Kilt AIIAI ,'.!'.( il HA 11 llAIA I'll! Mil I M! 139 S. R. Logan, Eundamentals oj Chemical Kinetics, Longman, Lsse* ( l'W(i| J. H. Kspenson, ťhcmunl Kinetics ami Reaction Mechanisms, Mctil.tw Hill. New Yoik. 1995. A treatment of statistical methods and their pilfalls in kinetics is given 111: A Cornish-Bowden, Analysis of Enzyme Kinetic Data, Oxford University Press, Oxford, UK, 1995. R. de Levie, When, why and how to use weighted least-squares, J. Chem. Educ, 63 10 (19X6). Grit. 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 (1) 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 methods 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 data. What are the advantages and disadvantages of each method? 3.4 Compare the various experimental methods in Table 3.1. How docs 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 plant! 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 youi everyday observations. (c) Pick one of the examples and explain how you would go aboul determining I direct measurement of the rate equation, He sun to .pii dually whai von would do. (d) For the same example, explain how you would |o il.......leti.....nlng ifl ituliici 1 BMUUremenl ol die rule equal..... H> .1...... ,i\ spci ilniilly whnl you WOtlld do 3.6 Ihe hall hie ol Milium is I l.d ve.us (11) (lalculate a rate constant for the decomposition of tritium. Assume a lirst-order reaction, (III How long will il lake lot 99.99'/» ol the tritium to disappear? 3.7 Assume thai you are working in the semiconductor industry. IBM just announced thai the) have a new process to replace aluminum with copper in their chips. Your tells you, "We need a copper process, too. Get me one." You look in the literature, and find that you can deposit copper via the chemical vapor deposition (CVD) reaction: Cu(hfac)2 + H2 Cu + H(hfac) where hfac is a hexalluoroacetylacetonate ligand. Your company already makes 1 VD reactors, so this seems like a good process for you to bring back to your lioss What would you do to measure the kinetics of the process to enable your . ompany 10 sell a copper deposition process, too? Be sure to say what you would do during the experiment, what you would measure, and how you would analyze your dala. * H A.Mime dial you are working in the pharmaceutical industry. Your company just sinned selling Interluken-ll and noticed that it degrades when it sits in a bottle for uIhiiii I weeks. How would you measure the kinetics of the process? Be sure to 1 onsider what criteria you would use to decide whether to make direct or indirect iiii'.isuieuieiiis, qualitatively how you would make the measurements, and how you will analyze your data. ' '> \ in si order polymerization reaction is being run in a batch reactor. A concentration ol (Mil)/ mol/liter of monomer is loaded into the reactor, and then a catalyst is added 10 iiuiiale Ihe reaction. Experiments show that the reaction is 30% complete in 10 minutes. In) Calculate Ihe rale constant, (in (lalculate the half-life. u 1 How long will il lake for the reaction to be 90% complete? nil llow would the time in (c) change if you increased the concentration in the reactot to 0,16 mol/liter? («•> Repeal for a second-order reaction. ' in 111 1 .in In- made via oxidation of ammonia over a platinum gauze. You do an ' iperimenl anil find that you gel 5096 conversion of the ammonia with a 0.1-second n lldence time HI in the reactor at 1000 K. tut Estimutc Ihe rate constant lor die reaction assuming that the reaction is first-onlei in ihe ammonia pressure and zero-order in the oxygen pressure. ilo I low Ion;1 ol ,i residence lime will you need lo gel lo 90% conversion at 1000 K? dl Now assume thai ihe reaction is instead second-order in ihe ammonia pressure, idl I Atimule ihe i.He constant lot ihe reaction assuming 50% conversion in 0.1 • . oml Assume a slouliioiiieliu leed ul I iilm pressure I iii ANAI YIIIMII HAII IIAIA I'll! Illl I Ml 139 S. R. Logan, Fundamentals i>l Chemical Kinetics, I .ongmun, lisitex ( 1996) J. H. Espenson, Chemical Kinetics ami Reaction Mechanisms. Midi.iw Hill. New Ymk. I'W.S. 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, UK. 1995, R. de Levie, When, why and how to use weighted least-squares, /. Chem. Educ, 63 10 (1986). Grit. 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 (k) CSTR (1) 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 (j) Batch reactor 3.2 What did you learn in this chapter that was new? Had you heard of direct methods 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 data. 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 plants 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 youi everyday observations. (c) Pick one of the examples and explain how you would go about determining I direct measurement of the rale equation. He sun- in \.i\ \|>< i ilu ,ill\ \\ I>.■ i \ hi would do, (d) For the same example, explain how you would go ihoul determining U indirect meiisureinenl ol I In- nilr cquiiliiin Hi si...... n\ specdu ally what (VOilld do 1 Ihc hall hie ol liihiiiu is I l.o years In) (lalculate a rale constant foi the decomposition of tritium. Assume a first-order reaction d>i How long will it lake lor 99.99% ol the tritium to disappear? 3.7 Assume thai you are working in the semiconductor industry. IBM just announced thai the) have a new process to replace aluminum with copper in their chips. Your buss tells you, "We need a copper process, too. Get me one." You look in the literature, and find that you can deposit copper via the chemical vapor deposition (CVD) reaction: Cu(hfac)2 + H2 Cu + H(hfac) where hfac is a hexalluoroacetylacctonate ligand. Your company already makes (VI) reactors, so this seems like a good process for you to bring back to your What would you do to measure the kinetics of the process to enable your . ompany to sell a copper deposition process, too? Be sure to say what you would .In during the experiment, what you would measure, and how you would analyze your data. < 'I assume thai you are working in the pharmaceutical industry. Your company just i.uled selling Interluken-II and noticed that it degrades when it sits in a bottle for uhoul I weeks. Mow would you measure the kinetics of the process? Be sure to 11insider what criteria you would use to decide whether to make direct or indirect measurements, qualitatively how you would make the measurements, and how you Will analyze your data. I v in i ordei polymerization reaction is being run in a batch reactor. A concentration itl (I (10/ mol/liler of monomer is loaded into the reactor, and then a catalyst is added in inni.ile the reaction. Experiments show that the reaction is 30% complete in 10 nnniiles In) (lalculate ihe rate constant, ilu (lalculate the half-life. () i How long will ii lake for the reaction to be 90% complete? nil How would the time in (c) change if you increased the concentration in the reat toi to 0.16 mol/liter? <«•> Repeal lor a second-order reaction. 1 in mi, .in In- made via oxidation of ammonia over a platinum gauze. You do an i iiniiii and find thai you get 50% conversion of the ammonia with a 0.1-second •1 idence lime (r) in the reactor at I(XX) K. (a) Estimate Ihe rate constant for the reaction assuming that the reaction is first-ordei in the ammonia pressure and zero-order in the oxygen pressure. lb) How long of a residence time will you need to get to 90% conversion at l(XX) K7 H I Now .issiiiih- I hill ihc read ion is instead second-order in Ihe ammonia pressure, nil Islnniile the lale constant loi die leaiiion assuming so1, conversion in 0.1 ii olid Assume u slim liiiiinili u leed ill I aim pressure I'll! iui I ms 141 I ..U. IM I.' Add.....mil d.il.i I..i I xmnpln i I Time, minutes ( '. .11. ruh .Ii 1. .11 Mini/liter Inn.' minutes ( ..II. rllll.llli.il, mol/litei 1..... Ill.....Ir . I .m. i nn.ilinn. mol/litei 30 0.25 no 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 for part (c). (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 the 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 get 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 a 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 r2 with the one bad point? (f) What do you conclude about the utility of r2 as a way of assessing the reliability of kinetic data? 1.13 in Example 1 F, we used Vhn I Hofl method to analyze the data m fable 1 P i (n) Sel up your own spreadshecl in calculate the conversions from the dala d>) Verify the numbers in Table ! F 2 (c) Verily the numbers in Table U'.3 (d) Analyze ihe dala using Essen's method. (e) Analyze the data using Powell's method, (ľ) How do your results differ? 1.14 In Example 3.K, we used Van't Hoff s method to analyze the dala in Table t K I (a) Set up your own spreadsheets and verify the results. (b) Analyze the data using Essen's method. (c) How do your results in (b) differ from those in Example 3.K? .».15 Steger and Masel examined the etching of copper in a reactor used to produce elec Ironic materials. The main reaction is Cu + 2hfacH + 0.5O2 —> H20 + Cu(hlac), where hfac is a hexafluoroacetylacetonate ligand. The following data were obtained: 3.16 HfacH HfacH HfacH Pressure, Etch Rate, Pressure, Etch Rate, Pressure, Etch Kale. torr u.m/minute torr |im/minute torr Urn/minute 0.25 0.031 0.35 0.081 0.45 0.113 0.30 0.055 0.40 0.099 0.50 0.126 (a) Fit these data to equation (2.12) to determine the order of the reaction. (b) Steger and Masel also measured the temperature dependence of the rate, and obtained the following data: Temperature, Etch rate, Temperature Etch rate, Temperature Etch rate. K |iin/minute K |im/minute K um/minute 548 0.101 573 0.132 598 0.189 563 0.123 583 0.162 613 0.214 Estimate the activation barrier for the reaction. (c) How well do these data fit Perrin's equation? Which fits better, Arrhenius' law or Perrin's equation'.' (d) Does the activation barrier agree with equation (2.31)? What is the significance of this result? Assume that you have modeled a reaction, A + B follows the rate equation products, and find that i I -rB k|K2[A] 1 + K2[A] (k4 + K3[B]) with known values of k| and K2. You do not know Kj and k4 so you decide to go into the lab and measure it. Your data are given in Table P3.16. 14? ANAI Yfllfl (II IIAII liAIA cm mi im'. 143 do Use llneai regreiiion tOMtlnute ■ value of K,. {Hint Plot in/|(k|K..|A|/l t K .| A|)| versus [B].) (b) How good is yom regression coefficient? (c) Make a plot of the calculated rate versus the predicted rale. How well does the model aetually lit the data? Now assume that the reaction follows the rate equation: rB = 1 + K2|A] (k4 + K3[BJ) (d) Use linear regression to estimate a value of K3. Hint: Plot re,/ k,K2|A| + K2[AL versus [BJ. (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 better 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. 3.17 Table P3.17 gives Schneider and Rabinovitz' data for the isomerization of CH3NC 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, [CH3NC]2/0 + K2[CH3NC]). How well does the equation fit? {Hint: You could plot [CH3NC]/rate vs. 1/[CH3NC]. 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), kiK2[A]/l + K2[A], -rB rB], kiK2[A]/l + K2|A], -rB mol/liter mol/(literhour) mol/(liter hour) mol/liter mol/(liter-hour) mol/(liter hour) 0.25 1.5 2 2.3 1.001 2.001 3.000 4.001 1.0 2.0 3.0 4.0 2.8 3.5 4.6 5 5.002 6.001 7.003 8.008 5.0 6.0 7.0 X.O I.•!>■«• IM I / II..- i.ill. ,.l iii. Ihyl l-.o, y......I,- r.omiM/.lll.m M.i lis 1 is. K iiiuli- Methyliscocinide Pratiun Rate Pressure Rale (mol/litei i (mol/litei) (mol/liter) (mol/liter) 10,520 9.8 18.1 0.0047 10,250 9.4 10.1 0.0019 9.880 9.1 8 0.0012 5,580 5.1 7.14 0.0010 4,020 3.5 5.1 0.00062 (.850 3.5 2.2 0.00014 3,610 3.3 1.39 0.000067 3,580 3.2 1.05 0.000039 1,757 1.5 0.95 0.000036 1,349 1.2 0.59 0.000014 1,050 0.85 0.56 0.000012 486 0.39 0.41 0.0000073 log 0.23 0.286 0.0000036 222 0.15 0.272 0.0000035 100 0.05 0.13 0.0OO00092 80.6 0.04 0.101 0.00000054 5g.6 0.027 0.0876 0.00000040 40.8 0.015 0.0725 0.00000029 2g.8 0.010 Source: Data of Schneider and Rabinovitz (1962). UH In our undergraduate labs, we measure the rate of oxidation of Red Dye 40 with bleach. The main reaction is Red Dye 4- CIO CI" + Yellow Dye 4- H20 Over the years, we have done many different measurements, and the data in Table P3.18 were obtained: The objective of this problem is to fit the data to equation (2.13) and determine the order of the reaction in bleach and dye. The easiest way to solve this problem is to use the regression capabilities of your spreadsheet. Inble P3.18 Rate data for Example 3.18 »ye Bleach Dye Bleach oncentration, Concentration, Rate, Concentration, Concentration, Rate, n.il/liter mol/liter mol/(literminute) mol/liter mol/(literminute) mol/liter 0.011 0.031 0.018 0.033 0.030 0.053 0.015 0.0315 0.023 0.034 0.039 0.073 0.018 0.0270 0.024 0.039 0.044 0.092 0.022 0.039 0.041 0.041 0.051 0.115 0.023 0.036 0.032 0.045 0.024 0.053 0.025 0.009 0.009 0.044 0.010 0.028 0.028 0.0189 0.023 0.052 0.052 0.145 H4 ANAI Y'.l'l I II HAH UAIA I'lli Mil I M'. 146 (a) Coiivi-it equation (.' I l) so Ilia! you Hi" I'M' linrw ivnivssinn (in Sel up youi spreadsheet to do Ihe regression using the Data Analysis/Regression tool in Microsoft Excel (c) Try nonlinear regression as in Table 3.A.4 to see how thai changes your answers. 3.19 Commercial sterilizers work by heating baeleria to high temperatures where the bacteria die. The FDA (U.S. Food and Drug Administration) requires all sterilizers 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 lest sterilizers with a thermobacteria spore that is particularly able to survive high temperatures. It is hard to detect a 1012 overkill, so people measure the time to a 106 overkill and assume that if they double the sterilization time, a 1012 overkill will be achieved. (a) Show that if the death of bacteria follow a first-order rate law, the time to 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? (Hint: Assume an initial concentration of 108/cm3. At a 106 overkill, you need to get to a final concentration of 102/cm\ At a 1012 overkill, you need to get to 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 out 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°C they 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 of the Time, of the ADN Time, of the ADN Time, of the ADN seconds Remaining seconds Remaining seconds Remaining 0 1.0 900 0.58 2400 0.24 300 0.84 1200 0.49 — — 600 0.70 1500 0.41 — — (C) Um Van'I Moll's method In III Ihese data to .i rale equation. (d) Use Powell's method i<> iii these data to a rate equation, (•) II you had lo process ADN al lot) (', how long could you run the process without blowing anything up7 Assume that there is an explosion hazard once v; ol Ihe ADN has reacted to form unstable intermediates. (f) If you wanted to process for 5 minutes, what temperature would you choose? Assume that the reaction follows Arrhenius' law with a preexponential of II)1'/second. {Hint: First, estimate the activation energy from your value of Ihe rate constant and the known preexponential.) 1.21 < hlcbicki, et al. IntJ. Chem. Kinetics, 29 (1997) 73, examined the sodium cresolate (S) catalyzed decomposition of epichlorohydrin (E). At 71°C they obtained the results in Table P3.21. (a) Is this a direct or indirect measurement of the rate? (b) Fit these data to a rate equation. (Hint: Assume that Cs is constant during each run. First, fit the rate data at each Cs to a rate equation, and then determine how the rate constant varies with Cs. Assume an initial concentration of 0.1 mol/liter.) 3.22 In Problem 3.21 we noted that Chlebicki, et al. IntJ. Chem. Kinetics, examined the sodium cresolate (S)-catalyzed decomposition of epichlorohydrin (E) in a batch reactor. However, they could have instead run the reaction in a CSTR. (a) Explain what they would have needed to do to measure the rate in a CSTR. (b) What value of the residence time, x, will give a conversion of 0.45 at Cs = 0.76 mol/dm3 (mole per cubic decimeter)? 3.23 Bodenstein and Lund Z. Physik Chem, 57, (1907)(168), examined the kinetics of the reaction H2 + Br2 => 2HBr (P3.23.1) 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. Table P3.21 The decomposition of epichlorhydrin in the presence of sodium cresolate Cs = 1.2 mol/dm3 Cs =0.88 mol/dm3 Cs =0.76 mol/dm3 Fraction Fraction lime, of the E Time, of the E minutes Remaining minutes Remaining Time, minutes Fraction of the E Remaining Cs = 0.65 mol/dm3 Fraction Time, of the E minutes Remaining 0 1.0 0 1 0 1.0 0 1.0 5 0.90 5 0.93 5 0.94 5 0.94 15 0.74 15 0.80 15 0.82 15 0.84 25 0.61 25 0.69 25 0.72 25 0.75 35 0.50 35 0.59 35 0.63 35 0.66 »5 0.41 45 0.51 45 0.55 45 0.59 55 0.33 55 0.44 55 0.48 55 0.53 Ill) ANAI Yfllll i H MAN IIAIA I'I li Mil I M' 147 I .1 I Is lllls I lllll'l I "I llllllll'l I 11II ■. I . 1111 ■ 11 u ■ 111 (ll tin- ■ (b) i)so Essen's method i<> in these data to a simple rate equation (c) Use Van't Hoffs method to in these data to a simple rate equation. (d) Use Powell's method lo lit these data to a simple rale equation. (e) What do you eoneludc from the nonlinearily of your plots? 3.24 In Problem 3.23 we noted that Bodenslein and Lund Z. Physik Chem, 57, (1907) 168, examined the kinetics of the reaction H2 + Br2 2HBr (P3.24.1) 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 ki[H2][Br2]'/2 [HBr] (P3.24.2) + K: IBM (a) Use the stoichiometric table to derive an expression for [H2] and [HBr] as a function of the Br2 conversion. (b) Plug into equation (P3.24.2) to prove dXBr2 K,(l - XBr2)1/2(C| - XBrC»r2) di 1 +2K2 Min (P3.24.3) (1 -XB„) where XBr2 is the conversion of Br2 and and CBr2 are the initial H2 and Br2 concentrations, (c) Show that the solution of equation (P3.24.3) is 4K, 1 -2K2 I 2K2^/1 -XBr2 3(l-XBr2)3/2 1 2 2K^ + 3 when C°Br2 = C°H2 4K2 \/CH2 ~ cb Br2 1 -2K2 2K2 V-Br2 'H2 c° Brj Table P3.23 Bodenstein and Lund's data for the reaction H2 + Br2 =>■ 2HBr Time, [H2l=[Br2], Time, [H2]=[Br2], Time, [H2]=|Br2], minutes mol/liter minutes mol/liter minutes mol/liter 0 0.2250 90 0.1158 300 0.0478 20 0.1898 128 0.0967 420 0.0305 60 0.1323 180 0.0752 .III I.Ill 11" i< "l'l.. -CUB,2+CSr2v/l+XBr2) ^h2 — cBr2 y y/i — x Mil when C°„2 > C(Br2 C^k, 2K2 - 2K2 K2 x In (\JCBT2\/1 ~ XBr2 + \ZCBr2 ~ CH2)(CBr2 _ \fCBt2 ~ CH2) (\JCBr2V^ " XBi"2 _ \/CBr2 ~ CH2)(CBr2 _ \/Cl nl.'s data loi ■<>.■< lion (I'M ;'",) Time, Pressure, Time, Pressure Time, 1 'ressure, minutes aim minutes aim minutes aim 0 0.223 9 0.295 18 0.355 3 0.249 12 0.316 21 0.372 6 0.273 15 0.336 — — Table P3.26 The rate of Si02 deposition from TEOS at 1070 K TEOS Deposition TEOS Deposition TEOS Deposition Pressure, Rate, Pressure, Rate, Pressure, Rate, torr pg/hour torr pg/hour torr ug/hour 0.15 148 0.29 175 0.42 190 0.55 200 0.68 209 0.81 215 (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 k,P. /2 tSiOi — lrTEOS 1 4- k,P1/2 1 -f K.2ITEOS (P3.26.1) How well does equation (P3.26) fit the data? (d) Assume that the reaction follows equation (P3.26.1). Derive an equation for 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(OC2H,)4 => Si02 + 2(C2H5)20 where Si(OC2H5) is TEOS. Calculate the TEOS pressure as a function of 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, first-order, or second-order rate equation. How well do your calculated results fit zero-order, half-order, first-order or second-order rate expressions? (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 of a polyethylene-styrene copolymer. Chung and Lu loaded ethylene into a reactor, added a small amount of styrene, and then initiated the reaction. Chung and Lu then measured the conversion of styrene as a function of time. They repeated the same experiments substituting methylstyrene for styrene. (The styrene and methylstyrene runs were done separately.) Some of Chung and Lu's results are given in Table P3.27. (a) Is this a direct or indirect measurement of the rate? (b) Use Essen's method to fit these data to a rate equation. Table P3.27 The conversion of styrene as a function of time and the conversion 1). Develop an equation expressing how quickly the population of bacteria doubles. (c) In the literature, it is common to report values at a constant kG, where ko is given by B Chang and Hong, J. Biotechnology, 42 (1995) 189, examined the growth of a potentially toxic bacteria, Pseudomonas aeruginosa, PU21 in a glucose solution, and obtained the data in Table P3.28. How well do these data fit Monod kinetics? 3.29 The adsorption and destruction of alcohol in a human body can be modeled as two first-order reactions in series. When you drink an alcoholic beverage, the alcohol in the beverage reacts with the blood in your stomach walls to yield an alcohol/blood complex. The alcohol/blood complex is then quickly transported throughout your entire body, including your liver. In a second process, the enzymes in your liver break down the alcohol into other products. (a) Assume that the adsorption and destruction of alcohol are first-order processes. Use the equations in this chapter to obtain an expression for your blood alcohol level as a function of time. TOO ANAIYM'icH MAM HAIA I'MDMIIMtl 151 tilhUt l>:).2U k<, foi llu> uiowth ul /'•iiiiiifmii.iiM', m>/n large exceu >>i bromine atoms In the reactor, the CMi() concentration will lollow |('ll;o|„ O] In - V ICH3 k2|Br]t (P3.30.3) where |CH30]0 is the initial CH30 concentration and t is time. (d) Table P3.30.1 shows some data for the reaction. Use Essen's method to determine the order of the reaction. (e) Use Van't Hoff s method to determine the order of the reaction. (f) Use Powell's method to determine the order of the reaction. (g) Aranda et al. also report values of ln{([CH30]0/[CH30])/t) for various bromine concentrations. Table P3.30.2 shows the data. Use an Essen plot (i.e., ln{([CH30]0/[CH30])/t} vs. [Br]) to see how well these data follow equation (P3.30.2). (h) Repeat part (g) using a Van't Hoff plot (i.e., k2 vs. [Br]). (i) Can you find another rate law that fits the data better? 3.31 In Section 3.9.1, we derived an expression for the average rate of a reaction as a function of the conversion. The objective of this problem is to see how the average rate compares to the rate at the average concentration. (a) Derive an expression for the average rate of a first-order reaction and a second-order reaction as a function of the conversion in a batch reactor. T.-ible P3.30.1 The CH3O conversion versus time reported by Aranda et al CH30 Conversion CH30 Conversion CH30 Conversion [Br] = 2.22 [Br] = 4.48 [Brl = 6.52 Time, ms xlO" molecules/cm3 xlO1' molecules/cm3 x 10" molecules/cm3 0 0 0 0 0.5 0.08 0.15 0.21 l 0.15 0.28 0.38 1.5 0.21 0.39 0.51 2 0.27 0.48 0.61 2.5 0.33 0.56 0.7 3 0.38 0.63 0.76 5 0.55 0.81 0.91 Table P3.30.2 Values of (ln([CH30]o/[CH30])l/t reported by Aranda et al [Br] .,o" molecules/cm' f>n(tCH30]0/[CH30|))/t molec'ulesW [ln([CH30|0/[CH30])l/t 1.59 116 6.96 503 2.94 210 7.26 506 3.38 250 8.71 578 4.78 334 10.8 755 5.07 427 1 1.84 913 6.23 505 12.46 823 I'IK Mil I M' | Derive .in expression loi the mlr ,u id. nvenifj.c coiicciiliiilion. (C) I lOW do llw tWO I c«lll|Mi, 1 (d) Find a concentration when- the average rate niu.ii>. thai rate al thai concentra I lull 3.32 In Section 3.13 wc derived a number of equations for the behavioi ol a reac lion A + B =» C + D (P3.32.J: (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 [A] = [B|. (c) How can you use the results in (a) and (b) to determine the kinetics of 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/liter. Calculate the 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 follows 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 [Aj = [B]? 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 acids. The main reaction is CH3COOCH2CH3 + H2Q CH3COOH + HOCH2CH3 (P3.34.1) The reaction obeys rEA = -k1[H+][CH3COOCH2CH3J + k2[H+][CH3COOH][HOCH2CH3] (P3.34.2) (ii) Develop .i stoichiometric table lor the reaction, tin Rearrange equation (P3, )0.2) i" prove thai ii then- is no ethanol or acetic acid in the reactoi al the beginning ol the reaction, then dX, \ dt -k,lH( |(l -X,A) + k2C»A|H+](XEA)2 (P3.34.3) where Xea is the conversion of ethylacetate and CEA is the initial ethylacetate concentration, (c) Show that the solution of equation (P3.34.3) is k,iH+]T: + 2X& J "' V(XeEqA)(XEA + 1 + XEqA) In (P3.34.4) with 2XEA = I »/4 k2CEA , (d) Make a plot of the rate with various values of the parameters. How does the rate of reaction vary as you vary kj and XEA? More Advanced Problems 3.35 People often use bacteria to digest hazardous materials in wastestreams. The rate usually follows Monod kinetics: d^ , rp1 KF[W] rB = "dT=kB[B]i+KF[W] d[W] KF[W] rw = —:— = -kw[BJ- (li + KF[W] (P3.35.1) (P3.35.2) where [B] is the bacteria concentration in bacteria/liter and [W] is the waste concentration in mol/liter. Assume KF = 220 liters/mol, kB = 0.35/hour, and kw = 2.5 x 10"6 (mol-hour)/bacteria. d[B] d[W]' (a) Derive an expression for (b) Integrate your expression in (a) to derive an expression for [B] as a function of [W], the waste concentration at any time, t, and [W)0 and [B]0, the initial bacteria and waste concentrations. (c) Rearrange your expression in (b) to derive an expression for [B| as a function of the Xw, the fractional conversion of the waste. (d) Compare your results to those in the stoichiometric table. Can you see that you are converting waste into bacteria? (e) Substitute your expression into equation (P3.35.2) to calculate the rate of waste reduction as a function of XW- (f) Integrate your expression to obtain an expression for the time to get a conversion Xw. rnifM iiiiHMI MM 1 I I IA 1 f\ I'Ml Mil I M\ 15B ill) Assume Mini you slnrl Willi ii)'1 h.u n i i.i/lilci .mil i mol/lilei nl waslc Ymi have n choice oi iw« bacteria! one wuh a k|. = 2.2 x hi' llten/mol, kg ■ 0.35/hour, kw — 2.5 x 10 8 (molhour)/bacterii a second with a Kp = 2.2 x 103 liters/mol, kB 0.35/hour, kw =2.5 x 10 ' (molhourj/bacteria. Which baclcria will get to 99% conversion lirsl? (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 thai starts with one bacteria, then adds a second bacteria to finish the job? 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 the 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 reactants of OH radicals with amides. Int. J. Chem. Kinet., 29, 81 (1997). (b) Crivello, J. V., and Liu, S. S. Synthesis and cationic polymerization of glycidyl ether. Poly. Sci. A, 36, 1017 (1998). (c) Simakov, P. A., Martinez, F. N., Horner, J. H., and Newcomb, M. Absolute rate constants for alkoxycarbonyl radical reactions. J. Org. Chem., 63, 1226 (1998). (d) Musa, O. M., Choi, S. Y., Horner, J. H., and Newcomb, M. Absolute rate constants for alpha-amide radical reactions. J. Org. Chem., 63, 786 (1998). (e) Kettling, U., Koltermann, A., Schwille, P., and Eigen, M. Real-time enzyme kinetics monitored by dual-color fluorescence cross-correlation spectroscopy. Proc. Nat. Acad. Sci. U.S., 95, 1416 (1998). (f) Wallington, T. J., Guschin, A., Steinn, T. N. N., Platz, J., Sehestcd, J., Christensen, L. K., and Nielsen, O. J. Atmospheric chemistry of CF3CH2OCH2CF3-UV spectra and kinetic data for CF3CH.ICH2CF3 and CF3CH.OCH2CF3 radicals and atmospheric fate of CF3CH.OCH2CF3 radicals. J. Phy. Chem., 102, 1152 (1998). (g) Tolti, N. P., and Leigh, W. J. Direct detection of 1,1-diphenylgermene in solution and absolute rate constants for germene trapping reactions. J. Amer. Chem. Soc, 120, 1172 (1998). (h) Lepicard, S. D., and Canosa, A. Measurement of the rate constant for the association reaction CH+N 2 at 53 K and its relevance to tritons atmosphere. Geophys. Res. Let., 25, 485 (1998). (i) Johnson, K. A. Advances in transient-state kinetics (review). Curr. Opin. BiotechnoL, 9, 87 (1998). (j) Campbell, M. L. Gas-phase kinetics of ground-state platinum with 0_2, NO, N20 and CH4. J. Chem. Soc. Faraday Trans., 94, 353 (1998). (k) Decker, C. The use of UV irradiation in polymerization (review). Polym. Int., 45, 133 (1998). (1) Wolter, S. D., Mohney, S. E., Venugopalan, H., Wickenden, A. E., and Koleske, D. D. Kinetic study of the oxidation of gallium nitride in dry air. J. Electrochem. Soc, 145, 629 (1998). urn it, mi.in v . 1 ,i\ tniii. (1 .mil 1 . in.1.. t; Low pressure stud) "i the reac Hun ol CI. Btomi wilh lioprcnc ./ Phys. Chem.. 102, 953 (1998). in) Blaser, ll U., Jalett, ll P., Garland, M, Studer, M, lines, II., and Wirthti- i.nii, A. Kinetic studies ill tin- enantioselective hydrogenation of ethyl pyruvate , atalyzed by a cinchona modified Pt/AI203 catalyst. J. Catal., 173, 282 (1998). <<>) Bradford, M. C. J. C02 reforming of CH4 over supported PT catalysts. J. Catal, 173, 157 (1998). (p) Madras, G., Smith, J. M., and McCoy, B. J. Thermal degradation kinetics of polystyrene in solution. Polym. Degradation Stab., 58, 131 (1997). H 2. Ber. Bunsenges. Phys. Chem., 102, 73 (1998). (s) Sehested, J., Christensen, L. K., Mogelberg, T., Nielsen, O. J., Wallington, T. J., Guschin, A., Orlando, J. J., and Tyndall, G. S. Absolute and relative rate constants for the reaction CH3C(0))_2 + NO and CH3C(0)O_2 + N02 and thermal stability of CH3C(0)02N02. /. Phys. Chem., 102, 1779 (1998). (t) Harwood, M. H., Rowley, D. M., Cox, R. A., and Jones, R. L. Kinetics and mechanism of the bro self-reaction-temperature-and pressure-dependent studies. J. Phys. Chem., 102, 1790 (1998). (u) Pereira, R. D., Baulch, D. L., Pilling, M. J., Robertson, S. H., and Zeng, G. Temperataure and pressure dependence of the multichannel rate coefficients for the CH3 + OH system. J. Phys. Chem., 101, 9681 (1997). (v) Stutz, J., Ezell, M. J., and Finlaysonpitts, B. J. Inverse kinetic isotope effect in the reaction of atomic chlorine with C2H4 and C2D4. J. Phys. Chem., 101, 9187 (1997). (w) Bokenkamp, D., Desai, A., Yang, X., Tai, Y. C, Marzluff, E. M., and Mayo, S. L. Microfabricated silicon mixers for submillisecond quench-How analysis. Anal. Chem., 70, 232 (1998). (x) Rotaru, P., Blejoiu, S. L., Constantinescu, R., Pometescu, N., Uliu, F., and Bunescu, O. Perfectly stirred catalytic reactor. Appl. Catal. A, 166, 363 (1998). (y) Manke, G. C, and Setser, D. W. Measuring gas-phase chlorine atom concentrations— Rate constants for CL + HN3, CF31, and C2F51. J. Phys. Chem., 102, 153 (1998). 3.37 Go to the (a) International Journal of Chemical Kinetics, or if this journal is not available in your library, try (b) the kinetics section of Physical Chemistry A, (c) J. Physical Organic Chemistry, (d) Biotechnology and Bioengineering, (e) Reaction Kinetics and Catalysis Letters, (f) J. Polymer Science A. Find an article where someone measures the kinetics of a reaction. Write a one-page report on the findings in the article to describe: (a) Why the study was undertaken (b) What techniques were used (c) How the data were analyzed (d) What the key results were