14.f^Chapter 14 Ending^499^509^,,^21553^22306%
Key Equations
 rate = k[A]x[B]y (14.1) Rate law expressions. The sum (x + y) gives the overall order of the reaction. (14.3) Relationship between concentration and time for a first-order reaction. ln [A]t = −kt + ln [A]0 (14.4) Equation for the graphical determination of k for a first-order reaction. (14.5) Half-life for a first-order reaction. (14.6) Relationship between concentration and time for a second-order reaction. [A]t = −kt + [A]0 (14.8) Relationship between concentration and time for a zero-order reaction. (14.10) The Arrhenius equation expressing the dependence of the rate constant on activation energy and temperature. (14.12) Equation for the graphical determination of activation energy. (14.13) Relationship of rate constants at two different temperatures.
Summary of Facts and Concepts
1. The rate of a chemical reaction is the change in the concentration of reactants or products over time. The rate is not constant, but varies continuously as concentrations change.

2. The rate law expresses the relationship of the rate of a reaction to the rate constant and the concentrations of the reactants raised to appropriate powers. The rate constant k for a given reaction changes only with temperature.

3. Reaction order is the power to which the concentration of a given reactant is raised in the rate law. Overall reaction order is the sum of the powers to which reactant concentrations are raised in the rate law. The rate law and the reaction order cannot be determined from the stoichiometry of the overall equation for a reaction; they must be determined by experiment. For a zero-order reaction, the reaction rate is equal to the rate constant.

4. Page 500
5. The half-life of a reaction (the time it takes for the concentration of a reactant to decrease by one-half) can be used to determine the rate constant of a first-order reaction.

6. In terms of collision theory, a reaction occurs when molecules collide with sufficient energy, called the activation energy, to break the bonds and initiate the reaction. The rate constant and the activation energy are related by the Arrhenius equation.

7. The overall balanced equation for a reaction may be the sum of a series of simple reactions, called elementary steps. The complete series of elementary steps for a reaction is the reaction mechanism.

8. If one step in a reaction mechanism is much slower than all other steps, it is the rate-determining step.

9. A catalyst speeds up a reaction usually by lowering the value of Ea. A catalyst can be recovered unchanged at the end of a reaction.

10. In heterogeneous catalysis, which is of great industrial importance, the catalyst is a solid and the reactants are gases or liquids. In homogeneous catalysis, the catalyst and the reactants are in the same phase. Enzymes are catalysts in living systems.

Questions and Problems
Reaction Rate
Review Questions
• 14.1 What is meant by the rate of a chemical reaction?

• 14.2 What are the units of the rate of a reaction?

• 14.3 What are the advantages of measuring the initial rate of a reaction?

• 14.4 Can you suggest two reactions that are very slow (take days or longer to complete) and two reactions that are very fast (are over in minutes or seconds)?

Problems
• 14.5 Write the reaction rate expressions for these reactions in terms of the disappearance of the reactants and the appearance of products:

1. H2(g) + I2(g) → 2HI(g)

2. 2H2(g) + O2(g) → 2H2O(g)

• 14.6 Consider the reaction

Suppose that at a particular moment during the reaction molecular hydrogen is reacting at the rate of 0.074 M/s. (a) At what rate is ammonia being formed? (b) At what rate is molecular nitrogen reacting?

Rate Laws
Review Questions
• 14.7 Explain what is meant by the rate law of a reaction.

• 14.8 What are the units for the rate constants of first-order and second-order reactions?

• 14.9 Write an equation relating the concentration of a reactant A at t = 0 to that at t = t for a first-order reaction. Define all the terms and give their units.

• 14.10 Consider the zero-order reaction A → product. (a) Write the rate law for the reaction. (b) What are the units for the rate constant? (c) Plot the rate of the reaction versus [A].

• 14.11 On which of these quantities does the rate constant of a reaction depend: (a) concentrations of reactants, (b) nature of reactants, (c) temperature?

• 14.12 For each of these pairs of reaction conditions, indicate which has the faster rate of formation of hydrogen gas: (a) sodium or potassium with water, (b) magnesium or iron with 1.0 M HCl, (c) magnesium rod or magnesium powder with 1.0 M HCl, (d) magnesium with 0.10 M HCl or magnesium with 1.0 M HCl.

Page 501
Problems
• 14.13 The rate law for the reaction

is given by . At 25°C, the rate constant is 3.0 × 10−4/M · s. Calculate the rate of the reaction at this temperature if M and .

• 14.14 Starting with the data in Table 14.1, (a) deduce the rate law for the reaction, (b) calculate the rate constant, and (c) calculate the rate of the reaction at the time when [F2] = 0.010 M and [ClO2] = 0.020 M.

• 14.15 Consider the reaction

From these data obtained at a certain temperature, determine the order of the reaction and calculate the rate constant:

[A] (M) [B] (M) Rate (M/s)
1.50 1.50 3.20 × 10−1
1.50 2.50 3.20 × 10−1
3.00 1.50 6.40 × 10−1
• 14.16 Consider the reaction

These data are obtained at 360 K:

Initial Rate of Disappearance of X (M/s) [X] [Y]
0.147 0.10 0.50
0.127 0.20 0.30
4.064 0.40 0.60
1.016 0.20 0.60
0.508 0.40 0.30

(a) Determine the order of the reaction. (b) Determine the initial rate of disappearance of X when the concentration of X is 0.30 M and that of Y is 0.40 M.

• 14.17 Determine the overall orders of the reactions to which these rate laws apply: (a) rate = k[NO2]2; (b) rate = k; (c) ; (d) rate = k[NO]2[O2].

• 14.18 Consider the reaction

The rate of the reaction is 1.6 × 10−2 M/s when the concentration of A is 0.35 M. Calculate the rate constant if the reaction is (a) first order in A, (b) second order in A.

Relationship Between Reactant Concentration and Time
Review Questions
• 14.19 Define the half-life of a reaction. Write the equation relating the half-life of a first-order reaction to the rate constant.

• 14.20 For a first-order reaction, how long will it take for the concentration of reactant to fall to one-eighth its original value? Express your answer in terms of the half-life () and in terms of the rate constant k.

Problems
• 14.21 What is the half-life of a compound if 75 percent of a given sample of the compound decomposes in 60 min? Assume first-order kinetics.

• 14.22 The thermal decomposition of phosphine (PH3) into phosphorus and molecular hydrogen is a first-order reaction:

The half-life of the reaction is 35.0 s at 680°C. Calculate (a) the first-order rate constant for the reaction and (b) the time required for 95 percent of the phosphine to decompose.

• 14.23 The rate constant for the second-order reaction

is 0.80/M · s at 10°C. (a) Starting with a concentration of 0.086 M, calculate the concentration of NOBr after 22 s. (b) Calculate the half-lives when [NOBr]0 = 0.072 M and [NOBr]0 = 0.054 M.

• 14.24 The rate constant for the second-order reaction

is 0.54/M · s at 300°C. (a) How long (in seconds) would it take for the concentration of NO2 to decrease from 0.62 M to 0.28 M? (b) Calculate the half-lives at these two concentrations.

• 14.25 Consider the first-order reaction A → B shown here. (a) What is the rate constant of the reaction? (b) How many A (yellow) and B (blue) molecules are present at t = 20 s and 30 s.

• 14.26 The reaction X → Y shown here follows first-order kinetics. Initially different amounts of X molecules are placed in three equal-volume containers at the same temperature. (a) What are the relative rates of the reaction in these three containers? (b) How would the relative rates be affected if the volume of each container were doubled? (c) What are the relative half-lives of the reactions in (i) to (iii)?

Page 502
Activation Energy
Review Questions
• 14.27 Define activation energy. What role does activation energy play in chemical kinetics?

• 14.28 Write the Arrhenius equation and define all terms.

• 14.29 Use the Arrhenius equation to show why the rate constant of a reaction (a) decreases with increasing activation energy and (b) increases with increasing temperature.

• 14.30 As we know, methane burns readily in oxygen in a highly exothermic reaction. Yet a mixture of methane and oxygen gas can be kept indefinitely without any apparent change. Explain.

• 14.31 Sketch a potential-energy-versus-reaction-progress plot for the following reactions:

1. S(s) + O2(g) → SO2(g) ΔH° = −296.06 kJ/mol

2. Cl2(g) → Cl(g) + Cl(g) ΔH° = 242.7 kJ/mol

• 14.32 The reaction H + H2 → H2 + H has been studied for many years. Sketch a potential-energy-versus-reaction-progress diagram for this reaction.

Problems
• 14.33 Variation of the rate constant with temperature for the first-order reaction

is given in the following table. Determine graphically the activation energy for the reaction.

T (K) k (s−1)
273 7.87 × 103
298 3.46 × 105
318 4.98 × 106
338 4.87 × 107
• 14.34 Given the same concentrations, the reaction

at 250°C is 1.50 × 103 times as fast as the same reaction at 150°C. Calculate the energy of activation for this reaction. Assume that the frequency factor is constant.

• 14.35 For the reaction

the frequency factor A is 8.7 × 1012 s−1 and the activation energy is 63 kJ/mol. What is the rate constant for the reaction at 75°C?

• 14.36 The rate constant of a first-order reaction is 4.60 × 10−4 s−1 at 350°C. If the activation energy is 104 kJ/mol, calculate the temperature at which its rate constant is 8.80 × 10−4 s−1.

• 14.37 The rate constants of some reactions double with every 10-degree rise in temperature. Assume a reaction takes place at 295 K and 305 K. What must the activation energy be for the rate constant to double as described?

• 14.38 The rate at which tree crickets chirp is 2.0 × 102 per minute at 27°C but only 39.6 per minute at 5°C. From these data, calculate the “energy of activation” for the chirping process. (Hint: The ratio of rates is equal to the ratio of rate constants.)

• 14.39 The diagram here describes the initial state of the reaction A2 + B2 → 2AB.

Suppose the reaction is carried out at two temperatures as shown below. Which picture represents the result at the higher temperature? (The reaction proceeds for the same amount of time at both temperatures.)

Reaction Mechanisms
Review Questions
• 14.40 What do we mean by the mechanism of a reaction? What is an elementary step?

• Page 503
• 14.41 Classify each of the following elementary steps as unimolecular, bimolecular, or termolecular.

• 14.42 Reactions can be classified as unimolecular, bimolecular, and so on. Why are there no zero-molecular reactions?

• 14.43 Explain why termolecular reactions are rare.

• 14.44 What is the rate-determining step of a reaction? Give an everyday analogy to illustrate the meaning of the term “rate determining.”

• 14.45 The equation for the combustion of ethane (C2H6) is

Explain why it is unlikely that this equation also represents the elementary step for the reaction.

• 14.46 Which of these species cannot be isolated in a reaction: activated complex, product, intermediate?

Problems
• 14.47 The rate law for the reaction

is given by rate = k[NO][Cl2]. (a) What is the order of the reaction? (b) A mechanism involving these steps has been proposed for the reaction

If this mechanism is correct, what does it imply about the relative rates of these two steps?

• 14.48 For the reaction X2 + Y + Z → XY + XZ it is found that doubling the concentration of X2 doubles the reaction rate, tripling the concentration of Y triples the rate, and doubling the concentration of Z has no effect. (a) What is the rate law for this reaction? (b) Why is it that the change in the concentration of Z has no effect on the rate? (c) Suggest a mechanism for the reaction that is consistent with the rate law.

Catalysis
Review Questions
• 14.49 How does a catalyst increase the rate of a reaction?

• 14.50 What are the characteristics of a catalyst?

• 14.51 A certain reaction is known to proceed slowly at room temperature. Is it possible to make the reaction proceed at a faster rate without changing the temperature?

• 14.52 Distinguish between homogeneous catalysis and heterogeneous catalysis. Describe some important industrial processes that utilize heterogeneous catalysis.

• 14.53 Are enzyme-catalyzed reactions examples of homogeneous or heterogeneous catalysis?

• 14.54 The concentrations of enzymes in cells are usually quite small. What is the biological significance of this fact?

Problems
• 14.55 Most reactions, including enzyme-catalyzed reactions, proceed faster at higher temperatures. However, for a given enzyme, the rate drops off abruptly at a certain temperature. Account for this behavior.

• 14.56 Consider this mechanism for the enzyme-catalyzed reaction

Derive an expression for the rate law of the reaction in terms of the concentrations of E and S. (Hint: To solve for [ES], make use of the fact that, at equilibrium, the rate of the forward reaction is equal to the rate of the reverse reaction.)

• 14.57 Suggest experimental means by which the rates of the following reactions could be followed:

1. CaCO3(s) → CaO(s) + CO2(g)

2. Cl2(g) + 2Br(aq) → Br2(aq) + 2Cl(aq)

3. C2H6(g) → C2H4(g) + H2(g)

• 14.58 The following diagrams represent the progress of the reaction A → B, where the red spheres represent A molecules and the green spheres represent B molecules. Calculate the rate constant of the reaction.

• Page 504
• 14.59 The following diagrams show the progress of the reaction 2A → A2. Determine whether the reaction is first order or second order and calculate the rate constant.

• 14.60 In a certain industrial process using a heterogeneous catalyst, the volume of the catalyst (in the shape of a sphere) is 10.0 cm3. Calculate the surface area of the catalyst. 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? Which of the two geometric configurations of the catalyst is more effective? Explain. (The surface area of a sphere is 4πr2, in which r is the radius of the sphere.)

• 14.61 When methyl phosphate is heated in acid solution, it reacts with water:

If the reaction is carried out in water enriched with 18O, the oxygen-18 isotope is found in the phosphoric acid product but not in the methanol. What does this tell us about the bond-breaking scheme in the reaction?

• 14.62 The rate of the reaction

shows first-order characteristics—that is, rate = k[CH3COOC2H5]—even though this is a second-order reaction (first order in CH3COOC2H5 and first order in H2O). Explain.

• 14.63 Explain why most metals used in catalysis are transition metals.

• 14.64 The bromination of acetone is acid-catalyzed:

The rate of disappearance of bromine was measured for several different concentrations of acetone, bromine, and H+ ions at a certain temperature:

[CH3COCH3] [Br2] [H+] Rate of Disappearance of Br2 (M/s)
(a) 0.30 0.050 0.050 5.7 × 10−5
(b) 0.30 0.10 0.050 5.7 × 10−5
(c) 0.30 0.050 0.10 1.2 × 10−4
(d) 0.40 0.050 0.20 3.1 × 10−4
(e) 0.40 0.050 0.050 7.6 × 10−5

(a) What is the rate law for the reaction? (b) Determine the rate constant.

• 14.65 The reaction 2A + 3B → C is first order with respect to A and B. When the initial concentrations are [A] = 1.6 × 10−2 M and [B] = 2.4 × 10−3 M, the rate is 4.1 × 10−4 M/s. Calculate the rate constant of the reaction.

• 14.66 The decomposition of N2O to N2 and O2 is a first-order reaction. At 730°C the half-life of the reaction is 3.58 × 103 min. If the initial pressure of N2O is 2.10 atm at 730°C, calculate the total gas pressure after one half-life. Assume that the volume remains constant.

• 14.67 The reaction proceeds slowly in aqueous solution, but it can be catalyzed by the Fe3+ ion. Given that Fe3+ can oxidize I and Fe2+ can reduce , write a plausible two-step mechanism for this reaction. Explain why the uncatalyzed reaction is slow.

• 14.68 What are the units of the rate constant for a third-order reaction?

• 14.69 Consider the zero-order reaction A → B. Sketch the following plots: (a) rate versus [A] and (b) [A] versus t.

• 14.70 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?

• 14.71 Referring to the decomposition of N2O5 in Problem 14.33, explain how you would measure the partial pressure of N2O5 as a function of time.

• 14.72 The rate law for the reaction 2NO2 (g) → N2O4(g) is rate = k[NO2]2.

Which of these changes will change the value of k? (a) The pressure of NO2 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.

• 14.73 The reaction of G2 with E2 to form 2EG is exothermic, and the reaction of G2 with X2 to form 2XG is endothermic. The activation energy of the exothermic reaction is greater than that of the endothermic reaction. Sketch the potential energy profile diagrams for these two reactions on the same graph.

• 14.74 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. (Hint: Radioactive decays obey first-order kinetics.)

• 14.75 Briefly comment on the effect of a catalyst on each of the following: (a) activation energy, (b) reaction mechanism, (c) enthalpy of reaction, (d) rate of forward step, (e) rate of reverse step.

• Page 505
• 14.76 A quantity of 6 g of granulated Zn is added to a solution of 2 M HCl in a beaker at room temperature. Hydrogen gas is generated. For each of the following changes (at constant volume of the acid) state whether the rate of hydrogen gas evolution will be increased, decreased, or unchanged: (a) 6 g of powdered Zn is used; (b) 4 g of granulated Zn is used; (c) 2 M acetic acid is used instead of 2 M HCl; (d) temperature is raised to 40°C.

• 14.77 These data were collected for the reaction between hydrogen and nitric oxide at 700°C:

Experiment [H2] [NO] Initial Rate (M/s)
1 0.010 0.025 2.4 × 10−6
2 0.0050 0.025 1.2 × 10−6
3 0.010 0.0125 0.60 × 10−6

(a) Determine the order of the reaction. (b) Calculate the rate constant. (c) Suggest a plausible mechanism that is consistent with the rate law. (Hint: Assume the oxygen atom is the intermediate.)

• 14.78 A certain first-order reaction is 35.5 percent complete in 4.90 min at 25°C. What is its rate constant?

• 14.79 The decomposition of dinitrogen pentoxide has been studied in carbon tetrachloride solvent (CCl4) at a certain temperature:

[N2O5] (M) Initial Rate (M/s)
0.92 0.95 × 10−5
1.23 1.20 × 10−5
1.79 1.93 × 10−5
2.00 2.10 × 10−5
2.21 2.26 × 10−5

Determine graphically the rate law for the reaction and calculate the rate constant.

• 14.80 The thermal decomposition of N2O5 obeys first-order kinetics. At 45°C, a plot of ln [N2O5] versus t gives a slope of −6.18 × 10−4 min−1. What is the half-life of the reaction?

• 14.81 When a mixture of methane and bromine is exposed to light, the following reaction occurs slowly:

Suggest a reasonable mechanism for this reaction. (Hint: Bromine vapor is deep red; methane is colorless.)

• 14.82 Consider this elementary step:

(a) Write a rate law for this reaction. (b) If the initial rate of formation of XY2 is 3.8 × 10−3 M/s and the initial concentrations of X and Y are 0.26 M and 0.88 M, what is the rate constant of the reaction?

• 14.83 Consider the reaction

How could you follow the progress of the reaction by measuring the electrical conductance of the solution?

• 14.84 A compound X undergoes two simultaneous first-order reactions as follows: X → Y with rate constant k1 and X → Z with rate constant k2. The ratio of k1/k2 at 40°C is 8.0. What is the ratio at 300°C? Assume that the frequency factor of the two reactions is the same.

• 14.85 In recent years ozone in the stratosphere has been depleted at an alarmingly fast rate by chlorofluoro-carbons (CFCs). A CFC molecule such as CFCl3 is first decomposed by UV radiation:

The chlorine radical then reacts with ozone as follows:

(a) Write the overall reaction for the last two steps. (b) What are the roles of Cl and ClO? (c) Why is the fluorine radical not important in this mechanism? (d) One suggestion to reduce the concentration of chlorine radicals is to add hydrocarbons such as ethane (C2H6) to the stratosphere. How will this work?

• 14.86 Consider a car fitted with a catalytic converter. The first 10 min or so after it is started are the most polluting. Why?

• 14.87 Strontium-90, a radioactive isotope, is a major product of an atomic bomb explosion. It has a half-life of 28.1 yr. (a) Calculate the first-order rate constant for the nuclear decay. (b) Calculate the fraction of 90Sr that remains after 10 half-lives. (c) Calculate the number of years required for 99.0 percent of 90Sr to disappear.

• 14.88 The following mechanism has been proposed for the reaction described in Problem 14.64:

Page 506

Show that the rate law deduced from the mechanism is consistent with that shown in (a) of Problem 14.64.

• 14.89 The integrated rate law for the zero-order reaction A → B is [A]t = [A]0kt. (a) Sketch the following plots: (i) rate versus [A]t and (ii) [A] t 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]t = 0.

• 14.90 Strictly speaking, the rate law derived for the reaction in Problem 14.77 applies only to certain concentrations of H2. The general rate law for the reaction takes the form

in which k1 and k2 are constants. Derive rate law expressions under the conditions of very high and very low hydrogen concentrations. Does the result from Problem 14.77 agree with one of the rate expressions here?

• 14.91 (a) What can you deduce about the activation energy of a reaction if its rate constant changes significantly with a small change in temperature? (b) If a bimolecular reaction occurs every time an A and a B molecule collide, what can you say about the orientation factor and activation energy of the reaction?

• 14.92 The rate law for this reaction

is rate = k[NO2]2. Suggest a plausible mechanism for the reaction, given that the unstable species NO3 is an intermediate.

• 14.93 Radioactive plutonium-239 ( = 2.44 × 105 yr) is used in nuclear reactors and atomic bombs. If there are 5.0 × 102 g of the isotope in a small atomic bomb, how long will it take for the substance to decay to 1.0 × 102 g, too small an amount for an effective bomb? (Hint: Radioactive decays follow first-order kinetics.)

• 14.94 Many reactions involving heterogeneous catalysts are zero order; that is, rate = k. An example is the decomposition of phosphine (PH3) over tungsten (W):

It is found that the reaction is independent of [PH3] as long as phosphine's pressure is sufficiently high (≥ 1 atm). Explain.

• 14.95 Thallium(I) is oxidized by cerium(IV) as follows:

The elementary steps, in the presence of Mn(II), are as follows:

(a) Identify the catalyst, intermediates, and the rate-determining step if the rate law is given by rate = k[Ce4+][Mn2+]. (b) Explain why the reaction is slow without the catalyst. (c) Classify the type of catalysis (homogeneous or heterogeneous).

• 14.96 Consider the following elementary steps for a consecutive reaction

(a) Write an expression for the rate of change of B. (b) Derive an expression for the concentration of B under steady-state conditions; that is, when B is decomposing to C at the same rate as it is formed from A.

• 14.97 For gas-phase reactions, we can replace the concentration terms in Equation (14.3) with the pressures of the gaseous reactant. (a) Derive the equation

where Pt and P0 are the pressures at t = t and t = 0, respectively. (b) Consider the decomposition of azomethane

The data obtained at 300°C are shown in the following table:

Time (s) Partial Pressure of Azomethane (mmHg)
0 284
100 220
150 193
200 170
250 150
300 132

Are these values consistent with first-order kinetics? If so, determine the rate constant by plotting the data as shown in Figure 14.7(b). (c) Determine the rate constant by the half-life method.

• 14.98 The hydrolysis of methyl acetate

Page 507

involves the breaking of a C—O bond. The two possibilities are

Suggest an experiment that would enable you to distinguish between these two possibilities.

• 14.99 The following gas-phase reaction was studied at 290°C by observing the change in pressure as a function of time in a constant-volume vessel:

Determine the order of the reaction and the rate constant based on the following data:

Time (s) P (mmHg)
0 15.76
181 18.88
513 22.79
1164 27.08

where P is the total pressure.

• 14.100 Consider the potential energy profiles for the following three reactions (from left to right). (1) Rank the rates (slowest to fastest) of the reactions. (2) Calculate ΔH for each reaction and determine which reaction(s) are exothermic and which reaction(s) are endothermic. Assume the reactions have roughly the same frequency factors.

• 14.101 Consider the following potential energy profile for the A → D reaction. (a) How many elementary steps are there? (b) How many intermediates are formed? (c) Which step is rate determining? (d) Is the overall reaction exothermic or endothermic?

• 14.102 Hydrogen and iodine monochloride react as follows:

The rate law for the reaction is rate = k[H2][ICl]. Suggest a possible mechanism for the reaction.

• 14.103 The activation energy for the decomposition of hydrogen peroxide

is 42 kJ/mol, whereas when the reaction is catalyzed by the enzyme catalase, it is 7.0 kJ/mol. Calculate the temperature that would cause the nonenzymatic catalysis to proceed as rapidly as the enzyme-catalyzed decomposition at 20°C. Assume the frequency factor A to be the same in both cases.

• 14.104 To carry out metabolism, oxygen is taken up by hemoglobin (Hb) to form oxyhemoglobin (HbO2) according to the simplified equation

where the second-order rate constant is 2.1 × 106/M · s at 37°C. (The reaction is first order in Hb and O2.) For an average adult, the concentrations of Hb and O2 in the blood at the lungs are 8.0 × 10−6 and 1.5 × 10−6 M, respectively. (a) Calculate the rate of formation of HbO2. (b) Calculate the rate of consumption of O2. (c) The rate of formation of HbO2 increases to 1.4 × 10−4 M/s during exercise to meet the demand of increased metabolism rate. Assuming the Hb concentration to remain the same, what must be the oxygen concentration to sustain this rate of HbO2 formation?

Special Problems
• 14.105 Polyethylene is used in many items such as water pipes, bottles, electrical insulation, toys, and mailer 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 (see p. 377). The initiation step is

The R · species (called a radical) reacts with an ethylene molecule (M) to generate another radical

Page 508

Reaction of M1 · with another monomer leads to the growth or propagation of the polymer chain:

This step can be repeated with hundreds of monomer units. The propagation terminates when two radicals combine

(a) The initiator used in the polymerization of ethylene is benzoyl peroxide [(C6H5COO)2]:

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−1) 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. (d) What condition would favor the growth of long high-molar-mass polyethylenes?

• 14.106 Ethanol is a toxic substance that, when consumed in excess, can impair respiratory and cardiac functions by interference with the neurotransmitters of the nervous system. In the human body, ethanol is metabolized by the enzyme alcohol dehydrogenase to acetaldehyde, which causes “hangovers.” (a) Based on your knowledge of enzyme kinetics, explain why binge drinking (that is, consuming too much alcohol too fast) can prove fatal. (b) Methanol is even more toxic than ethanol. It is also metabolized by alcohol dehydrogenase, and the product, formaldehyde, can cause blindness or death. An antidote to methanol poisoning is ethanol. Explain how this procedure works.

• 14.107 At a certain elevated temperature, ammonia decomposes on the surface of tungsten metal as follows:

From the following plot of the rate of the reaction versus the pressure of NH3, describe the mechanism of the reaction.

• 14.108 The following expression shows the dependence of the half-life of a reaction () on the initial reactant concentration [A]0:

where n is the order of the reaction. Verify this dependence for zero-, first-, and second-order reactions.

• 14.109 The rate constant for the gaseous reaction

is 2.42 × 10−2/M · s at 400°C. Initially an equimolar sample of H2 and I2 is placed in a vessel at 400°C and the total pressure is 1658 mmHg. (a) What is the initial rate (M/min) of formation of HI? (b) What are the rate of formation of HI and the concentration of HI (in molarity) after 10.0 min?

• 14.110 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. (Hint: Use the equation in Problem 14.108.)

• 14.111 The activation energy for the reaction

is 2.4 × 102 kJ/mol at 600 K. Calculate the percentage of the increase in rate from 600 K to 606 K. Comment on your results.

• 14.112 The rate of a reaction was followed by the absorption of light by the reactants and products as a function of wavelengths (λ1, λ2, λ3) as time progresses. Which of the following mechanisms is consistent with the experimental data?

1. A → B, A → C

2. A → B + C

3. A → B, B → C + D

4. A → B, B → C

• 14.113 A gas mixture containing CH3 fragments, C2H6 molecules, and an inert gas (He) was prepared at 600 K with a total pressure of 5.42 atm. The elementary reaction

Page 509

has a second-order rate constant of 3.0 × 104/M · s. Given that the mole fractions of CH3 and C2H6 are 0.00093 and 0.00077, respectively, calculate the initial rate of the reaction at this temperature.

• 14.114 To prevent brain damage, a drastic medical procedure is to lower the body temperature of someone who has suffered cardiac arrest. What is the physiochemical basis for this treatment?

• 14.115 The activation energy (Ea) for the reaction

is 240 kJ/mol. What is Ea for the reverse reaction?

• 14.1

• 14.2

(a) 0.013 M/s, (b) −0.052 M/s.

• 14.3

• 14.4

66 s.

• 14.5

1.2 × 103 s.

• 14.6

(a) 3.2 min, (b) 2.1 min.

• 14.7

240 kJ/mol.

• 14.8

3.13 × 10−9 s−1.

• 14.9

(a) NO2 + CO → NO + CO2, (b) NO3, (c) the first step is rate-determining.