Chapter 12 Problems - 500 Chapter 12: Chemical Kinetics...

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Unformatted text preview: 500 Chapter 12: Chemical Kinetics Problems Reaction Order, Rate Law 12.1 Write the rates for the following reactions in terms of the disappearance of reactants and 12.2 12.3 12.4 12.5 12.6 12.7 12.8 12.9 appearance of products: (a) 302 —> 203 (b) C2H5 -—> C2H4 + H2 (c) ClO‘ + Br‘ —> BrO‘ + C1" (d) (CH3)3CC1+ H20 —> (CH3)3COH + H+ + Cl‘ (e) 2AsH3 —> 2As + 3H2 The rate law for the reaction NHIWI) + N02‘(aq) ~* N2(g) + 2H20(l) is given by rate = k[NHI][N02_]. At 25 °C, the rate constant is 3.0 x 10’4 M ‘1 3“. Calculate the rate of the reaction at this temperature if = 0.26 M and [NO;] 2 0.080 M. What are the units of the rate constant for a third-order reaction? The following reaction is found to be first order in A: A —> B + C If half of the starting quantity of A is used up after 56 s, calculate the fraction that will be used up after 6.0 min. A certain first-order reaction is 34.5% complete in 49 min at 298 K. What is its rate constant? (a) The half-life of the first-order decay of radioactive 14C is about 5720 years. Calculate the rate constant for the reaction. (b) The natural abundance of 14C isotope is 1.1 x 10‘13 mol % in living matter. Radiochemical analysis of an object obtained in an archeological excavation shows that the 14C isotope content is 0.89 x 10‘14 mol %. Calculate the age of the object. State any assumptions. The first-order rate constant for the gas-phase decomposition of dimethyl ether, . (CH3)20 —> CH4 + H2 + CO is 3.2 x 10‘4 s‘1 at 450 °C. The reaction is carried out in a constant-volume container. Initially, only dimethyl ether is present, and the pressure is 0.350 atm. What is the pressure of the system after 8.0 min? Assume ideal-gas behavior. When the concentration of A in the reaction A —> B was changed from 1.20 M to 0.60 M, the half-life increased from 2.0 min to 4.0 min at 25 °C. Calculate the order of the reaction and the rate constant. The progress of a reaction in the aqueous phase was monitored by the absorbance of a reactant at various times: Time/s 0 54 171 390 720 1010 1190 Absorbance 1.67 1.51 1.24 0.847 0.478 0.301 0.216 Determine the order of the reaction and the rate constant. Problems 12.10 Cyclobutane decomposes to ethylene according to the equation C4H8(g) -* 2CzH4(9) Determine the order of the reaction and the rate constant based on the following pressures, which were recorded when the reaction was carried out at 430 °C in a constant—volume vessel: f Time/s Pans / mmH g 0 400 2000 3 16 4000 248 6000 196 8000 1 55 10000 122 12.11 What is the half-life of a compound if 75% of a given sample of the compound decomposes in 60 min? Assume first-order kinetics. 12.12 The rate constant for the second-order reaction 2N02(g) —> 2N0(g)+02(g) is 0.54 M ‘1 s‘1 at 300 °C. How long (in seconds) would it take for the concentration of N02 to decrease from 0.62 M to 0.28 M? 12.13 The decomposition of N20 to N2 and 02 is a first-order reaction. At 730 °C, the half-life of the reaction is 3.58 x 103 min. If the initial pressure of N20 is 2.10 atm at 730°C, calculate the total gas pressure after one half—life. Assume that the volume remains constant. 12.14 The integrated rate law for the zero-order reaction A —> B is [A] = [A]0 — kt. (a) Sketch the following plots: (i) rate versus [A] and (ii) [A] versus t. (b) Derive an expression for the half-life of the reaction. (c) Calculate the time in half-lives when the integrated rate law is no longer valid, that is, when [A] = 0. 12.15 In the nuclear industry, workers use a rule of thumb that the radioactivity from any sample will be relatively harmless after 10 half-lives. Calculate the fraction of a radioactive sample that remains after this time period. (Hint: Radioactive decays obey first-order kinetics.) 12.16 Many reactions involving heterogeneous catalysis are zero order; that is, rate = k. An example is the decomposition of phosphine (PH3) over tungsten (W): 4PH3(9) —+ P4(g)+6H2(g) The rate for this reaction is independent of [PH3] as long as phosphine’s pressure is sufficiently high (21 atm). Explain. 12.17 If the first half-life of a zero-order reaction is 200 s, what will be the duration of the next half- life? 12.18 Consider the following nuclear decay 64cu —» 64Zn+ 33/3 t1/2 = 12.8 hr Starting with one mole of 64Cu, calculate the number of grams of 64Zn formed after 25.6 hours. 501 Chapter 12: Chemical Kinetics Reaction Mechanisms 12.19 The reaction S20; + 21- —> 230}- +12 proceeds slowly in aqueous solution, but it can be catalyzed by the Fe3+ ion. Given that Fe3+ can oxidize I‘ and“ Fe2+ can reduce 5202‘, write a plausible two-step mechanism for this reaction. Explain why the uncatalyzed reaction is slow. 12.20 Derive Equation 12.22 using the steady-state approximation for both the H and Br atoms. 12.21 An excited ozone molecule, 0;, in the atmosphere can undergo one of the following reactions: 0; L 03 (1) fluorescence 0; O + 02 (2) decomposition o; + M i; 03 + M (3) deactivation where M is an inert molecule. Calculate the fraction of ozone molecules undergoing decomposition in terms of the rate constants. 12.22 The following data were collected for the reaction between hydrogen and nitric oxide at 700 °C: 2H2(g) + 2N0(g) 2. 2H20(g) +N2(g) Experiment [H2]/M [NO]/M Initial rate/M - s—l _____________—-—————— 1 0.010 0.025 2.4 X 10—6 2 0.0050 0.025 1.2 x 10—6 3 0.010 0.0125 0.60 X 10—6 (a) What is the rate law for the reaction? (b) Calculate the rate constant for the reaction. (c) Suggest a plausible reaction mechanism that is consistent with the rate law. (Hint: Assume that the oxygen atom is the intermediate.) ((1) More careful studies of the reaction show that the rate law over a wide range of concentrations of reactants should be _ k1[NO]2[H2] rate ‘ 1 + k2[H2] What happens to the rate law at very high and very low hydrogen concentrations? 12.23 The rate law for the decomposition of ozone to molecular oxygen 203 (g) —’ 302(9) is 10312 rate = k [02] The mechanism proposed for this process is k 03 7—1: O+Oz —1 0+03 11» 202 Problems Derive the rate law from these elementary steps. Clearly state the assumptions you use in the derivation. Explain why the rate decreases with increasing 02 concentration. 12.24 The gas-phase reaction between H2 and 12 to form HI involves a two-step mechanism: 12 : 21 H2+21 ——> 2H1 The rate of formation of H1 increases with the intensity of visible light. (a) Explain why this fact supports the two-step mechanism given. (Him: The color of 12 vapor is purple.) (b) Explain why the visible light has no effect on the formation of H atoms. 12.25 In recent years, ozone in the stratosphere has been depleted at an alarmingly fast rate by chlorofiuorocarbons (CFCs). A CFC molecule such as CFC13 is first decomposed by UV radiation: CFC13 —-> CFClz + C1 The chlorine radical then reacts with ozone as follows: Cl+03 —+ ClO+02 ClO+O —> Cl+02 (a) Write the overall reaction for the last two steps. (b) What are the roles of Cl and C10? (c) Why is the fluorine radical not important in this mechanism? (11) One suggestion for reducing the concentration of chlorine radicals is to add hydrocarbons such as ethane (C2H6) to the stratosphere. How will this approach work? (e) Draw potential energy versus reaction progress diagrams for the uncatalyzed and catalyzed (by C1) destruction of ozone: 03 + O ——> 202. Use the thermodynamic data in Appendix B to determine whether the reaction is exothermic or endothermic. Activation Energy 12.26 Use Equation 12.23 to calculate the rate constant at 300 K for Ea Assume that A = 1011 s“1 in each case. 12.27 Many reactions double their rates with every 10° rise in temperature. Assume that such a reaction takes place at 305 K and 315 K. What must its activation energy be for this statement to hold? 12.28 Over a range of about i 3 by MT = M3701)”, where M37 equation in terms of a possible molecular interpretation. [Source: Campbell, J. Chem. Educ. 52, 327 (1975).] 12.29 The rate of bacterial hydrolysis of fish muscle is twice as great at 2.2 °C as at —l .1 °C. Estimate a AEa value for this reaction. Is there any relation to the problem of storing fish for food? [Source: “Eco—Chem,” J. A. Campbell, J. Chem. Educ. 52, 390 (1975)]. 12.30 The rate constants for the first-order decomposition of an organic compoun measured at several temperatures: = 0, 2, and 50 k] mol‘l. °C from normal body temperature the metabolic rate, MT, is given is the normal rate and AT is the change in T. Discuss this “Eco-Chem,” J. A. din solution are i; k/s—l 4.92x10—3 0.0216 0.0950 0.326 1.15 t/°C 5.0 15 25 35 45 Determine graphically the pre-exponential factor and the energy of activation for the reaction. 503 ___.. we"... wflw_v....,mwgr~,wm..,w J .15, ,. Chapter 12: Chemical Kinetics 12.31 The energy of activation for the reaction 2H1 —> H2 +12 is 180 kJ mol‘1 at 556 K. Calculate the rate constant using Equation 12.23. The collision diameter for HI is 3.5 x 10‘8 cm. Assume that the pressure is 1 atm. 12.32 The rate constant of a first-order reaction is 4.60 x 10‘4 s‘1 at 350 °C. If the activation energy is i 104 kJ mol‘l, calculate the temperature at which its rate constant is 8.80 x 10‘4 s“. l 12.33 The rate at which tree crickets chirp is 2.0 x 102 per minute at 27 °C but only 39.6 per minute at 5 °C. From these data, calculate the “activation energy” for the chirping process. (Hint: The ratio of rates is equal to the ratio of rate constants.) Find the chirping rate at 15 °C. 12.34 Consider the following parallel reactions The activation energies are 45.3 kJ mol‘1 for k1 and 69.8 kJ mol‘1 for k2. If the rate constants are equal at 320 K, at what temperature will k1 /k2 = 2.00? Thermodynamic Formulation of Transition-State Theory 12.35 The thermal isomerization of cyclopropane to propene in the gas phase has a rate constant of 5.95 x 10‘4 s‘1 at 500°C. Calculate the value of AG“1 for the reaction. 12.36 The rate of the electron-exchange reaction between naphthalene (Clng) and its anion radical (Clng) are diffusion controlled: (:1ng + Clng ‘: C10H}; + CIOHs— The reaction is bimolecular and second order. The rate constants are T /K 307 299 289 273 k/lO9 M‘1 -s‘1 2.71 2.40 1.96 1.43 Calculate the values of Ea, AH °I, AS °i and AG°¢ at 307 K for the reaction. [Hints Rearrange Equation 12.36 and plot ln(k/ T) versus 1/T.] 12.37 (a) The pre-exponential factor and activation energy for the hydrolysis of t-butyl chloride are 2.1 x 10“5 s—1 and 102 kJ mol'l, respectively. Calculate the values of AS °1 and AH °l at 286 K for the reaction. (b) The pre-exponential factor and activation energy for the gas-phase cycloaddition of maleie anhydride and cyclopentadiene are 5.9 X 107 M ‘1 s‘1 and 51 kJ mol‘l, respectively. Calculate the values of AS °1 and AH °t at 293 K for the reaction. Kinetic Isotope Effect 12.38 A person may die after drinking D20 instead of H20 for a prolonged period (on the order of days). Explain. Because D20 has practically the same properties as H2O, how would you test the presence of large quantities of the former in a victim’s body? 12.39 The rate-determining step of the bromination of acetone involves breaking a carbon-hydrogen bond. Estimate the ratio of the rate constants kc_H/kc_D for the reaction at 300 K. The frequencies of vibration for the particular bonds are 1701.; z 3000 crn‘l and 7cm z 2100 cm“1. The wavenumber (fl) is given by v/c, where v is the frequency and c is the velocity of light. 12.40 Lubricating oils for watches or other mechanical objects are made of long-chain hydrocarbons. Over long periods of time they undergo auto-oxidation to form solid polymers. The initial step in this process involves hydrogen abstraction. Suggest a chemical means for prolonging the life of these oils. Problems Additional Problems 12.41 A flask contains a mixture of compounds A and B. Both compounds decompose by first-order kinetics. The half-lives are 50.0 min for A and 18.0 min for B. If the concentrations of A and B are equal initially, how long will it take for the concentration of A to be four times that of B? 12.42 The term reversible isused in both thermodynamics (see Chapter 4) and in this chapter. Does it convey the same meaning in these two instances? 12.43 The recombination of iodine atoms in an organic solvent, such as carbon tetrachloride, is a diffusion-controlled process: 1+1 —> 12 Given that the viscosity of CC14 is 9.69 x 10’4 N s In“2 at 20 °C, calculate the rate of recombination at this temperature. 12.44 The equilibrium between dissolved C02 and carbonic acid can be represented by + — is H + Hcoa T H2003 21 k13J[k31 keel [1‘32 co2 + H20 Show that _ dicozl dt = ([631 + k32)[C02] — (km + [H+][HCO3] where K = [H+][HCO3‘]/[H2CO3]. 12.45 Polyethylene is used in many items, including water pipes, bottles, electrical insulation, toys, and mailing envelopes. It is a polymer, a molecule with a very high molar mass made by joining many ethylene molecules (the basic unit is called a monomer) together. The initiation step is k, . .. . R2 ——> 2R- Initiation The R- species (called a radical) reacts with an ethylene molecule (M) to generate another radical R°+M —> M1- Reaction of M1' with another monomer leads to the growth or propagation of the polymer chain: k Ml' + M —"> My propagation This step can be repeated with hundreds of monomer units. The propagation terminates when two radicals combine M" + M”' 3» M’—M” termination The initiator in the polymerization of ethylene commonly is benzoyl peroxide [(C6H5COO)2]: [(C5H5COO)2] —> 2C6H5COO- 505 506 Chapter 12: Chemical Kinetics 12.46 12.47 12.48 12.49 12.50 12.51 12.52 12.53 This is a first-order reaction. The half-life of benzoyl peroxide at 100 °C is 19.8 min. (a) Calculate the rate constant (in min‘l) of the reaction. (b) If the half-life of benzoyl peroxide is 7.30 h, or 438 min, at 70 °C, what is the activation energy (in kJ/mol) for the decomposition . of benzoyl peroxide? (c) Write the rate laws for the elementary steps in the above polymerization process and identify the reactant, product, and intermediates. ((1) What condition would favor the growth of long high-molar—mass polyethylenes? In a certain industrial process involving a heterogeneous catalyst, the volume of the catalyst (in the shape of a, sphere) is 10.0 cm3. (3) Calculate the surface area of the catalyst. (b) If the sphere is broken down into eight spheres, each of which has a volume of 1.25 cm3, what is the total surface area of the spheres? (c) Which of the two geometric configurations is the more effective catalyst? (Him: The surface area of a sphere is 4nr2, where r is the radius of the sphere.) Explain why grain dust in elevators can be explosive. At a certain elevated temperature, ammonia decomposes on the surface of tungsten metal as follows: NH3 —» §N2+§H2 The kinetic data are expressed as the variation of the half-life with the initial pressure of NH3: P/torr 264 130 59 16 t1 )2 /s 456 228 102 60 (3) Determine the order of the reaction. (1)) How does the order depend on the initial pressure? (c) How does the mechanism of the reaction vary with pressure? The activity of a radioactive sample is the number of nuclear disintegrations per second, which is equal to the first-order rate constant times the number of radioactive nuclei present. The fundamental unit of radioactivity is the curie (Ci), where 1 Ci corresponds to exactly 3.70 x 1010 disintegrations per second. This decay rate is equivalent to that of l g of radium- 226. Calculate the rate constant and half-life for the radium decay. Starting with 1.0 g of the radium sample, what is the activity after 500 years? The molar maSs of Ra—226 is 226.03 g mol“. The reaction X —> Y has a reaction enthalpy of —64 kJ mol‘1 and an activation energy of 22 kJ mol‘l. What is the activation energy for the Y —> X reaction? Consider the following parallel first-order reactions: (:1) Write the expression. for d [B] /dt at time t, given that [A]0 is the concentration of A at t : 0. (b) What is the ratio of [B]/[C] upon completion of the reactions? As a result of being exposed to the radiation released during the Chernobyl nuclear accident, a person had a level of iodine-131 in his body equal to 7.4 mCi (1 mCi = l x 10‘3 Ci). Calculate the number of atoms of I-131 to which this radioactivity corresponds. Why were people who lived close to the nuclear reactor site urged to take large amounts of potassium iodide after the accident? A certain protein molecule, P, of molar mass J1 dimerizes when it is allowed to stand in solution at room temperature. A plausible mechanism is that the protein molecule is first denatured before it dimerizes: k P —> P*(denatured) slow 2Fpk —> P2 fast Problems The progress of this reaction can be followcil by making viscosity measurements of the average molar mass, .11. Derive an expression for J! in terms of the initial concentration, [P]0, and the concentration at time t, [P], and .11. Write a rate equation consistent with this scheme. 12.54 The bromination of acetone is acid catalyzed: CH3COCH3 + Bu 113 CH3COCH2Br + H+ + Br‘ The rate of disappearance of bromine was measured for several different concentrations of acetone, bromine, and H‘r ions at a certain temperature: Rate of Disappearance [CH3COCH3]/M [Br2]/M [H+]/M of Brz/M - s—1 (1) 0.30 0.050 0.050 5.7 x 10‘5 (2) 0.30 0.10 0.050 5.7 x 10“5 (3) 0.30 0.050 0.10 1.2 x 10‘4 (4) 0.40 0.050 0.20 3.1 x 10‘4 (5) 0.40 0.050 0.050 7.6 x 10~5 (a) What is the rate law for the reaction? (b) Determine the rate constant. (c) The following mechanism has been proposed for the reaction: ‘1? i?” CHa—C—CHa + H30+ \———‘ CHa—C—CHa + H20(fastequilibrium) +fiH oH CH3—c—CHa + H20 —> CHa—C=CH2 + H30+ (slow) OH 0 II I CH3—C=CH2 + ar2 —-+ CHa—C—CHzBr + HBr (fast) Show that the rate law deduced from the mechanism is consistent with that shown in (a). 12.55 The rate law for the reaction 2N02(g) —* N204(g) is rate = k[N02]2. Which of the following changes will alter the value of k? (a) The pressure of N02 is doubled. (b) The reaction is run in an organic solvent. (c) The volume of the container is doubled. (d) The temperature is decreased. (e) A catalyst is added to the container. 12.56 For the cyclic reactions shown on p. 465, show that k_1k2k3 = k1k_2k_3. 12.57 Oxygen for metabolism is taken up by hemoglobin (Hb) to form oxyhemoglobin (HbOg) according to the simplified equation mm) + 02(0‘1) L Hb02<aq> where the second-order rate constant is 2.1 x 106 M ‘1 s‘1 at 37°C. For an average adult, the concentrations of Hb and 02 in the blood in the lungs are 8.0 x 10‘6 M and 1.5 X 10‘6 M, respectively. (a) Calculate the rate of formation of HbOz. (b) Calculate the rate of consumption of 02. (c) The rate of formation of HbOz increases to 1.4 x 10‘4 M 5‘1 during exercise to meet the demand of an increased metabolic rate. Assuming the Hb concentration remains the same, what oxygen concentration is necessary to sustain this rate of Hb02 formation? 508 Chapter 12: Chemical Kinetics 12.58 Sucrose (C12H22011), commonly called table sugar, undergoes hydrolysis (reaction with water) to produce fructose (C6H1206) and glucose (C5H1206): C12H22011+ H20 —> C6H1206 + C6H1206 fructose glucose This reaction has particular significance in the candy industry. First, fructose is sweeter than sucrose. Second, a mixture of fructose and glucose, called invert sugar, does not crystallize, so candy made With this combination is chewier and not brittle as crystalline sucrose is. Sucrose is dextrorotatory (+), whereas the mixture of glucose and fructose resulting from inversion is levorotatory (—). Thus, a decrease in the concentration of sucrose will be accompanied by a proportional decrease in the optical rotation. (a) From the following kinetic data, show that the reaction is first order, and determine the rate constant: time/min 0 7.20 18.0 27.0 00 optical rotation (at) +24.08° +21.40° +17.73 +15.01° —10.73° (b) Explain why the rate law does not include [H20] even though water is a reactant. 12.59 Thallium(I) is oxidized by cerium(IV) in solution as follows: T1+ + 2Ce4+ —» T13+ + 2Ce3+ The elementary steps, in the presence of Mn(II), are as follows: C6” + Mn2+ —» Ce3+ + Mn3+ Ce4+ + Mn3+ __’ Ce3+ + Mn4+ T1+ + Mn4+ —» n“ + Mn2+ (a) Identify the catalyst, intermediates, and the rate-determining step if the rate law is rate = k[Ce4+][Mn2+]. (b) Explain why the reaction is slow without the catalyst. (c) Classify the type of catalysis (homogeneous or heterogeneous). 12.60 Under certain conditions the gas-phase decomposition of ozone is found to be second order in 03 and inhibited by molecular oxygen. Apply the steady-state approximation to the following mechanism to show that the rate law is consistent with the experimental observation: 1‘1 O3 : O2+O k—l o + 03 it 202 State any assumption made in the derivation. 12.61 The rate constants for the reaction 0 II C\ CH2=CH—CH=CH2 + CH2=CH—CHO ——> U H — Problems have been measured at several temperature: 103k/M‘1-s‘1 0.138 1.63 7.2 36.8 81 t/°C 155.3 208.3 246.5 295.8 330.8 Calculate the values of the pre-exponential factor, Ea, AS °*, and AH °1 for the reaction. Use 516 K as the mean temperature for your calculation. [Data taken from G. B. Kistiakowsky and J. R. Lacher, J. Am. Chem. Soc. 58, 123 (1936).] ...
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This note was uploaded on 07/25/2008 for the course CEM 383 taught by Professor Mccracken during the Fall '07 term at Michigan State University.

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Chapter 12 Problems - 500 Chapter 12: Chemical Kinetics...

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