hetter regression coefficient but does not fit the data at all. What does this result tell you about the utility of using regression coefficients to distinguish between kinetic models? (h) Use the variances to see which model works best. (i) Do an F test to see if the difference is statistically significant. Table P3.17 gives Schneider and Rabinovitz' data for the isomerization of CHtNC to CH3CN. (a) Try to fit the data with a simple first- or second-order rate law. How well does it work? (b) Try fitting the data to rate = k,[CH;,NC]2/(1 + K2[CH3NC]). How well does the equation fit? (Hint: You could plot [CH3NC]/rate vs. I/[CH1NC|. However, I find it more accurate to simply program the rate equation in a spreadsheet and use the solver function to find k, and K2 until the rate equation fits all the data.) (c) Are the differences statistically significant? Do an F test on the error in the natural logarithm of the rate. Table P3.16 Rate data for Example 3.16 [B|, k,K2|A|/l+K2|A], -rB [B], k, K2[A|/l + K2| A|, mol/liter mol/(literhour) moI/(literhour) mol/liter mol/(liter-hour) in IlKll/l lik'l 111 IUI I 0.25 1.5 2 2.3 1.001 2.001 3.000 4.001 1.0 2.0 3.0 I 0 2.X 3.5 I I, 5 Min' 1,0111 /(MM X OOX 5.0 i, (I 7.0 X 0 Table P3.17 The rat* of malhyl laocyanlda Isomerization Methylltoclnlde Methyliscocinide Pressure Rnli Pressure Ritt I lll,,l/llll'l I (llliil/lllei ) 1 lll.il/llUl 1 (mol/lltei i 10,520 9.8 18.1 0.0047 10.250 9.4 10.1 0.0019 9.XX0 9 1 X 0.0012 5.5X0 5.1 7.14 0.0010 1,020 3.5 5.1 0.00062 1,890 3.5 2.2 ( ) i ii ii i i i 1,610 3.3 1.39 ii in ii ii ii, (.5X0 3.2 1.05 II (HKMM'i 1,757 1.5 0.95 0.000036 1,349 1.2 0.59 0,000014 1,050 0.85 0.56 0.000012 ■1X6 0.39 0.41 0.0000073 109 0.23 0.2X6 0.0000036 ii i 0.15 0.272 O.IKKHKMS um 0.05 0.13 ().0000009.' 80.6 0.04 1) IUI 0.0000003 i vi I, 0.027 0.0876 ,:, in ii ii ii in in 40.8 0.015 0.0725 0.00000029 .'•IX 0.010 V.«<».•(•: Dula nl Schneider iind RahinoviCz (1462). i ill lii our undergraduate labs, we measure the rate of oxidation of Red Dye 1(1 with III.,nil. The main reaction is Red Dye + CIO CI" + Yellow Dye + H20 i Km ihc years, we have done many different ineasiircmcnls, and the dttl III liihle I'UK were obtained: I In- objective of llus problem is lo lil the data lo equation (2 1 I) and dele.......r ih, onlei nl I he reaction in bleach and dye. The easiest way lo solve llns problem Ii in use the regression capabilities of your spreadsheet. i..i.i.. IM HI Rate data for Example 3.18 11,, Hleai-li Dye Bleach 1 ihm rnti Hin hi. ('iinccnliatinn. Rale ('urnvntialion. < mi. inlialimi. Rat.'. ,ii.,l/lllri innl/liti'i iiiul/dik'i ininiitel nml/lili'i inol/dilii i.....mil .....l/lllrl 0,011 mm (MUX 0.033 0.010 0.05 1 0,019 0.0313 0.023 0.034 0.039 0.073 mux OO.'/O 0,024 0.039 mill 0,093 nil.'.' 0.039 0.041 0.041 0.051 0 115 hum 0.036 0.03S 0.043 0,024 0,053 no'-, IMKr=> 0,009 OIMI mini IIO.'H no 'S 0 t > 1 K«> 0.02 I (Mm 0 05.' 0 145 144 ANAI r.r.....IAII HAIA I'll! IMI I M'. I4B (a) Convert equation (.' I t) so lli.il you can use liucai regression. (b) Scl up your spreadsheet lo do the regression using ihc l).ii.i Analysis/Regression tool in Microsofl Excel. (c) Try nonlinear regression as in Table 3.A.4 lo see bow thai changes youi answers. 3.19 Commercial sterilizers work by heating bacteria to high temperatures where (lie bacteria die. The FDA (U.S. Food and Drug Administration) requires all sterilizer! to meet a standard of an overkill of 1012; specifically, that each bacterial or bacteria spore has one chance in 1012 of surviving. Generally people test sterilizers with a thermobacteria spore that is particularly able to survive high temperatures. Ii is hard to detect a 1012 overkill, so people measure the time to a 10'' overkill and assume that if they double the sterilization time, a I012 overkill will he achieved. (a) Show that if the death of bacteria follow a first-order rate law, the time In achieve a 1012 overkill is twice the time to achieve a 106 overkill. (b) What will the overkill be if the reaction is instead second-order? (Him: Assume an initial concentration of 108/cm3. At a 106 overkill, you need lo get to a final concentration of 102/cm3. At a 1012 overkill, you need to get lo a final concentration of 10~4/cm3. Calculate the time in each case.) (c) You can increase the overkill by increasing the temperature. How much would you have to increase the temperature to get the overkill up to 1012 in the case in (b)? (d) Assume that you are a canned milk manufacturer who uses a sterilizer to kill the bacteria in the cans before the cans leave your plant. The cans start OUl with 10,000 thermobacteria each. If the reaction is first-order, what fraction of the cans will have at least one bacterium left after sterilization? (e) If you produce 50,000,000 cans/per year, how many will go bad? (f) How would your results in (e) change if the reaction were second-order? 3.20 Ammonium dinitramide (ADN), NH4N(N02)2, is an oxidant used in solid fuel rockets and plastic explosives. The ADN is difficult to process because it can blow up. Oxley et al. J. Phys Chem A, 101 (1997) 5646, examined the decomposition of ADN to try to understand the kinetics of the explosion process. At 160 ( ihc\ obtained the data in Table P3.20. (a) Is this a direct or indirect measurement of the rate? (b) Use Essen's method to fit these data to a rate equation. Assume an initial concentration of 10-3 molar. Table P3.20 Oxley's measurements of the decomposition of dinitramide at 160°C Fraction Fraction Fraction ol thi Time, of the ADN Time, of the ADN Time, of the ADN seconds Remaining seconds Remaining seconds Remaining 0 1.0 ')()() 0.58 2400 0.24 300 0.84 1200 0.49 — — 600 0.70 1500 0.41 — — 11 l Use Vnn' I I lull's 11 it-11 it i* I ii< Iii ilu .<- data lo a rule equation. lil) Um Powell'I method lo III these dnln lo a rale equation. (rl II vou had lo process ADN ill |6()'C, how long could you run Ihc piocess without blowing anything up? Assume that I here is an explosion hti/.urd once >'. ol the ADN has reacted to form unstable intermediates. (0 II you wauled to process for 5 minutes, what temperature would you choose'' Assume that the reaction follows Arrhenius' law with a preexponenlial ol I01'/second. (Hint: First, estimate the activation energy from your value ol the rate constant and the known preexponential.) lil i hlchicki. el al. //;/./. Chem. Kinetics, 29 (1997) 73, examined the sodium crcsolulc (S) catalyzed decomposition of epiehlorohydrin (li). Al 71 (' Ihey oblaincd I lit-ft nils in Table P3.21. In) Is ilns a direct or indirect mcasurcmcnl of the rale? (h( hit these data to a rale equation. (Hint: Assume that Cs is constant during em Ii inn first, lit the rate data at each Cs to a rate equation, and then de termini how the rale constant varies with Cs. Assume an initial concentration ol 0.1 inol/hlcr.) ' ' ' In Problem 3.21 we noted that Chlebicki, el al. hit J. (.'Item. Kinetics, examined ilu- • ••Ii..... desolate (S)-catalyzcd decomposition of epiehlorohydrin (F) in a batch 11 m lot However, they could have instead run the reaction in a ('STR mi Explain what they would have needed to do lo measure the rale in a (NIK V loading equal amounts of bromine an hydrogen into a reactor and ineasi.....i- II it- concentration as a function ol time, fable P3.23 shows sonic ol then dala i a.i, imím The decomposition of epichlorhydrin in the presence of sodium cronolnln • i 1.2 iiiiilAIni' Cs = 0.88 mol/dm Cs = 0.76 mol/dm3 Cs - 0.65 mol/dm1 Fraction Fraction Fraction i i.i. i..... linii'. ol the I Time, ni the I Time of the E rime. Ill Ilu- 1 HlllMlll-N Remaining minutes Remaining minutes Rema.....is minutes Remaining II 1.0 0 1 0 1 0 o i o 5 ().«)() J 0.93 5 (I'M 5 II 'M 19 0.74 15 0.80 Is 0.82 15 0 81 19 0.61 25 0.69 25 0.72 25 0.75 19 0.50 35 0.59 .35 ik,I 35 n || 41 i) II 45 0.51 45 0.55 49 0.59 99 0 M 55 0.44 55 048 55 0.51 14(1 ANAI Y'.ľ.l II MAM HAIA I'll, MU I M' 11/ (ii) is iins .1 direct oi Indirect measurement of the rate? (b) Use Essen's method to lit these data to ;i simple rate equation. (c) Use Van't Hoffs method to tit these data to a simple rate equation. (d) Use Powell's method to fit these data to a simple rate equation. (e) What do you conclude from the nonlinearity of your plots'.' 3.24 In Problem 3.23 we noted that Bodenstein and Lund Z. Physik Chem, 57, (1407) 168, examined the kinetics of the reaction H2 + Br2 2HBr (P3.24.I) by loading equal amounts of bromine an hydrogen into a reactor and measuring the concentration as a function of time. Table P3.23 shows some of their data. Bodenstein and Lund fit their data to the expression rHBr k,[H2]LBr2] i n 1 +K [HBr] [Br2l (P3.24.2) (a) Use the stoichiometric table to derive an expression for [H2] and |HBr| as function of the Br2 conversion. (b) Plug into equation (P3.24.2) to prove dXBr2 = Ki(l-XBr2)|/2(C°H2-XBrC0Br2) XBr, dt (P3.24.0 1 +2K2 (1-X„r2) where XBr, is the conversion of Br2 and C^2 and CBr2 are the initial H: and Br2 concentrations, (c) Show that the solution of equation (P3.24.3) is C° k, 4K2 -2K, 2K2/T : + 3(1-XBr,)3/2 2K2+3 when C° = C°H H2 4K, 2K. Brj 2K, r0 ,-.(> *-H2 ^Br2 \/CH2 - CBr Table P3.23 Bodenstein and Lund's data for the reaction H2 + Br2 2HBr Time, [H2|=|Br2J, Time, [H2]=[Br2|, Time, minutes mol/liter minutes mol/liter Mlillllll-s 0 0.2250 90 0.1158 11 HI 20 0.1898 128 0.0967 i to 60 0.1323 180 0.07V IH.'I lllr.l, mol/llta 0.0471 0.0303 - .m i.m C" 1 u. H2 ('" V (CÍ, C • (h..V> 1 X'"-'> whenC1/,. - c;,,, I - 2K2 ,'K. K i *~Br2 Mt2 n ■ in ,— /ca. tí I C" 11 2C°Br, c°Br2-cnHr2 Vv/nôč til) Use your results in (c) to devise new Van't Holt and lissen plots loi the reaction. (c) Construct the Van't Holt and lissen plots and see if they work. « • I r. 11111 ■ \. Uusi and Vaughn. ./ACS' 70 (1948) 88 examined the decomposition ol ili tertiary butyl peroxide. The main reaction is (CM,),('()()C(CI1,), 2CII,('( )C (P3 13 11 l'.inlľV el al. loaded (he ditertiarybulyl peroxide inlo u batch reitcloi .n ľ> I <> C ,iii,l measured tlie pressure as a ľunction ol lime. ľhey obtained Ihe dala lisleil in i ,1.1, im 25 in) K iins b direcl or indirect measuremenl of the rate ' (tu Develop a itoichiometric table for the reaction, (»•) Ciilculate Ihe conversion as a funclion ol lime trom the dala in Table (ľ* ".i (d) lise lissen's mclhod (o til (hese dala to a simple rate cquatioti (t) Um Vani llolľs mclhod lo lil (hese dala to a simple rate equalion |ľ) tise ľowelľs nielhod lo til lliese tlala lo a simple rate equalion l|{) llow long of a residence lime would you need lo deeompose 99.9H <'l thl ilileiliaivbiilyl pcioxide in a ČSTK'.' Silicon dioxide (SiO.) lilms aie used as diclcclrics m cleetronk dcvlotl SIO] litins nív m.i,lc bs ileeomposmg IT.OS |ietriielhylorlhosiliciitc, (SkOCII i,i| M a silnou walei Kim and Cill / Il<< tfOi Ikiiii, ,il Smith 142 i | <><»■, > <,/(, exiiuiiiud Ihe lliľiinal deeomposilion ol TIÍOS .........iiobnliuuľ Tlie dulu '.tmu n in ľahli- ľ * .' <> vm-ii- ol)lnuiľil 1411 ANAIYSISOI KAU DA IA I IM Hli I M' I '111 Table P3.25 Raney, et al.'s data for reaction (P3.25) Time, minute* Pressure, atm Time, minutes Pressure, atm Time, minutes Pressure, aim 0 3 6 0.223 0.249 0.273 9 12 15 0.295 0.316 0.336 I8 21 0.355 0.372 Table P3.26 The rate of Si02 deposition from TEOS at 1070 K TEOS Pressure, torr Deposition Rate, Hg/hour TEOS Pressure, torr Deposition Rate, ug/hour TEOS Pressure, torr Deposition Rate, ug/hour 0.15 0.55 148 200 0.29 0.68 175 209 0.42 0.81 190 215 (a) Is this a direct or indirect measurement of the rate? (b) What is the order of the reaction? (c) Kim and Gill fit the data to rsiOi „1/2 TEOS 1 + k2PTEo: (P3.26.I) How well does equation (P3.26) fit the data? (d) Assume that the reaction follows equation (P3.26.1). Derive an equation foi the TEOS pressure as a function of time when TEOS is loaded in a batch reactor and the reactor is heated to 1070°C. Assume the following overall reaction: Si(OC2H5)4 Si02 + 2(C2H5)20 where Si(OC2H5) is TEOS. Calculate the TEOS pressure as a function ol time, starting with an initial TEOS pressure of 1 torr. Calculate for a long enough period that 60% of the TEOS is used up. (e) Use Essen's method to fit your results in (d) to a zero-order, half-order, lirsl-ordcr, or second-order rale equation. How well do your calculated rcsulis In zero-order, half-order, first-order or second-order rate expressions'1 (f) Do an F test to see which model fits best. 3.27 Chung and Lu, J. Polymer Sci A, 36 (1998) 1017, studied the production ol I polyethylcne-styrene copolymer. Chung and Lu loaded ethylene into a rcactoi added a small amount of styrcne, and then initiated the reaction, (hung and In then measured the conversion of styrene as a function ol lime, ľhey repeated the same experiments substituting methylstyrene for styrene. (The styrene und methylstyrene runs were done separately.) Some ol ('hung and l.u's results lire given in Table P3.27. (a) Is this a dun I m induct I inrasiiiemciil o| itV mil ' (I)) Use Essen's melhod In lu these dnln lo n inlľ ct|uulinii Tabl« P3.27 Th« oonver «Ion of •tyrsn* .i linu hon "I I"'"' ......ivcimom ol 1111 ■ 111 v i' -1 v' i*'ii' •' I'"" I'"" 'u'"' .m>.I n-poi It'll l>y CIhiiki .in«! I n Time, si\ rene Methylstyrene m.....tea Conversion Conversion s 13 i S 19 '/ in tx 53 IS 52 70 60 60 85 1.1 Um Van'l Hoffs method to in these data u> a rate equation. Kl) I Ise Powells method lo lil these dala lo a rale equation. iri llow long WOUld you have to run lo gel 90'/«. conversion ol styrene? - | 11„ irowth ol bacteria is often thought to follow Monod kinelics, where the growlli MI "I bacteria, .„, in bacteria/dilerhour) is related lo Ihe bacteria eoncenlrnlion by 'li k„|H| ^"rl- (|M 21 I 1 II K, (!■ | uinie 11i| is the bacteria concentration in bacteria/liter and M li the Food i inu eiilralioii in mol/liler lul Whal are the unils ol ktl and K| ? (lil Assuine lhal the bacteria are growing under condilions where linie is a l.uef iM css ol lood (K| |l| •• I ). I )evclop au equaliou expressing how t|iut kly llie |ii>|iiil.iliini ni bacteria doubles. (C) In lbe literatuře, il in common to report values al a consiaul k,.. wherc k,, Is giveu by B 1 li.ui)' and llong. ./ Hinlii IihiiIdí;v, 42 (1995) |K'>. examiued Ihe giowlh ni a potenlially loxic bacteria, 1'seuihmumus twrufiinosa, PU2I in u ithicosc ■olution, and iiiii.niirii Miř duia m Table pcx iiow well do these data In Minuul kinelics',' I "» Mu iidsoiplion and deslruclion ni alcohol in a luiuian body ciin be modclctl || ivmi In.l Ofdei reactioni in senes When you ■lnul an alcoholu beveiagi-. lbe . ■ I < nimi ni Ihe brveiage reacls wilh lbe blood in your sloni.ub walls lo yield au aKobul/bloml loniplex lbe iilcohol/hlnod cmuplex is ihen quickly transporleil Ihroughoul mhu . niiiť l«Mly, nu hiding your liver In a second process, lbe en/ymes in yiiui livei lni ,ik diiwn Ihe akohol uilu ullui piniím Is (II) Assiniir lhal lile lldsorplioil .nul ili".lnu lion ol II11 nimi nie lllsl inilei pnu ■ I Ke lbe ri|iiiiluuis in ibis i Implei lo oblinu nu rnptcssinn lni yitm IiIimkI .ili nimi level ns a linu linu ol Ume ISO ANAI VMM i| IIAII I )A IA I'lKIIIMM'. 181 Table P3.28 kg for the growth of Pseudomonaa aeruginosa PU21 In glucose solution Glucose Concentration grams/ml kG. hour"1 Glucose Concentration grams/ml ko, hour 0.0 0.0 0.7 0.80 0.01 0.4 1.0 0.82 0.05 0.65 1.25 0.85 0.3 0.74 2 0.91 Glucose < loncentration granu/ml 2.25 4 8 kei ivc an expression lor Ihe average rale of a lirst order reaction and a set ond milci reaction as a function of the conversion in a batch reactoi l,il.ln I'.I 30.1 The CH30 conversion versus time reported by Aranda et al I n>>. ins II 11 1 I I ) ' 1,5 I ( 111<) (lonvei sion [Br] = 2.22 < 10" molecules/cm1 I) 0.08 0.15 o 21 0.27 0.33 0.38 0.55 CH3O < tonversion |Br| = 4.48 k|0" molecules/cm1 0 0.15 0.28 (I |i) 0.48 0.56 0.63 0.81 1 11 111 lonvei ilon [Br] 6.S2 xlO" inoleciilcsA 111' 0 0.21 0.31 0.51 0.61 0.7 0.76 0.91 1 ......v 1 :i() V V..UM-S ol |ln([CH:,0]o/[CH;101)|/t reported by A..11..I., ,1 ..I 1111 'In llles/i iii I 11' 2.94 I 18 I IH .1.07 (, M lnl|('ll,<>l,,/|Clli('|l|/l [Br] inn molecules/em' I II. 210 250 334 427 505 <>.<><> 7.26 871 10.8 I I 81 I ' It. [ln([CHjO]o/[CHj mm 506 578 755 'lit KM 152 ANAI YMM II HAM IIAIA I'lli till I M' (b) Derive an expression foi the rate al the average concentration, (c) How do the two compare? (d) Find a concentration where the average rate equals that rate al dial concentll tion. 3.32 In Section 3.13 we derived a number of equations for the behavior of a reaction A + B C + D (P3.32.1) (a) Show that equation (3.60) goes to equation (3.61) in the limit that [B] » |A|. (b) Show that equation (3.60) goes to equation (3.64) in the limit that [AJ = [B] (c) How can you use the results in (a) and (b) to determine the kinetics ol a reaction? (d) Assume that you try to run reaction (P3.32.1) with [A] = [B], but make a mistake so [A] = 0.30 mol/liter, and [B] = 0.32 mol/Iitcr. Calculate iln concentration as a function of time with k2 = 0.45 liter/(molhour). Assume that your final A concentration is 0.01 mol/liter. (e) Make an Essen plot of your results in (d) assuming that the reaction follow! equation (3.64). (f) Make a Van't Hoff plot of your results. (g) Repeat for [A] = 0.30 [B] = 0.62. (h) What do the results in (e)-(g) tell you about the utility of running the reaction with [A] = [BJ? 3.33 Estenfelder, Lintz, Stein Gaube, Chemical Engineering & Processing, 37, (1998) 109, compared the use of an integral and differential reactor to measure the partial oxidation of an unsaturated aldehyde. (a) Describe the integral reactor use in these studies. (b) Describe the differential reactor used in these studies. (c) How do the data obtained by the two methods compare? (d) Are there any unexpected findings in the paper? (e) When do the authors say that each method should be used? (f) How do the findings compare to your expectations from this chapter? 3.34 The hydrolysis of ethylacetate is a reversible reaction, which is catalyzed by a< idl The main reaction is CH3COOCH2CH3 + H2Q ^ CH,COOH + HOCH,CH( (P3.34.il The reaction obeys ran = -ki i( i x ten.ci i, i i i,, i .......H][HOCHjCHj] (IM l| ,'| (n) Develop a stoichiometric tuhle loi the reaction. tin Rearrange equation (P3 10.2) to prove thai if there is no ethanol or acetii acid in the reactor al the beginning <>i the reaction, then di -k,[H+](l Xea) I k.c;.'A|ir |(X,,Ar (P3.34 I) where Xea is ihe conversion of ethylacetate and ('j'A is the initial ethylacetate concentration, (c) Show thai the solution of equation (P3.34.3) is / i \, ((x?A-xbaHi -t v,\i k||m ]x-{tTWJ \(^)(^ + \+^) (P3 U h with (d) Make a plot of the rale with various values of the parameters. How does th( rate of reaction vary as you vary k, and Xj'V- Mnio Advanced Problems i IS People often use bacteria to digest hazardous materials in wastestreams. The rate usually follows Monod kinetics: d|B| K,.|W| rB = _ = kB[B]H K,|W| d|W| K,|W| ^- — .-kwlBI, ( K||W| (P3.33.1) (P3.3.V2) where |U| is the bacteria concentration in bacteria/liter and IW| is the wastt concentration in mol/liter. Assume Kp = 220 liters/mol, kM 0, 15/hour, and kw 2.5 x 10 " (molhourVbacteria. . d|B] la) l)en\e .in expression lor -—-. d| W| (b) Integrate your expression in (a) to derive an expression for 11* I as a i um. tion of IWI. the wasle concentration al any time, I, and |W|„ mid |H|n. the nuii.il bacteria and waste concentrations. (c) Rearrange your expression in (b) to derive an expression for |H| as a luneiioii ol the \\v. the fractional conversion of the waste. Hit Compare youi results io those in ihe sioiehiometric table <'.in you see thai you are t onverting waste into bacteria1 (t) Siilislilule voiii expiession into e(|iialion (P3. 15.2) to calculate Ihe tale ol wasle reduction as a function of Xw. (f) Inleei.He yimu expiession lo nlil.uu .in expiession I'm Ihe Mine lo |'el ,i idiiveisioii Xyv, ňu llll I M'. ľ.I ■ IM H HA II IIAI A (g) Assume Ihal you slait with II)1' bacteria/liter and I mol/liler of wasle. You | have a choice of iwo bacteria: one with a K|. = 2.2 x l(r liters/mol, kh 0.35/hour, kw = 2.5 x 10 6 (molhour)/bacteria a second with a K| = 2 ' 105 liters/mol, kB = 0.35/hour, kw = 2.5 x 10 7 (mol-hour)/bacleria. Which | bacteria will get to 99% conversion first? (h) Repeat (f) for 99.999% conversion. (i) How would your results change with a CSTR? (j) On the basis of your results in (f) and (g), could you design a system ili.il starts with one bacteria, then adds a second bacteria to finish the job? 3.36 Read the following papers and write a one-page report on the kinetics described in each paper. Why were kinetics measured? What techniques were used to do I lie kinetic measurements? How were the kinetic data analyzed? What were the key results? (a) Koch, R., Palm, Wu., and Setzsch, C. The first rate constants for the reaclanls of OH radicals with amides. Int. J. Chem. Kinet., 29, 81 (1997). (b) Crivello, J. V., and Liu, S. S. Synthesis and cationic polymerization ol glycidyl ether. Poly. Sci. A, 36, 1017 (1998). (e) Simakov, P. A.. Martinez, F. N., Horner, J. H, and Newcomb, M. Absolute rale constants for alkoxycarbonyl radical reactions. 7. Org. Chem., 63. 12 !6 11998), Hi) Miis.i, (). M., Choi, S. Y., Horner, J. H., and Newcomb, M. Absolute rate. Constants fol alpha amide radical reactions. ./. Org. Chem., 63, 786 (1998). (<•) Kettling, I1 . Kolteiin.inn. A., Schwille, P., and Eigen, M. Real-time enzymi kinetics monitored by dual color fluorescence cross-correlation spectroscopy. Pmt Nat \cad. Sci. U.S., 95, 1416 (1998). (f) Wellington, T. J., Guschin, A., Steinn, T. N. N., Platz, J., Sehcsted. I . Chrislensen, L. K„ and Nielsen, O. J. Atmospheric chemistry ol CF3CH2OCH2CF3-UV spectra and kinetic data for CFsCH.ICHjCF, and CF3CH.OCH2CF3 radicals and atmospheric fate of CF3CH.OCH2CF, radl cals. J. Phy. Chem., 102, 1152 (1998). (g) Tolti, N. P., and Leigh, W. J. Direct detection of 1,1-diphenylgermenc in solution and absolute rate constants for germene trapping reactions. 7. Ann 1 Chem. Soc., 120, 1172 (1998). (h) Lepicard, S. D., and Canosa, A. Measurement of the rate constant for tlie association reaction CH+N_2 at 53 K and its relevance to tritons atmosphoN Geophys. Res. Let., 25, 485 (1998). (i) Johnson, K. A. Advances in transient-state kinetics (review). Citrr. ()pU Biotechnol, 9, 87 (1998). (j) Campbell, M. L. Gas-phase kinetics of ground-state platinum with O ..No NzO and CH4. J. Chem. Soc. Faraday Trans., 94, 353 (1998). (k) Decker, C. The use of UV irradiation in polymerization (review). Polvm Inl 45, 133 (1998). (1) Wolter, S. D„ Mohney, S. E., Vcnugopalan.il.. Wickenden, A I . and Koleske, D. D. Kinetic study of flic oxidation "I gallium nitride In 'li y ail ' Electrochem. Soc, 145, 62«) (1998) Hill llcd|aiiiaii. Y , I.averdcl, (1 . and U-bias, (i Low picssuie study ol the rem lion ol CI. atoms with Isoprcnc 7 Phys. Chem., 102,933(1998) in) III.isci. lid. Jalell. II P. Garland. M . Sludcr. M . lines. II . and Wiiilm l.iiii. A Kinelic studies of the enanlioseleclive hydiogcnaiion ol elliyl pyruvate catalysed by a cinchona modified IM/AI203 catalyst. 7. (ami.. 173. 282 (1998) to) lliadloid. M.C.J. CO; reforming ol < 'I I., over supporled PT catalysis ./. ( ,u,il. 173. 157 i l')98). <|il Madias. 0., Smith, .1. M., and McCoy. I). J. Thermal degradation kinetic! Oi polystyréne in solution. Polym, Degradation Stab., 58, Mil I1)')/) li|) Deleis. K , Oiling. M.. Wagnci. II (!.. Temps, ľ., I.as/lo, H , Dobe, S., and lleices. ľ. A ilirecl investigation ol the reaction CILOII Oveiall talc eonslanl and CIL formation al ľ 2l>8 K. Her. Hnnsenges. Phys. (hem . 102. 58 (1998). hi Kunz, A., and Roth, P. A high temperature study of the reaction SIH4 1 n ll [, Ber. Bunsenges. Phys. (linn.. 102, 73 (1998). Is) Sehcsted, I . Chrislensen, L. K., Mogelberg, I'., Nielsen, O. I , Walluiglon. ľ I . (luschin. A., Orlando, .1. J., and Tyndall. G S. Absolute and relative rati constants lor the reaction (II,('(())) . + NO and CH,C(0)() .. i NO. and thermal stability of Oil ,C(())(),NO... 7. Phys. Chem.. 102. 1779 (1998) II) llaiwood. M. II., Rowley, I). M., Cox. R. A., and Jones. R. L. Kinelics and mechanism ol the bro sell reaction temperature and pressure dependent .indies. ./. Phys. (Inn,.. 102. 1790(1998). Hi) Percira, R. D., Danielí. D. I... Pilling, M. .1., Robertson, S. II., and Zcng, 1. Temperataure and pressure dependence ol die multichannel rate coefficients 1..1 iiu-ciL 1 oil sysu-m .1 Phys. Chem., 101,9681 (1997) (v) Slut/. J., E/cll, M. J.. and linlaysonpilts, IJ. J. Inverse kinetic isotope elicit in the reaction of atomic chlorine with C2H4 and C2D4. / Phys. Chem . MM ')|87 (1997). (w) liokenkamp, I)., Desai, A., Yang, X.. Tai, Y. ('.. Mar/luff, E M . and Mayo, S. L. Microľabricaled silicon mixers for submillisecond quench flow analysis Anal. (item.. 70. 232 l il»(>8). I\) Rotaru, P., Hlejoiu, S. 1.., Conslanlinescu, R.. Poinelescu, N., llliu, I., and llunescu. O. Perfectly slirreil catalytic reactor. A/i/il. ('ami. A. 166. Id I (I99H) ly) Manke. (!. C, and Sclsei. D. W. Measuring gas phase chlorine atom 101..... trillions Rale constants for CI. i HNi. CIM. and (I'm 7 /Viva Chem . 102. I5( 11998). ' O On lo the (11) International Journal of Chemical Kinetics, or il llus journal is not available m yOUl library, try (b) the kinelics section of Physical ('hemistry A. (e) 7 Physical Organic Chemistry, (d) Biotechnology ami liioengineering. (ť) Reaction kinetics ami Catalysis letters, (f) J. Polymer Science A Find an article when-someone measures the kinelics ol a reaction. Write a one page report on the findings 111 the .iilu Ic in describe: (ill Why the sludy was undertaken lb) What tii liniqiiis were used Ic) How die data were iiiiuly/ed III) Wllill llll ki \ ICMllf. «111