Understanding Kinetics: Rates & Mechanisms of Chemical Reactions
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College of San Mateo**We aren't endorsed by this school
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CHEM 220
Subject
Chemistry
Date
Dec 11, 2024
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6
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536 BRIEF SOLUTIONS TO FOLLOW-UP PROBLEMS (CONTINUED) (b) At 10.0 min (4 half-lives), there are (.75 particles of X. 0.20 mol X Amount (mol) = 0.75 particles X - =0.15mol X | pamde 0.15 mol X M=———=030M 0.50 L 16.7 1., = (In 20k: k = 0.693/13.1 h = 5.29% 102 h ! 4 0.286 L/mol-s _ 1.00X10° J/mol 6.8 n = k 8.314 J/mol-K st W 500. K 490. K = ().491 ky = 0.175 Limol+s Chapter 16 ¢ Kinetics: Rates and Mechanisms of Chemical Reactions ' .Sg A O...H...Q\H ____________ Tla_ns:_ition state AN T 20H B [Eagwa|= 78 kJ Eafrev) = 6 kJ 2 o] 3 AHpn ={72 K o 2 o [ 0 + M0 T Reaction progress 16.10 (1) Balanced equation (after doubling step 4): 2NO(g) + 2H,(g) — Ny(g) + 2H,0(g) (b) Step 2 is unimolecular. All others are bimolecular. {¢) Rate, = k,INOJ%; rate, = ko[ HyJ; rate; = ky|N,O,]|H]; ratey = k,|HOJ[H]; rates = 4. IH]IN ,0]. m Problems with colored numbers are answered in Appendix E. Sec- tions match the text and provide the numbers of relevant sample problems. Bracketed problems are grouped in pairs (indicated by a short rule) that cover the same concept. Comprehensive Problems are based on material from any section or pravious chapter. Ffocusing on Reaction Rate 16.1 What variable of a chemical reaction is measured over time to obtain the reaction rate? 5.2 How does an increase in pressure affect the rate of a gas- phase reaction? Explain. 5.3 A reaction is carried out with water as the solvent. How does the addition of more water to the reaction vessel affect the rate of the reaction? Explain. 16.4 A gas reacts with a solid that is present in large chunks. Then the reaction is run again with the solid pulverized. How does the increase in the surface area of the solid affect the rate of its reaction with the gas? Explain. 155 How does an increase in temperature affect the rate of a reaction’? Explain the two factors involved. 16.6 In a Kinetics experiment. a chemist places crystals of iodine in a closed reaction vessel. introduces a given quantity ot H, gas, and obtains data to calculate the rate of HI formation. In a second cxperiment, she uses the same amounts of iodine and hydrogen. but first warms the flask 10 130°C. a temperature above the sublimation point of iodine. In which of these experiments does the reaction proceed at a higher rate”? Explain. Ixpressing the deaction Bate (Sample Problem 16.1) 16.7 Define reaction rare. Assuming constant temperature and a vlosed reaction vessel. why does the rate change with time? +5 (1) What is the difference between an average rate and an instantaneous rate? (b) What is the difference between an initial rate and an instantaneous rate? 16.9 Give two reasons to measure initial rates in a kinetics study. .10 For the reaction A(g) — B(g). skelch (wo curves on the same set of axes that show () The formation of product as a function of time (b) The consumption of reactant as a function of time 16.11 For the reaction C(g) — D(g). [C] vs. time is plotted: L X Time (a) The average rate over the entire experiment b) The reaction rate at time x ¢) The initial reaction rate (d) Would the values in parts (a), plotted [D] vs. time? Explain. (b). and (¢) be different if you 5.12 The compound AX, decomposes according to the equation 2AXS(g) — 2AX(g) + X+(g). In one experiment. [AXS] measured at various times and these data were obtained: Wits How do you determine each of the following? l [ 3 e Time (s} [AX,] (mol/L) 0.0 0.0500 2.0 0.0448 0.0 0.0300 3.0 0.0249 10.0 0.0209 20.0 0.0088 ta) Find the average rate over the entire experiment. : (b) Is the initial rate higher or Jower than the rate in part (a)? U | araphical methods to estimate the initial rate.
13 (a) Use the data from Problem 16.12 to calculate the average from 8.0 to 20.0 s, Is the rate at exactly 5.0 s higher or lower than the rate in t{a)? Use graphical methods to estimate the rate at 5.0 s. ‘4 Express the rate of reaction in terms of the change in wentration of each of the reactants and products: Alg) + 2B(g) — Clg) en | B} is decreasing at 0.5 mol/L-s. how fast is [A] decreasing? 15 Express the rate of reaction in terms of the change in wentration of each of the reactants and products: 2D(g) + 3E(g) + F(g) — 2G(g) + H(g) wn D] is decreasing at 0.1 mol/L-s, how fast is |H] increasing? 4 Reaction rate is expressed in terms of changes in concen- son of reactants and products. Write a balanced equation for R I AIN,Os] 1 A[NO,] A0, ate = — - = - = AN Vs 4 A At I7 Reaction rate is expressed in terms of changes in concen- won of reactants and products. Write a balanced equation for A[CH,] I A[H,0] A[CO,] Qate = — = o — — ate Y, 2 A 2 Ar Az 3 The decomposition of NOBr is studied by measuring pres- . because the number of moles of gas changes; it cannot be stud- ~olorimetrically because both NOBr and Br, are reddish brown: INOBr(g) — 2NO(g) + Bra(g) * the data below to answer the following: Determine the average rate over the entire experiment. Determine the average rate between 2.00 and 4.00 s. tise graphical methods to estimate the inital reaction rate. (Jse graphical methods to estimate the rate at 7.00 s. At what time does the instantaneous rate equal the average rate r the entire experiment? Time (s) [NOBr] {mol/L)} (.00 0.0100 2.00 0.0071 4.00 0.0055 6.00 0.0045 8.00 0.0038 10.00 0.0033 1 Although the depletion of stratospheric ozone threatens lile Earth today. its accumulation was one ot the crucial processes allowed life to develop in prehistoric times: 305(g) — 204g) Express the reaction rate in terms of [O,] and ]O,]. At a given instant. the reaction rate in terms of [O,] is 7107 mol/L-s. What 1s it in terms of |O,[? + Aate Law and {ts Components mple Problems 16.2 to 16.4) } The rate law for the general reaction dA+HB + - — cCHdD+ - we = K[A]BI"- - - . (a) Explain the meaning of k. (b) Explain meanings of m and n. Does m = a and n = h? Explain. (¢) If reaction is first order in A and second order in B. and time is wsured in minutes (min), what are the units for &? Chapter 16 = Problems 537 16.21 By what factor does the rate change in each of the following cases (assuming constant temperature)? (a) A reaction is first order in reactant A, and [A] is doubled. (b) A reaction is second order in reactant B, and [B] is halved. (¢) A reaction is second order in reactant C. and [C] is tripled. 16.22 Give the individual reaction orders for all substances and the overall reaction order from the following rate law: Rate = A[BrQ; |[Br J[H'} 16.23 Give the individual reaction orders for all substances and the overall reaction order from the following rate law: [0, Rate = k& RO 1628 By what factor does the rate in Problem 16.22 change if cach of the following changes occurs: (a) |BrO,7| is doubled: (b) |Br™| is halved; (¢) [H"] is quadrupled? 16.25 By what factor does the rate in Problem 16.23 change if each of the following changes occurs: (a) {O,] is doubled; (b) [O.] is doubled; (c) |0,] is halved? '5.26 For the reaction 1A(g) + 3B(g) — 2C(g) the following data were obtained at constant temperature: Initial Rate Initial [A] Initial [B] Experiment (mol/L-min) {mol/L}) (mol/L} | 5.00 0.100 0.100 2 45.0 0.300 0.100 3 10.0 0. 100 0.200 4 90.0 0.300 0.200 (a) What is the order with respect to each reactant? (b) Write the rate law. (¢) Calculate k (using the data from Expt 1). 16.27 For the reaction Alg) + B(g) + Clg) — D(») the following data were obtained at constant temperature: Initial Rate Initial [A] Initial [B] Initial [C] Expt (mol/L-s} (mol/L} {mol/L} (mol/L} | 6.25% 1073 (.0500 0.0500 0.0100 2 £25x1072 0.1000 (.0500 0.0100 3 5.00x10712 0.1000 0.1000 0.0100 4 6.25%X 1073 (.0500 0.0500 0.0200 (a) What is the order with respect to each reactant? (b) Write the rate law. (¢) Caleulate & (using the data trom Expt 1). 16.28 Phosgene is a toxic gas prepared by the reaction of carbon inonoxtde with chlorine: CO(g) + Clg) — COCl(g) These data were obtained in a kinetics study of its formation: Initial Rate Initial [CO] Initial [C},] Experiment {mol/L-s}) (mol/L}) {mol/L)} | 1.29x 10~ 1.00 0. 100 e 1.33x 10~ (.100 0.100 3 1.30x 107 0.100 1.00 4 1.32x 107 0.100 0.0100 (a) Write the rate law for the formation of phosgene. (b) Calculate the average value of the rate constant. - . S kg SRRGATIR S ST s L I I A A o N AR T T A T A —— - .
T PR R SRR B Ly o Contact Time {min) Percent {%]) Inactivation 0.00 0.0 0.50 68.3 1.00 90.0 1.50 96.8 2.00 99.0 2.50 99.7 3.00 99.9 (a) Determine the first-order inactivation constant, k. |Hint: % inactivation = 100 X (| = |A}/IA}) ] (b) How much contact time is required for 95% inactivation? 16.85 The reaction and rate law for the gas-phase decomposition of dinitrogen pentaoxide are 2N-04(g) — 4NO,(g) + Os(g) rate = k[N,O«] Which of the following can be considered valid mechanisms for the reaction?’ I One-step collision I 2N,04(g) —— 2NOs(g) + 2NOs(g) [slow] 2NOy(g) — 2NOs(g) + 20(2) |fast] 20(g) — Os(g) [fast] HE N,Os(g) === NO,(g) + NO,(g) [fast] NOy(g) + N1Os(g) — 3INO.(g) + O(g) [slow] NOs(g) + O{g) — NO,g) + Oyg) [fast] IV 2N,05(¢) === 2NOL(g) + N,Oy(g) + 30(g) |fast] N.Os(g) + O(g) — 2NO,(g) |stow| 20(g) — Os(g) [fast] V' 2N,05(8) — NO (o) | stow] N4Oy(g) — 4NO4(g) + Os(g) [fast] 16.86 Like any catalyst, palladium. platinum. and nickel catalyze both directions of a reaction: addition of hydrogen to (hydrogenation) and its elimination from (dehydrogenation) carbon-carbon double bonds. (a) Which variable determines whether an alkene will be hydro- genated or dehydrogenated? (b) Which reaction requires a higher temperature? (¢) How can all-rrans fats arise during hydrogenation of fats that contain some cis- double bonds? 16.87 The molecular scenes below represent the first-order reaction in which cyclopropane (red) is converted to propene (green). Determine (a) the half-life and (b) the rate constant. t=20min t = 60 min t=0 min 16.88 Consider the following organic reaction, in which one halogen replaces another in an atkyl halide: BrCH,CH; + KI — CH;CH,l + KBr In acetone, this particular reaction goes to completion because KI is soluble in acetone but KBr is not. In the mechanism, I~ approaches the carbon opposite to the Br (see Figure 16.16, with 17 instead of OH™). After Br™ has been replaced by I~ and precipitates as KBr. other I ions react with the ethyl iodide by the same mechanism. Chapter 16 ¢ Problems 541 (a) If we designate the C bonded to the halogen as C-1. what is the shape around C-1 and the hybridization of C-1 in ethyl iodide” (b) In the transition state., one of the two lobes of the unhybridized 2p orbital of C-1 overlaps a p orbital of 1. while the other lobe overlaps a p orbital of Br. What is the shape around C-1 and the hybridization of C-1 in the transition state? (¢) The deuterated reactant. BrCHDCH, (where D is deuterium. “H). has two optical isomers because C-1 is chiral. If the reaction is run with one of the isomers. the ethyl iodide is nor optically active. Explain. 16.89 The scenes depict four initial reaction mixtures for the reaction of A (blue) and B (vellow), with and without a solid present (gray cubes). The initial rate. —A|AVAr (in mol/L+s). is shown, with each sphere representing 0.010 mol and the container volume at 0.50 L. m 56x107 IV 4.9x107 (a) What is the rate law in the absence of a catalyst? (b) What is the overall reaction order? (¢) Find the rate constant. (d) Do the gray cubes have a catalytic effect? Explain. 16.90 Figure 16.2] (p. 532) shows key steps in the metal-catalyzed (M) hydrogenation of ethylenc: CoHy(@) + Hag) = CHy(g) Use the following symbols to write a mechanism that gives the overall equation: H,(ads) adsorbed hydrogen molecules M—H hydrogen atoms bonded to metal atoms C,Hy(ads) adsorbed ethylene molecules C,Hs(ads) adsorbed ethyl radicals 16.91 A (green), B (blue), and C (red ) are structural isomers. The molecular filmstrip depicts them undergoing a chemical change as time proceeds. (a) Write a mechanism for the reaction. (b) What role does C play?
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1l 3 or ul at kil i) What is the overall equation? (h) ldentily the reaction intermediate(s). if any. t¢) What are the molecularity and the rate law for each step? (d) Is the mechanism consistent with the actual rate law: rate = k|CO,j|OH |7 16.60 A proposed mechanism for the gas-phase reaction between chlorine and nitrogen dioxide is (1) ClL(g) + NO.(g) — Cl(g) + NO,Cl(g) [slow] (2) Cl(g) + NO,(g) — NO,Cl(g) | fast] (a) What is the overall equation” (b) Identify the reaction intermediate(s), if any. ic) What are the molecularity and the rate law for each step? (d) Is the mechanism consistent with the actual rate law: rate = k[CL]INO,]? 16.61 The proposed mechanism for a reaction is (1)A(g) + Blg) == X(g) [fast] (2) X(g) + Clg) — Y(g) [slow] (3) Y(2) — D(g) Jfast] (a) What is the overall equation? (b) Identify the intermediate(s), if any. (c) What are the molecularity and the rate law for each step? (d) Is the mechanism consistent with the actoual rate law: rate = k|A]IBJ(C]? (e) Is the following one-step mechanism equally wvalid: A(g) + B(g) + C(g) — D(y)? 16.62 Consider the following mechanism: (1) ClO " (ag) + H,O(/) === HCIO{aqg) + OH (aq) [fast] 2) 1" (ag) + HCIO(ag) — HIO(ug) + Cl (aq) |slow] (3) OH " (ag) + HIO(ag) — H,O(/) + 10 (ag) |fast] (a) What is the overall equation? (b) Identify the intermediate(s). if any. (¢c) What are the molecularity and the rate law for each step” (d) Is the mechanism consistent with the actval rate law: rate = k[CIO{[17]? 16.63 In a study of nitrosyl halides, a chemist proposes the follow- ing mechanism for the synthesis of nitrosy! bromide: NO(g) + Bri(g) === NOBr,(g) [fast} NOBry(g) + NO(g) — 2NOBr(g) |slow] If the rate law is rate = k[NOJ?[Br,], is the proposed mechanism valid? If so, show that it satisfies the three criteria for validity. 16.64 The rate law for 2NO(g) + O,(g) —— 2NO,(g) is rate = k[NO]z[OQ]. in addition to the mechanism in the text (p. 529), the following three have been proposed: I 2NO(g) + O(g) — 2NOy(g) II 2NO(g) == N,O,(g) [fast] N.O,(g) + O5(g) — 2NOs(g) [slow] I 2NO(g) == Ny(g) + O.(g) [fast] N,(g) + 204(g) — 2NO,(g) |slow} (a) Which of these mechanisms is consistent with the rate law? (b) Which of these mechanisms is most reasonable? Why? Catalysis: Speeding Up a Reaction 1665 Consider the reaction N;O(g) 2% Ny(g) + 304(g). (a) Does the gold catalyst (Au, above the yield arrow) act as a homogeneous or a heterogeneous catalyst? Chapter 16 « Probiem: 53¢ (b) On the same set of axes. skeich the reaction energy diagrams for the catalyzed and the uncatalyzed reaction. 16.66 Does a catalyst increase reaction rate by the same means as a rise in temperature does? Explain. Comprehensive Probient: 16.67 Consider the following reaction energy diagram: Potential energy Reaction progress (a) How many elementary steps are in the reaction mechanism? (b) Which step is rate limiting” (¢) Is the overall reaction exothermic or endothermic? 16.68 The catalytic destruction of ozone occurs via a two-step mechanism. where X can be any of several species: (HhX+0,— X0+ 0, [slow] (HXO+0— X+ 0, |fast] (a) Write the overall reaction. (b) Write the rate law for each step. (c) X acts as , and XO acts as . (d) High-flying aircraft release NO. which catalyzes this process. into the stratosphere. When O, and NO concentrations arc 5% 10" molecules/cm?® and 1.0 10? molecules/cm?, respectively. what is the rate of O, depletion (k for the rate-determining step 15 6> 1071 em*/molecule-s)? 16.65 A slightly bruised apple will rot extensively in about 4 days al room temperature (20°C). I it is kept in the refrigerator at (’C. the same extent of rotting takes about 16 days. What is the activation energy for the rotting reaction? 16.70 Benzoyl peroxide, the substance most widely used against acne, has a half-life of 9.8X10* days when refrigerated. How long will it take to lose 5% of its potency (95% remaining)? 16.71 The rate law for the reaction NOi(g) + CO(g) — NO(g) + COs(g) is rate = kK[NO,}*: one possible mechanism is shown on p. 527. (a) Draw a reaction energy diagram for that mechanism, given that AH o = —226 kl/mol. (b) Consider the following alternative mechanism: (1) 2NOy(g) —— Ny(g) + 20,(g) {slow] (2) 2CO(g) + Oy(8) — 2C0(g) [fast] (3) Na(g) + Oy(g) — 2NO(g) [fast] Is the alternative mechanism consistent with the rate law? Is one mechanism more reasonable physically? Explain. 16.72 In acidic solution, the breakdown of sucrose into glucose and fructose has this rate law: rate = k[H"}|sucrose]. The initial rate of sucrose breakdown is measured in a solution that is 0.01 M H~, 1.0 M sucrose, 0.1 M fructose. and 0.1 M glucose. How does the rate change if (a) [Sucrose] is changed to 2.5 M? (b) {Sucrose], [fructose], and [glucose] are all changed to 0.5 M? (c) [H*] is changed to 0.0001 M? (d) [Sucrose] and [H*] are both changed to 0.1 M?
538 Chapter 16 ¢ Kinetics: Rates and Mechanisms of Chemical Reactione intearated hate Laws: Concentration Chanage. over Tin (Sample Problems 16.5 (0 16.7) 16.25 How are integrated rate laws used to determine reaction order? What is the order with respect to reactant if a plot of (a) The natural togarithm of [reactant] vs. time is lincar? (b) The inverse ol [reactant| vs. time is linear? (¢) IReactant| vs. time is lincar”? 16.30 Define the half-life of a reaction. Explain on the molecular level why the half-life of a first-order reaction is constant, 163 For the simple decomposition reaction AB(g) — Alg) + Biy) rate = A|ABJ and £ = (.2 L/mol-s. How tong will it take for |AB] to reach one-third of its initial concentration of L.50 Ar? 16.32 For the reaction in Problem 16.3 I. what is [AB] after 10.0 5? 1635 In a first-order decomposition reaction. 50.0% of a com- pound decomposes in 10.5 min. (a) What is the rate constant of the reaction? (b) How long does it take for 75.0% of the compound to decompose? 16.34 A decomposition reaction has a rate constant of 0.0012 yr 1, {a) What is the half-life of the reaction” (b) How long does it take for [reactant] to reach 12.5% of its original value? Theories of Chemical Kinetics (Sample Problems 16.8 and 16.9) 16.35 What is the central idea of collision theory? How does this model explain the effect of concentration on reaction rate’? 16.36 Is collision frequency the only factor affecting rate”? Explain. 16.37 Arrhenius proposed that each reaction has an energy threshold that must be reached for the particles to react. The kinetic theory of gases proposes that the average kinetic energy of the particles is proportional to the absolute temperature. How do these concepts relate to the effect of temperature on rate? 16.38 Use the exponential term in the Arrhenius equation to explain how temperature affects reaction rate, 16.35 How is the activation energy determined from the Arrhenius equation”’ 16.40 (a) Graph the relationship between k (vertical axis) and 7' (horizontal axis). (b) Graph the relationship between In k (vertical axis) and /T (horizontal axis). How is the activation energy determined from this graph” 16.41 (a) For a reaction with a given E,. how does an increase in T affect the rate? (b) For a reaction at a given T, how does a decrease in £ affect the rate? 16.42 Assuming the activation energies are equal. which of the following reactions will proceed at a higher rate at 50°C? Explain. NH;(g) + HClg) — NH,Cl(s) N(CH;)s(g) + HCl(g) —— (CH,);NHCl(s) 16.42 For the reaction A(g) + B(g) — AB(g). how many unigue collisions between A and B are possible if there are four particles of A and three particles of B present in the vessel? 16.44 For the reaction A(g) + B(g) — AB(g). how many unique collisions between A and B are possible if 1.01 mol of A(g) and 2.12 mol of B(g) are present in the vessel”? 16.45 AL 25°C. what is the fraction of collisions with energ: to or greater than an activation energy of 100, kJ/mol”? 1646 If the temperature in Problem 16.45 is increased 1o 50 what factor does the fraction of collisions with energy equ greater than the activation encrgy change? 16.47 The rate constant of a reaction is 4.7x 03 s lhat 25 the activation energy is 33.6 kJ/mol. What is & at 75°C 16.48 The rate constant of a reaction is 450107 L/me 195°C and 3.20x 10" L/mol-s at 258°C. What is the acti energy ol the reaction” 1645 For the reaction ABC + D === AR + CD. AH =55 k¥/mol and £, , = 215 ki/mol. Assuming a on reacuon, (a) draw a reaction energy diagran: (b) calculate , and (¢) sketch a possible transition state if ABC is V-shaped. 1650 For the reaction A, + B, — 2AB, Eopwgy = 125 kd/me Ly = 85 kJ/mol. Assuming the reaction occurs in onc (a) draw a reaction energy diagram: (b) calculate AH,,, (¢) sketch a possible transition state. 16.51 Understanding the high-temperature formation and b down of the nitrogen oxides is essential for controlling the lutants generated from power plants and cars. The firsi- breakdown of dinitrogen monoxide 1o its elements has rat stants of 0.76/s at 727°C and 0.87/s at 757°C. What is the 1. tion energy of this reaction” 16.52 Aqua regia. a mixture of HCI and HNO;, has been since alchemical times to dissolve many metals. including go: orange color is due to the presence of nitrosyl chloride. Con this one-step reaction for the formation of this compound: NO(g) + Clyg) — NOCl(g) + Cl(g) AH®= 831 (@) Draw a reaction energy diagram, given L fog, 18 86 KI/mi {b) Calculate £, .., (¢) Sketch a possible transition state for the reaction. (Note atom sequence of nitrosyl chloride is C—N—0Q.) Reaction Niechanisms: The Steps from Reacta:. to Product (Sample Problem 16.10) 16.53 Is the rate of an overall reaction lower, higher, or equatl «: average rate of the individual steps? Explain. 16.54 Explain why the coefficients of an elementary step ¢ the reaction orders of its rate law but those of an overall re. do not. 16.55 Is it possible for more than one mechanisim to be consi- with the rate law of a given reaction? Explain. 16.56 What is the difference between a reaction intermediatc . a transition state? 16.57 Why is a bimolecular step more reasonable physically ¢! a termolecular step? 16.58 If a slow step precedes a fast slep in a two-step mechar do the substances in the fast step appear in the rate law? Expluis: 1652 A proposed mechanism for the reaction of carbon dio:. with hydroxide ion in aqueous solution is (1) COy(ag) + OH (ag) — HCO; (ug) [slow (2) HCO; (ag) + OH (ag) —— CO;* " (ag) + HyO() [fasr: