Use the exponential term in the Arrhenius equation to

Problem 89P Consider the following organic reaction, in which one halogen replaces another in an alkyl halide: CH3CH2Br + KI ? CH3CH2I + 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 16.19, with I? instead of OH?). After Br" has been replaced by F and precipitates as KBr, other I? ions react with the ethyl iodide by the same mechanism. (a) If we designate the carbon bonded to the halogen as C-l, what is the shape around C-l and the hybridization of C-l in ethyl iodide? ________________ (b) In the transition state, one of the two lobes of the unhybridized 2 p orbital of C-l overlaps a p orbital of I, while the other lobe overlaps a p orbital of Br. What is the shape around C-l and the hybridization of C-l in the transition state? ________________ (c) The deuterated reactant, CH3CHDBr (where D is deuterium, 2H), has two optical isomers because C-l is chiral. If the reaction is run with one of the isomers, the ethyl iodide is not optically active. Explain.

\(A\) (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? Equation Transcription: Text Transcription: A B C

Problem 87P Chlorine is commonly used to disinfect drinking water, and inactivation of pathogens by chlorine follows first-order kinetics. The following data show E. coli inactivation: 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 × (1 ? [A]t/[A]0).] ________________ (b) How much contact time is required for 95% inactivation?

Figure \(16.21\) (p. \(542\)) shows key steps in the metal-catalyzed (M) hydrogenation of ethylene: \(\mathrm{C}_{2} \mathrm{H}_{4}(g)+\mathrm{H}_{2}(g) \stackrel{\mathrm{M}}{\longrightarrow} \mathrm{C}_{2} \mathrm{H}_{6}(g)\) Use the following symbols to write a mechanism that gives the overall equation: \(\mathrm{H}_{2}(\mathrm{ads})\) adsorbed hydrogen molecules M?H hydrogen atoms bonded to metal atoms \(\mathrm{C}_{2} \mathrm{H}_{4}(\mathrm{ads})\) adsorbed ethylene molecules \(\mathrm{C}_{2} \mathrm{H}_{5} \text { (ads) }\) adsorbed ethyl radicals Equation Transcription: H2(ads) C2H4(ads) C2H5(ads) Text Transcription: 16.21 542 C_2H_4(g)+H_2(g) rightarrow^M C_2H_6(g) H_2(ads) C_2H_4(ads) C_2H_5(ads)

The reaction and rate law for the gas-phase decomposition of dinitrogen pentaoxide are \(2 \mathrm{~N}_{2} \mathrm{O}_{5}(g) \longrightarrow 4 \mathrm{NO}_{2}(g)+\mathrm{O}_{2}(g) \quad \text { rate }=k\left[\mathrm{~N}_{2} \mathrm{O}_{5}\right]\) Which of the following can be considered valid mechanisms for the reaction? Equation Transcription: Text Transcription: 2N_2O_5(g) rightarrow 4NO_2(g)+O_2(g) rate=k[N_2O_5]

Problem 1P What variable of a chemical reaction is measured over time to obtain the reaction rate?

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.

Problem 6P In a kinetics experiment, a chemist places crystals of iodine in a closed reaction vessel, introduces a given quantity of hydrogen gas, and obtains data to calculate the rate of hydrogen iodide formation. In a second experiment, she uses the same amounts of iodine and hydrogen, but first warms the flask to 130°C, a temperature above the sublimation point of iodine. In which of these experiments does the reaction proceed at a higher rale? Explain.

Problem 5P How does an increase in temperature affect the rate of a reaction? Explain the two factors involved.

Problem 2P How does an increase in pressure affect the rate of a gas- phase reaction? Explain.

Problem 4P 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.

Problem 7P Define reaction rate. Assuming constant temperature and a closed reaction vessel, why does the rate change with time?

Problem 8P (a) 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?

Problem 9P Give two reasons to measure initial rates in a kinetics study.

For the reaction \(C(g) D(g), [C]\) vs. time is plotted: How do you determine each of the following? (a) The average rate over the entire experiment (b) The reaction rate at time \(x\) (c) The initial reaction rate (d) Would the values in parts (a), (b), and (c) be different if you plotted [D] vs. time? Explain. Equation Transcription: Text Transcription: C(g) D(g), [C] ????

Problem 10P For the reaction A(g) ? B(g), sketch two curves on the same set of axes that show (a) The formation of product as a function of time ________________ (b) The consumption of reactant as a function of time

Problem 12P The compound AX2 decomposes according to the equation 2AX2( g) ?2AX( g) + X2( g). In one experiment, [AX2] was measured at various times and these data were obtained: Time (s) [AX2] (mol/L) 0.0 0.0500 2.0 0.0448 6.00 0.0300 8.0 0.0249 10.0 0.0209 20.0 0.0088 (a) Find the average rate over the entire experiment. ________________ (b) Is the initial rate higher or lower than the rate in part (a)? Use graphical methods to estimate the initial rate.

Reaction rate is expressed in terms of changes in concentration of reactants and products. Write a balanced equation for \(\text { Rate }=-\frac{1}{2} \frac{\Delta\left[\mathrm{N}_{2} \mathrm{O}_{5}\right]}{\Delta t}=\frac{1}{4} \frac{\Delta\left[\mathrm{NO}_{2}\right]}{\Delta t}=\frac{\Delta\left[\mathrm{O}_{2}\right]}{\Delta t}\) Equation Transcription: Text Transcription: Rate=-1/2 Delta[N_2O_5]/Delta t = 1/4 Delta[NO_2]/Delta t=Delta[O_2]/Detla t

Reaction rate is expressed in terms of changes in concentration of reactants and products. Write a balanced equation for \(\text { Rate }=-\frac{\Delta\left[\mathrm{CH}_{4}\right]}{\Delta t}=\mid-\frac{1}{2} \frac{\Delta\left[\mathrm{O}_{2}\right]}{\Delta t}=\frac{1}{2} \frac{\Delta\left[\mathrm{H}_{2} \mathrm{O}\right]}{\Delta t}=\frac{\Delta\left[\mathrm{CO}_{2}\right]}{\Delta t}\) Equation Transcription: Text Transcription: Rate=-Delta[CH_4]/Delta t=|-½ Delta[O_2]/Detla t=1/2 Delta[H_2O]/Delta t=Delta[CO_2]/Delta t

Problem 13P (a) Use the data from Problem 16.12 to calculate the average rate from 8.0 to 20.0 s. ________________ (b) Is the rate at exactly 5.0 s higher or lower than the rate in part (a)? Use graphical methods to estimate the rate at 5.0 s.

The rate law for the general reaction \(a \mathrm{~A}+b \mathrm{~B}+\cdots \longrightarrow c \mathrm{C}+d \mathrm{D}+\cdots\) is rate = \(k[\mathrm{~A}]^{m}[\mathrm{~B}]^{n} \cdots\) (a) Explain the meaning of ????. (b) Explain the meanings of ???? and ????. Does ???? = ???? and ???? = ????? Explain. (c) If the reaction is first order in A and second order in B, and time is measured in minutes (min), what are the units for ????? Equation Transcription: Text Transcription: aA+bB+... rightarrow cC+dD+... k[A]^m[B]^n...

Problem 19P Although the depletion of stratospheric ozone threatens life on Earth today, its accumulation was one of the crucial processes that allowed life to develop in prehistoric times: 3O2(g)?2O3( g) (a) Express the reaction rate in terms of [O2] and [O3]. ________________ (b) At a given instant, the reaction rate in terms of fo2] is 2.17 × 10?5 mol/L·s. What is it in terms of [O3]?

Problem 18P The decomposition of NOBr is studied manometrically because the number of moles of gas changes; it cannot be studied colorimetrically because both NOBr and Br2 are reddish brown: 2NOBr(g) ?2NO(g) + Br2(g) Use the data below to answer the following: (a) Determine the average rate over the entire experiment. ________________ (b) Determine the average rate between 2.00 and 4.00 s. ________________ (c) Use graphical methods to estimate the initial reaction rate. ________________ (d) Use graphical methods to estimate the rate at 7.00 s. ________________ (e) At what time does the instantaneous rate equal the average rate over the entire experiment? Time (s) [NOBr] (mol/L) 0.00 0.0100 2.00 0.0071 4.00 0.0055 6.00 0.0045 8.00 0.0038 10.00 0.0033

Problem 21P 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. ________________ (c) A reaction is second order in reactant C, and [C] is tripled.

Give the individual reaction orders for all substances and the overall reaction order from the following rate law: \(\text { Rate }=k \frac{\left[\mathrm{O}_{3}\right]^{2}}{\left[\mathrm{O}_{2}\right]}\) Equation Transcription: Text Transcription: Rate=k [O_3]^2/[O_2]

Give the individual reaction orders for all substances and the overall reaction order from the following rate law: \(\text { Rate }=k\left[\mathrm{BrO}_{3}{ }^{-}\right]\left[\mathrm{Br}^{-}\right]\left[\mathrm{H}^{+}\right]^{2}\) Equation Transcription: Text Transcription: Rate=k[BrO_3^-][Br^-][H^+]^2

Problem 26P For the reaction 4A(g) + 3B(g) ?2C(g) the following data were obtained at constant temperature: Experiment (mol/L) Initial [A] (mol/L) Initial [B] (mol/L·min) Initial Rate 1 0.100 0.100 5.00 2 0.300 0.100 45.0 3 0.100 0.200 10.0 4 0.300 0.200 90.0 (a) What is the order with respect to each reactant? (b) Write the rate law. (c) Calculate k (using the data from experiment 1).

Problem 28P Phosgene is a toxic gas prepared by the reaction of carbon monoxide with chlorine: CO(g) + Cl2(g)?COCl2(g) These data were obtained in a kinetics study of its formation: Experiment Initial [CO] (mol/L) Initial [Cl2] (mol/L) Initial Rate (mol/L·s) 1 1.00 0.100 1.29 × 10?29 2 0.100 0.100 1.33 × 10?30 3 0.100 1.00 1.30 × 10?29 4 0.100 0.0100 1.32 × 10?31 (a) Write the rate law for the formation of phosgene. ________________ (b) Calculate the average value of the rate constant.

Problem 25P By what factor does the rate in Problem 16.27 change if each of the following changes occurs: (a) [O3] is doubled; (b) [O2] is doubled; (c) [O2] is halved?

Problem 27P For the reaction A(s) + B(g) + C(g)?D(s) the following data were obtained at constant temperature: Expt (mol/L) Initial [A] (mol/L) Initial [B] (mol/L) Initial [C] (mol/L·s) Initial Rate 1 0.0500 0.0500 0.0100 6.25X10-3 2 0.1000 0.0500 0.0100 1.25X10-2 3 0.1000 0.1000 0.0100 5.00X10-2 4 0.0500 0.0500 0.0200 6.25 × 10-3 (a) What is the order with respect to each reactant? (b) Write the rate law. (c) Calculate k (using the data from experiment 1).

Problem 24P By what factor does the rate in Problem 16.26 change if each of the following changes occurs: (a) [BrO3?] is doubled; (b) [Br ?] is halved; (c) [H+] is quadrupled?

Problem 29P How are integrated rate laws used to determine reaction order? What is the order in reactant if a plot of (a) The natural logarithm of [reactant] vs. time is linear? ________________ (b) The inverse of [reactant] vs. time is linear? ________________ (c) [Reactant] vs. time is linear?

Problem 30P Define the half-life of a reaction. Explain on the molecular level why the half-life of a first-order reaction is constant.

Problem 32P For the reaction in Problem 16.41, what is [AB] after 10.0 s?

Problem 33P In a first-order decomposition reaction, 50.0% of a compound 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?

For the simple decomposition reaction \(\mathrm{AB}(g) \longrightarrow \mathrm{A}(g)+\mathrm{B}(g)\) \(\text { rate }=k[\mathrm{AB}]^{2}\) and \(k=0.2 \mathrm{~L} / \mathrm{mol} \cdot \mathrm{s}\). How long will it take for [AB] to reach \(\frac{1}{3}\) of its initial concentration of \(1.50 M\)? Equation Transcription: rate ? ????[AB]2 ???? ? 0.2 L/mols 1.50 M Text Transcription: AB(g) rightarrow A(g)+B(g) rate ? ????[AB]^2 ???? ? 0.2 L/mols 1/3 1.50 M

Problem 35P Use the exponential term in the Arrhenius equation to explain how temperature affects reaction rate.

Problem 34P 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?

Problem 36P How is the activation energy determined from the Arrhenius equation?

Problem 40P Understanding the high-temperature formation and breakdown of the nitrogen oxides is essential for controlling the pollutants generated from power plants and cars. The first-order breakdown of dinitrogen monoxide to its elements has rate constants of 0.76/s at 727°C and 0.87/s at 757°C. What is the activation energy of this reaction?

Problem 41P What is the central idea of collision theory? How does this idea explain the effect of concentration on reaction rate?

Problem 37P (a) Graph the relationship between k (y axis) and T (x axis), (b) Graph the relationship between In k (y axis) and 1/T (x axis). How is the activation energy determined from this graph?

Problem 38P The rate constant of a reaction is 4.7 × 10?3 s?1 at 25°C, and the activation energy is 33.6 kJ/mol. What is k at 75°C?

Problem 42P Is collision frequency the only factor affecting rate? Explain.

Problem 39P The rate constant of a reaction is 4.50 × 10?5 L/mol-s at 195°C and 3.20 × 10?3 L/mol·s at 258°C. What is the activation energy of the reaction?

Problem 45P Assuming the activation energies are equal, which of the following reactions will occur at a higher rate at 50°C? Explain. NH3(g) + HCl(g)?NH4C1(S) N(CH3)3(g) + HCl(g)?(CH3)3NHCl(s)

Problem 44P (a) For a reaction with a given Ea, how does an increase in T affect the rate? (b) For a reaction at a given T, how does a decrease in Ea affect the rate?

Problem 46P For the reaction A(g) + B(g) ? AB(g), how many unique collisions between A and B are possible if there are four particles of A and three particles of B present in the vessel?

Problem 43P 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?

Problem 47P 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?

Problem 48P At 25°C, what is the fraction of collisions with energy equal to or greater than an activation energy of 100. kJ/mol?

For the reaction \(\mathrm{ABC}+\mathrm{D} \rightleftharpoons \mathrm{AB}+\mathrm{CD}\), \(\Delta H_{rxn}^{\circ}=-55 \mathrm{~kJ} / \mathrm{mol}\) and \(\mathrm{E}_{\text {a(fwd) }} 215 \mathrm{~kJ} / \mathrm{mol}\). Assuming a one-step reaction, (a) draw a reaction energy diagram; (b) calculate \(E_{a(r e v)}\); and (c) sketch a possible transition state if ABC is V-shaped. Equation Transcription: <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ABC</mi><mo>&#xA0;</mo><mo>+</mo><mo>&#xA0;</mo><mi mathvariant="normal">D</mi><mo>&#xA0;</mo><mo>&#x21CC;</mo><mi>AB</mi><mo>&#xA0;</mo><mo>+</mo><mo>&#xA0;</mo><mi>CD</mi></math> <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>&#x2206;</mo><msubsup><mi>&#x397;</mi><mi mathvariant="italic">rxn</mi><mo mathvariant="italic">&#xB0;</mo></msubsup><mo mathvariant="italic">&#xA0;</mo><mo mathvariant="italic">=</mo><mo>-</mo><mn>55</mn><mo>&#xA0;</mo><mi>kJ</mi><mo>/</mo><mi>mol</mi></math> Ea(fwd) 215 kJ/mol Ea(rev) Text Transcription: ABC+D rightleft harpoon AB+CD Delta H^degree_rxn=-55kJ/mol E_a(fwd) 215 kJ/mol E_a(rev)

Problem 54P Explain why the coefficients of an elementary step equal the reaction orders of its rate law but those of an overall reaction do not.

Problem 53P Is the rate of an overall reaction lower, higher, or equal to the average rate of the individual steps? Explain.

For the reaction \(\mathrm{A}_{2}+\mathrm{B}_{2} \rightarrow 2 \mathrm{AB}, E_{\mathrm{a}(\text { fwd })}=125 \mathrm{~kJ} / \mathrm{mol}\) and \(E_{\mathrm{a}(\mathrm{rev})}=85 \mathrm{~kJ} / \mathrm{mol}\). Assuming the reaction occurs in one step, (a) draw a reaction energy diagram; (b) calculate \(\Delta H_{r x n}^{\circ}\); and (c) sketch a possible transition state. Equation Transcription: A2 + B2 2AB, Ea(fwd) = 125 kJ/mol Ea(rev) = 85 kJ/mol Text Transcription: A_2+B_2 rightarrow 2AB,E_a(fwd)=125kJ/mol E_a(rev)=85kJ/mol Delta H^degree_rxn

Problem 49P If the temperature in Problem 16.60 is increased to 50.°C, by what factor does the fraction of collisions with energy equal to or greater than the activation energy change?

Problem 56P What is the difference between a reaction intermediate and a transition state?

Aqua regia, a mixture of HCl and \(\mathrm{HNO}_{3}\), has been used since alchemical times to dissolve many metals, including gold. Its orange color is due to the presence of nitrosyl chloride. Consider this one-step reaction for the formation of this compound: \(\mathrm{NO}(g)+\mathrm{Cl}_{2}(g) \longrightarrow \mathrm{NOCl}(g)+\mathrm{Cl}(g) \quad \Delta H^{\circ}=83 \mathrm{~kJ}\) (a) Draw a reaction energy diagram, given \(E_{\mathrm{a}(\text { fwd })} \text { is } 86 \mathrm{~kJ} / \mathrm{mol} \text {. }\). (b) Calculate \(E_{\mathrm{a}(\mathrm{rev})}\). (c) Sketch a possible transition state for the reaction. (Note: The atom sequence of nitrosyl chloride is Cl?N?O.) Equation Transcription: HNO3 Ea(fwd) is 86 kJ/mol Ea(rev) Text Transcription: HNO_3 NO(g)+Cl_2(g) rightarrow NOCl(g)+Cl(g) Delta H^degree=83kJ E_a(fwd) is 86 kJ/mol E_a(rev)

Problem 57P Why is a bimolecular step more reasonable physically than a termolecular step?

Problem 58P If a slow step precedes a fast step in a two-step mechanism, do the substances in the fast step appear in the rate law? Explain.

Problem 55P Is it possible for more than one mechanism to be consistent with the rate law of a given reaction? Explain.

The proposed mechanism for a reaction is (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 actual rate law: \(\text { rate }=k[\mathrm{~A}][\mathrm{B}][\mathrm{C}]\)? (e) Is the following one-step mechanism equally valid: \(\mathrm{A}(g)+\mathrm{B}(g)+\mathrm{C}(g) \longrightarrow \mathrm{D}(g) ?\) Equation Transcription: rate = ????[A][B][C] Text Transcription: rate=k[A][B][C] A(g)+B(g)+C(g) rightarrow D(g)

Consider the following mechanism: (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 actual rate law: \(\text { rate }=k\left[\mathrm{ClO}^{-}\right]\left[\mathrm{I}^{-}\right] ?\) Equation Transcription: Text Transcription: rate=k[ClO^-][I^-]?

In a study of nitrosyl halides, a chemist proposes the following mechanism for the synthesis of nitrosyl bromide: If the rate law is \(\text { rate }=k[\mathrm{NO}]^{2}\left[\mathrm{Br}_{2}\right]\), is the proposed mechanism valid? If so, show that it satisfies the three criteria for validity. Equation Transcription: rate = ????[NO]2[Br2] Text Transcription: rate = ????[NO]^2[Br_2]

Problem 66P Does a catalyst increase reaction rate by the same means as a rise in temperature does? Explain.

The rate law for \(2 \mathrm{NO}(g)+\mathrm{O}_{2}(g) \rightarrow 2 \mathrm{NO}_{2}(g)\) is \(\text { rate }=k[\mathrm{NO}]^{2}\left[\mathrm{O}_{2}\right]\). In addition to the mechanism in the text, the following ones have been proposed: (a) Which of these mechanisms is consistent with the rate law? (b) Which is most reasonable chemically? Why? Equation Transcription: 2NO(????) + O2(????) 2NO2(????) rate = ????[NO]2[O2] Text Transcription: 2NO(g)+O_2(g) rightarrow 2NO_2(g) rate=k[NO]^2[O_2]

Consider the reaction \(\mathrm{N}_{2} \mathrm{O}(g) \stackrel{\mathrm{Au}}{\longrightarrow} \mathrm{N}_{2}(g)+\frac{1}{2} \mathrm{O}_{2}(g)\). (a) Is the gold a homogeneous or a heterogeneous catalyst? (b) On the same set of axes, sketch the reaction energy diagrams for the catalyzed and the uncatalyzed reactions. Equation Transcription: Text Transcription: N_2O(g) rightarrow^Au N_2(g)+1/2O_2(g)

Consider the following reaction energy \(diagram\): (a) How many elementary steps are in the reaction mechanism? (b) Which step is rate limiting? (c) Is the overall reaction exothermic or endothermic? Equation Transcription: Text Transcription: diagram

Problem 68P The catalytic destruction of ozone occurs via a two-step mechanism, where X can be any of several species: (1) X + O3?XO + O2 [slow] (2) XO + O ?X + O2 [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 into the stratosphere, which catalyzes this process. When O3 and NO concentrations are 5 × 1012 molecule/cm3 and 1.0 × 109 molecule/cm, respectively, what is the rate of O3 depletion ( k for the rate-determining step is 6 × 10?15 cm3/molecule·s)?

Problem 69P A slightly bruised apple will rot extensively in about 4 days at room temperature (20°C). If it is kept in the refrigerator at 0°C, the same extent of rotting takes about 16 days What is the activation energy for the rotting reaction?

Problem 70P Benzoyl peroxide, the substance most widely used against acne, has a half-life of 9.8 × 103 days when refrigerated. How long will it take to lose 5% of its potency (95% remaining)?

The rate law for the reaction is \(\text { rate }=k\left[\mathrm{NO}_{2}\right]^{2}\); one possible mechanism is shown on p. 537. (a) Draw a reaction energy diagram for that mechanism, given that \(\Delta H_{\text {overall }}^{\circ}=226 \mathrm{~kJ} / \mathrm{mol}\). (b) The following alternative mechanism has been proposed: Is the alternative mechanism consistent with the rate law? Is one mechanism more reasonable physically? Explain. Equation Transcription: rate = ????[NO2]2 = 226 kJ/mol Text Transcription: rate = ????[NO_2]^2 Delta H_overall°= 226 kJ/mol

The following molecular scenes represent starting mixtures ? and ? for the reaction of A (black) with B (orange): Each sphere counts as \(0.010 mol\), and the volume is \(0.50 L\). If the initial rate in ? is \(8.3 \times 10^{-4} \mathrm{~mol} / \mathrm{L} \cdot \min\), what is the initial rate in ?? Equation Transcription: 8.310-4 mol/Lmin Text Transcription: 0.010 mol 0.50 L 8.310^-4 mol/L times min

Problem 75P At body temperature (37°C), k of an enzyme-catalyzed reaction is 2.3 × 1014 times greater than k of the uncatalyzed reaction. Assuming that the frequency factor A is the same for both reactions, by how much does the enzyme lower the Ea ?

Problem 76P A biochemist studying breakdown of the insecticide DDT finds that it decomposes by a first-order reaction with a half-life of 12 yr. How long does it take DDT in a soil sample to decompose from 275 ppbm to 10. ppbm (parts per billion by mass)?

Problem 72P 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 ?

The hydrolysis of sucrose occurs by this overall reaction: A nutritional biochemist obtains the following kinetic data: (a) Determine the rate constant and the half-life of the reaction. (b) How long does it take to hydrolyze \(75%\) of the sucrose? (c) Other studies have shown that this reaction is actually second order overall but appears to follow first-order kinetics. (Such a reaction is called a pseudo–first-order reaction.) Suggest a reason for this apparent first-order behavior. Equation Transcription: Text Transcription: 75%

The molecular scenes below represent the first-order reaction as cyclopropane \((red)\) is converted to propene \((green)\): Determine (a) the half-life and (b) the first-order rate constant. Equation Transcription: Text Transcription: (red) (green)

Even when a mechanism is consistent with the rate law, later experimentation may show it to be incorrect or only one of several alternatives. As an example, the reaction between hydrogen and iodine has the following rate law: \(\text { rate }=k\left[\mathrm{H}_{2}\right]\left[\mathrm{I}_{2}\right]\). The long-accepted mechanism proposed a single bimolecular step; that is, the overall reaction was thought to be elementary: In the 1960s, however, spectroscopic evidence showed the presence of free I atoms during the reaction. Kineticists have since proposed a three-step mechanism: Equation Transcription: rate = ????[H2][I2] Text Transcription: rate = ????[H_2][I_2]

Problem 79P Is each of these statements true? If not, explain why. (a) At a given T, all molecules have the same kinetic energy. ________________ (b) Halving the P of a gaseous reaction doubles the rate. ________________ (c) A higher activation energy gives a lower reaction rate. ________________ (d) A temperature rise of 10°C doubles the rate of any reaction. ________________ (e) If reactant molecules collide with greater energy than the activation energy, they change into product molecules. ________________ (f) The activation energy of a reaction depends on temperature. ________________ (g) The rate of a reaction increases as the reaction proceeds. ________________ (h) Activation energy depends on collision frequency. ________________ (i) A catalyst increases the rate by increasing collision frequency, ________________ (j) Exothermic reactions are faster than endothermic reactions, ________________ (k) Temperature has no effect on the frequency factor (A). ________________ (l) The activation energy of a reaction is lowered by a catalyst, ________________ (m) For most reactions, ? Hrxn is lowered by a catalyst, ________________ (n) The orientation probability factor (p) is near 1 for reactions between single atoms. ________________ (o) The initial rate of a reaction is its maximum rate. ________________ (p) A bimolecular reaction is generally twice as fast as a uni-molecular reaction. ________________ (q) The molecularity of an elementary reaction is proportional to the molecular complexity of the reactant(s).

Problem 82P Many drugs decompose in blood by a first-order process. (a) Two tablets of aspirin supply 0.60 g of the active compound. After 30 min, this compound reaches a maximum concentration of 2 mg/100 mL of blood. If the half-life for its breakdown is 90 min, what is its concentration (in mg/100 mL) 2.5 h after it reaches its maximum concentration? ________________ (b) For the decomposition of an antibiotic in a person with a normal temperature (98.6°F), k = 3.1 × 10?5 s?l for a person with a fever at 101.9°F, k = 3.9 × 10?5 s?l. If the person with the fever must take another pill when ? of the first pill has decomposed, how many hours should she wait to take a second pill? A third pill? (Assume the pill is effective immediately.) ________________ (c) Calculate Ea for decomposition of the antibiotic in part (b).

The scenes depict four initial reaction mixtures for the reaction of A (blue) and B (yellow), with and without a solid present (gray cubes). The initial rate, \(\Delta[\mathrm{A}] \Delta / \mathrm{t}(\text { in } \mathrm{mol} / \mathrm{L} \cdot \mathrm{s})\), is shown for each sphere representing 0.010 mol and the container volume at \(0.50 L\). (a) What is the rate law in the absence of a catalyst? (b) What is the overall reaction order? (c) Find the rate constant. (d) Do the gray cubes have a catalytic effect? Explain. Equation Transcription: [A]/t (in mol/Ls) Text Transcription: Delta [A]Delta/t (in mol/L timess) 0.50 L

Problem 86P Like any catalyst, palladium, platinum, and nickel catalyze both directions of a reaction: addition of hydrogen to (hydrogénation) and its elimination from (dehydrogenation) carbon double bonds. (a) Which variable determines whether an alkene will be hydrogenated or dehydrogenated? ________________ (b) Which reaction requires a higher temperature? ________________ (c) How can all- Trans fats arise during hydrogénation of fats that contain some cis- double bonds?

In the lower atmosphere, ozone is one of the components of photochemical smog. It is generated in air when nitrogen dioxide, formed by the oxidation of nitrogen monoxide from car exhaust, reacts by the following mechanism: Assuming the rate of formation of atomic oxygen in \(step 1\) equals the rate of its consumption in \(step 2\), use the data below to calculate (a) the concentration of atomic oxygen [O]; (b) the rate of ozone formation. Equation Transcription: Text Transcription: step 1 step 2