The effect of substrate concentration on the first-order growth rate of a microbial

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

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

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.

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.

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

In a kinetics experiment, a chemist places crystals of iodine in a closed reaction vessel, introduces a given quantity of H2 gas, and obtains data to calculate the rate of HI formation. In a second experiment, she uses the same amounts of iodine and hydrogen, but first warms the flask to 1308C, a temperature above the sublimation point of iodine. In which of these experiments does the reaction proceed at a higher rate? Explain.

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

(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?

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

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

For the reaction C(g) - D(g), [C] vs. time is plotted: x [C] Time 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.

The compound AX2 decomposes according to the equation 2AX2(g) - 2AX(g) 1 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 6.0 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.

(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.

Express the rate of this reaction in terms of the change in concentration of each of the reactants and products: 2A(g) - B(g) 1 C(g) When [C] is increasing at 2 mol/Ls, how fast is [A] decreasing?

Express the rate of this reaction in terms of the change in concentration of each of the reactants and products: D(g) - 3 2E(g) 1 5 2F(g) When [E] is increasing at 0.25 mol/Ls, how fast is [F] increasing?

Express the rate of this reaction in terms of the change in concentration of each of the reactants and products: A(g) 1 2B(g) - C(g) When [B] is decreasing at 0.5 mol/Ls, how fast is [A] decreasing?

Express the rate of this reaction in terms of the change in concentration of each of the reactants and products: 2D(g) 1 3E(g) 1 F(g) - 2G(g) 1 H(g) When [D] is decreasing at 0.1 mol/Ls, how fast is [H] increasing?

Reaction rate is expressed in terms of changes in concentration of reactants and products. Write a balanced equation for Rate 5 2 1 2 D3N2O5 4 Dt 5 1 4 D3NO2 4 Dt 5 D3O2 4 Dt

Reaction rate is expressed in terms of changes in concentration of reactants and products. Write a balanced equation for Rate 5 2 D3CH4 4 Dt 5 2 1 2 D3O2 4 Dt 5 1 2 D3H2O4 Dt 5 D3CO2 4 Dt

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) 1 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

The formation of ammonia is one of the most important processes in the chemical industry: N2(g) 1 3H2(g) - 2NH3(g) Express the rate in terms of changes in [N2], [H2], and [NH3].

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 [O2] is 2.1731025 mol/Ls. What is it in terms of [O3]?

The rate law for the general reaction aA 1 bB 1 # # # - cC 1 dD 1 # # # is rate 5 k[A]m[B]n . . . .(a) Explain the meaning of k. (b) Explain the meanings of m and n. Does m 5 a and n 5 b? 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 k?

You are studying the reaction A2(g) 1 B2(g) - 2AB(g) to determine its rate law. Assuming that you have a valid experimental procedure for obtaining [A2] and [B2] at various times, explain how you determine (a) the initial rate, (b) the reaction orders, and (c) the rate constant.

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: Rate 5 k3BrO3 2 4 3Br2 4 3H14 2

Give the individual reaction orders for all substances and the overall reaction order from the following rate law: Rate 5 k 3O3 4 2 3O2 4

By what factor does the rate in Problem 16.26 change if each of the following changes occurs: (a) [BrO3 2] is doubled; (b) [Br2] is halved; (c) [H1] is quadrupled?

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?

Give the individual reaction orders for all substances and the overall reaction order from this rate law: Rate 5 k3NO2 4 2 3Cl2 4

Give the individual reaction orders for all substances and the overall reaction order from this rate law: Rate 5 k 3HNO2 4 4 3NO4 2

By what factor does the rate in Problem 16.30 change if each of the following changes occurs: (a) [NO2] is tripled; (b) [NO2] and [Cl2] are doubled; (c) [Cl2] is halved?

By what factor does the rate in Problem 16.31 change if each of the following changes occurs: (a) [HNO2] is doubled; (b) [NO] is doubled; (c) [HNO2] is halved?

For the reaction 4A(g) 1 3B(g) - 2C(g) the following data were obtained at constant temperature: Initial Rate Initial [A] Initial [B] Experiment (mol/Lmin) (mol/L) (mol/L) 1 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. (c) Calculate k (using the data from Expt 1).

For the reaction A(g) 1 B(g) 1 C(g) - D(g) the following data were obtained at constant temperature: Initial Rate Initial [A] Initial [B] Initial [C] Expt (mol/Ls) (mol/L) (mol/L) (mol/L) 1 6.2531023 0.0500 0.0500 0.0100 2 1.2531022 0.1000 0.0500 0.0100 3 5.0031022 0.1000 0.1000 0.0100 4 6.2531023 0.0500 0.0500 0.0200 (a) What is the order with respect to each reactant? (b) Write the rate law. (c) Calculate k (using the data from Expt 1).

Without consulting Table 16.3, give the units of the rate constants for reactions with the following overall orders: (a) first order; (b) second order; (c) third order; (d) 5 2 order.

Give the overall reaction order that corresponds to a rate constant with each of the following units: (a) mol/Ls; (b) yr21; (c) (mol/L)1/2s21; (d) (mol/L)25/2?min21.

Phosgene is a toxic gas prepared by the reaction of carbon monoxide with chlorine: CO(g) 1 Cl2(g) - COCl2(g) These data were obtained in a kinetics study of its formation: Initial Rate Initial [CO] Initial [Cl2] Experiment (mol/Ls) (mol/L) (mol/L) 1 1.29310229 1.00 0.100 2 1.33310230 0.100 0.100 3 1.30310229 0.100 1.00 4 1.32310231 0.100 0.0100 (a) Write the rate law for the formation of phosgene. (b) Calculate the average value of the rate constant.

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?

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

For the simple decomposition reaction AB(g) - A(g) 1 B(g) rate 5 k[AB]2 and k 5 0.2 L/mols. How long will it take for [AB] to reach one-third of its initial concentration of 1.50 M?

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

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?

A decomposition reaction has a rate constant of 0.0012 yr21. (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?

In a study of ammonia production, an industrial chemist discovers that the compound decomposes to its elements N2 and H2 in a first-order process. She collects the following data: Time (s) 0 1.000 2.000 [NH3] (mol/L) 4.000 3.986 3.974 (a) Use graphical methods to determine the rate constant. (b) What is the half-life for ammonia decomposition?

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

Is collision frequency the only factor affecting rate? Explain.

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?

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

How is the activation energy determined from the Arrhenius equation?

(a) Graph the relationship between k (vertical axis) and T (horizontal axis). (b) Graph the relationship between ln k (vertical axis) and 1/T (horizontal axis). How is the activation energy determined from this graph?

(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?

In the reaction AB 1 CD BA EF, 431025 mol of AB molecules collide with 431025 mol of CD molecules. Will 431025 mol of EF form? Explain.

Assuming the activation energies are equal, which of the following reactions will proceed at a higher rate at 508C? Explain. NH3(g) 1 HCl(g) - NH4Cl(s) N(CH3)3(g) 1 HCl(g) - (CH3)3NHCl(s)

For the reaction A(g) 1 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?

For the reaction A(g) 1 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?

At 258C, what is the fraction of collisions with energy equal to or greater than an activation energy of 100. kJ/mol?

If the temperature in Problem 16.57 is increased to 50.8C, by what factor does the fraction of collisions with energy equal to or greater than the activation energy change?

The rate constant of a reaction is 4.731023 s21 at 258C, and the activation energy is 33.6 kJ/mol. What is k at 758C?

The rate constant of a reaction is 4.5031025 L/mols at 1958C and 3.2031023 L/mols at 2588C. What is the activation energy of the reaction?

For the reaction ABC 1 D BA AB 1 CD, DH8 rxn 5 255 kJ/mol and Ea(fwd) 5 215 kJ/mol. Assuming a one-step reaction, (a) draw a reaction energy diagram; (b) calculate Ea(rev); and (c) sketch a possible transition state if ABC is V shaped.

For the reaction A2 1 B2 - 2AB, Ea(fwd) 5 125 kJ/mol and Ea(rev) 5 85 kJ/mol. Assuming the reaction occurs in one step, (a) draw a reaction energy diagram; (b) calculate DH8 rxn; and (c) sketch a possible transition state.

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 7278C and 0.87/s at 7578C. What is the activation energy of this reaction?

Aqua regia, a mixture of HCl and HNO3, 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: NO(g) 1 Cl2(g) - NOCl(g) 1 Cl(g) DH8 5 83 kJ (a) Draw a reaction energy diagram, given Ea(fwd) 5 86 kJ/mol. (b) Calculate Ea(rev). (c) Sketch a possible transition state for the reaction. (Note: The atom sequence of nitrosyl chloride is ClNO.)

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

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

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

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

Why is a bimolecular step more reasonable physically than a termolecular step?

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.

If a fast step precedes a slow step in a two-step mechanism, how is the fast step affected? How is this effect used to determine the validity of the mechanism?

The proposed mechanism for a reaction is (1) A(g) 1 B(g) BA X(g) [fast] (2) X(g) 1 C(g) - Y(g) [slow] (3) Y(g) - D(g) [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 actual rate law: Rate 5 k[A][B][C]? (e) Is the following one-step mechanism equally valid: A(g) 1 B(g) 1 C(g) - D(g)?

Consider the following mechanism: (1) ClO2(aq) 1 H2O(l) BA HClO(aq) 1 OH2(aq) [fast] (2) I 2(aq) 1 HClO(aq) - HIO(aq) 1 Cl2(aq) [slow] (3) OH2(aq) 1 HIO(aq) - H2O(l) 1 IO2(aq) [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 actual rate law: Rate 5 k[ClO2][I2]?

In a study of nitrosyl halides, a chemist proposes the following mechanism for the synthesis of nitrosyl bromide: NO(g) 1 Br2(g) BA NOBr2(g) [fast] NOBr2(g) 1 NO(g) - 2NOBr(g) [slow] If the rate law is rate 5 k[NO]2 [Br2], is the proposed mechanism valid? If so, show that it satisfies the three criteria for validity.

The rate law for 2NO(g) 1 O2(g) - 2NO2(g) is rate 5 k[NO]2[O2]. In addition to the mechanism in the text (p. 709), the following ones have been proposed: I 2NO(g) 1 O2(g) - 2NO2(g) II 2NO(g) BA N2O2(g) [fast] N2O2(g) 1 O2(g) - 2NO2(g) [slow] III 2NO(g) BA N2(g) 1 O2(g) [fast] N2(g) 1 2O2(g) - 2NO2(g) [slow] (a) Which of these mechanisms is consistent with the rate law? (b) Which of these mechanisms is most reasonable? Why?

Consider the reaction N2O(g) -Au N2(g) 1 1 2O2(g). (a) Does the gold catalyst (Au, above the arrow) act as a homogeneous or a heterogeneous catalyst? (b) On the same set of axes, sketch the reaction energy diagrams for the catalyzed and the uncatalyzed reaction.

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

In a classroom demonstration, hydrogen gas and oxygen gas are mixed in a balloon. The mixture is stable under normal conditions, but if a spark is applied to it or some powdered metal is added, the mixture explodes. (a) Is the spark acting as a catalyst? Explain. (b) Is the metal acting as a catalyst? Explain.

A principle of green chemistry is that the energy needs of industrial processes should have minimal environmental impact. How can the use of catalysts lead to greener technologies?

Enzymes are remarkably efficient catalysts that can increase reaction rates by as many as 20 orders of magnitude. (a) How does an enzyme affect the transition state of a reaction, and how does this effect increase the reaction rate? (b) What characteristics of enzymes give them this effectiveness as catalysts?

Experiments show that each of the following redox reactions is second order overall: Reaction 1: NO2(g) 1 CO(g) - NO(g) 1 CO2(g) Reaction 2: NO(g) 1 O3(g) - NO2(g) 1 O2(g) (a) When [NO2] in reaction 1 is doubled, the rate quadruples. Write the rate law for this reaction. (b) When [NO] in reaction 2 is doubled, the rate doubles. Write the rate law for this reaction. (c) In each reaction, the initial concentrations of the reactants are equal. For each reaction, what is the ratio of the initial rate to the rate when the reaction is 50% complete? (d) In reaction 1, the initial [NO2] is twice the initial [CO]. What is the ratio of the initial rate to the rate at 50% completion? (e) In reaction 2, the initial [NO] is twice the initial [O3]. What is the ratio of the initial rate to the rate at 50% completion?

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

Reactions between certain organic (alkyl) halides and water produce alcohols. Consider the overall reaction for t-butyl bromide (2-bromo-2-methylpropane): (CH3)3CBr(aq) 1 H2O(l) - (CH3)3COH(aq) 1 H1(aq) 1 Br2(aq) The experimental rate law is rate 5 k[(CH3)3CBr]. The accepted mechanism for the reaction is (1) (CH3)3CiBr(aq) - (CH3)3C1(aq) 1 Br2(aq) [slow] (2) (CH3)3C1(aq) 1 H2O(l) - (CH3)3COH2 1(aq) [fast] (3) (CH3)3COH2 1(aq) - H1(aq) 1 (CH3)3COH(aq) [fast] (a) Why doesnt H2O appear in the rate law? (b) Write rate laws for the elementary steps. (c) What reaction intermediates appear in the mechanism? (d) Show that the mechanism is consistent with the experimental rate law.

Archeologists can determine the age of an artifact made of wood or bone by measuring the amount of the radioactive isotope 14C present in the object. The amount of this isotope decreases in a first-order process. If 15.5% of the original amount of 14C is present in a wooden tool at the time of analysis, what is the age of the tool? The half-life of 14C is 5730 yr.

A slightly bruised apple will rot extensively in about 4 days at room temperature (208C). If it is kept in the refrigerator at 08C, the same extent of rotting takes about 16 days. What is the activation energy for the rotting reaction?

Benzoyl peroxide, the substance most widely used against acne, has a half-life of 9.83103 days when refrigerated. How long will it take to lose 5% of its potency (95% remaining)?

The rate law for the reaction NO2(g) 1 CO(g) - NO(g) 1 CO2(g) is rate 5 k[NO2] 2; one possible mechanism is shown on p. 708. (a) Draw a reaction energy diagram for that mechanism, given that DH8 overall 5 2226 kJ/mol. (b) Consider the following alternative mechanism: (1) 2NO2(g) - N2(g) 1 2O2(g) [slow] (2) 2CO(g) 1 O2(g) - 2CO2(g) [fast] (3) N2(g) 1 O2(g) - 2NO(g) [fast] Is the alternative mechanism consistent with the rate law? Is one mechanism more reasonable physically? Explain.

Consider the following general reaction and data: 2A 1 2B 1 C - D 1 3E Initial Rate Initial [A] Initial [B] Initial [C] Expt (mol/Ls) (mol/L) (mol/L) (mol/L) 1 6.031026 0.024 0.085 0.032 2 9.631025 0.096 0.085 0.032 3 1.531025 0.024 0.034 0.080 4 1.531026 0.012 0.170 0.032 (a) What is the reaction order with respect to each reactant? (b) Calculate the rate constant. (c) Write the rate law for this reaction. (d) Express the rate in terms of changes in concentration with time for each of the components.

In acidic solution, the breakdown of sucrose into glucose and fructose has this rate law: Rate 5 k[H1][sucrose]. The initial rate of sucrose breakdown is measured in a solution that is 0.01 M H1, 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) [H1] is changed to 0.0001 M? (d) [Sucrose] and [H1] are both changed to 0.1 M?

The citric acid cycle is the central reaction sequence in the cellular metabolism of humans and many other organisms. One of the key steps is catalyzed by the enzyme isocitrate dehydrogenase and the oxidizing agent NAD1. In yeast, the reaction is eleventh order: Rate 5 k3enzyme4 3isocitrate4 4 3AMP4 2 3NAD14 m 3Mg214 2 What is the order with respect to NAD1?

The following molecular scenes represent starting mixtures I and II for the reaction of A (black) with B (orange): I II Each sphere represents 0.010 mol, and the volume is 0.50 L. If the reaction is first order in A and first order in B and the initial rate for I is 8.331024 mol/Lmin, what is the initial rate for II?

Experiment shows that the rate of formation of carbon tetrachloride from chloroform, CHCl3(g) 1 Cl2(g) - CCl4(g) 1 HCl(g) is first order in CHCl3, 1 2 order in Cl2, and 3 2 order overall. Show that the following mechanism is consistent with the rate law: (1) Cl2(g) BA 2Cl(g) [fast] (2) Cl(g) 1 CHCl3(g) - HCl(g) 1 CCl3(g) [slow] (3) CCl3(g) 1 Cl(g) - CCl4(g) [fast]

A biochemist studying the 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 decrease from 275 ppbm to 10. ppbm (parts per billion by mass)?

Insulin is a polypeptide hormone that is released into the blood from the pancreas and stimulates fat and muscle to take up glucose; the insulin is used up in a first-order process. In a certain patient, it has a half-life of 3.5 min. To maintain an adequate blood concentration of insulin, it must be replenished in a time interval equal to 1/k. How long is the time interval for this patient?

For the reaction A(g) 1 B(g) - AB(g), the rate is 0.20 mol/Ls, when [A]0 5 [B]0 5 1.0 mol/L. If the reaction is first order in B and second order in A, what is the rate when [A]0 5 2.0 mol/L and [B]0 5 3.0 mol/L?

The acid-catalyzed hydrolysis of sucrose occurs by the following overall reaction, whose kinetic data are given below: C12H22O11(s) 1 H2O(l) - C6H12O6(aq) 1 C6H12O6(aq) sucrose glucose fructose [Sucrose] (mol/L) Time (h) 0.501 0.00 0.451 0.50 0.404 1.00 0.363 1.50 0.267 3.00 (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 pseudofirst-order reaction.) Suggest a reason for this apparent first-order behavior.

At body temperature (378C), the rate constant of an enzymecatalyzed decomposition is 2.331014 times that of the uncatalyzed reaction. If the frequency factor, A, is the same for both processes, by how much does the enzyme lower the Ea?

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 108C 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, DHrxn 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 unimolecular reaction. (q) The molecularity of an elementary reaction is proportional to the molecular complexity of the reactant(s).

For the decomposition of gaseous dinitrogen pentoxide, 2N2O5(g) - 4NO2(g) 1 O2(g) the rate constant is k 5 2.831023 s21 at 608C. The initial concentration of N2O5 is 1.58 mol/L. (a) What is [N2O5] after 5.00 min? (b) What fraction of the N2O5 has decomposed after 5.00 min?

Even when a mechanism is consistent with the rate law, later work may show it to be incorrect. For example, the reaction between hydrogen and iodine has this rate law: Rate 5 k[H2][I2]. The long-accepted mechanism had a single bimolecular step; that is, the overall reaction was thought to be elementary: H2(g) 1 I2(g) - 2HI(g) In the 1960s, however, spectroscopic evidence showed the presence of free I atoms during the reaction. Kineticists have since proposed a three-step mechanism: (1) I2(g) BA 2I(g) [fast] (2) H2(g) 1 I(g) BA H2I(g) [fast] (3) H2I(g) 1 I(g) - 2HI(g) [slow] Show that this mechanism is consistent with the rate law.

Suggest an experimental method for measuring the change in concentration with time for each of the following reactions: (a) CH3CH2Br(l) 1 H2O(l) - CH3CH2OH(l) 1 HBr(aq) (b) 2NO(g) 1 Cl2(g) - 2NOCl(g)

An atmospheric chemist fills a container with gaseous N2O5 to a pressure of 125 kPa, and the gas decomposes to NO2 and O2. What is the partial pressure of NO2, PNO2 (in kPa), when the total pressure is 178 kPa?

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 (98.68F), k 5 3.131025 s21; for a person with a fever (temperature of 101.98F), k 5 3.931025 s21. If the person with the fever must take another pill when 2 3 of the first pill has decomposed, how many hours should she wait to take a second pill? A third pill? (Assume that the pill is effective immediately.) (c) Calculate Ea for decomposition of the antibiotic in part (b).

While developing a catalytic process to make ethylene glycol from synthesis gas (CO 1 H2), a chemical engineer finds the rate is fourth order with respect to gas pressure. The uncertainty in the pressure reading is 5%. When the catalyst is modified, the rate increases by 10%. If you were the company patent attorney, would you file for a patent on this catalyst modification? Explain.

Iodide ion reacts with chloromethane to displace chloride ion in a common organic substitution reaction: I 2 1 CH3Cl - CH3I 1 Cl2 (a) Draw a wedge-bond structure of chloroform and indicate the most effective direction of I2 attack. (b) The analogous reaction with 2-chlorobutane results in a major change in specific rotation as measured by polarimetry. Explain, showing a wedge-bond structure of the product. (c) Under different conditions, 2-chlorobutane loses Cl2 in a rate-determining step to form a planar intermediate. This cationic species reacts with HI and then loses H1 to form a product that exhibits no optical activity. Explain, showing a wedge-bond structure. +

Assume that water boils at 100.08C in Houston (near sea level), and at 90.08C in Cripple Creek, Colorado (near 9500 ft). If it takes 4.8 min to cook an egg in Cripple Creek and 4.5 min in Houston, what is Ea for this process?

Sulfonation of benzene has the following mechanism: (1) 2H2SO4 - H3O1 1 HSO4 2 1 SO3 [fast] (2) SO3 1 C6H6 - H(C6H5 1)SO3 2 [slow] (3) H(C6H5 1)SO3 2 1 HSO4 2 - C6H5SO3 2 1 H2SO4 [fast] (4) C6H5SO3 2 1 H3O1 - C6H5SO3H 1 H2O [fast] (a) Write an overall equation for the reaction. (b) Write the overall rate law in terms of the initial rate of the reaction.

In the lower troposphere, 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: (1) NO2(g) - k1 hn NO(g) 1 O(g) (2) O(g) 1 O2(g) - k2 hn O3(g) 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. k1 5 6.031023 s 21 3NO2 4 5 4.031029 M k2 5 1.03106 L/mols 3O2 4 5 1.031022 M

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 5 100 3 (1 2 [A]t/[A]0).] (b) How much contact time is required for 95% inactivation?

The overall equation and rate law for the gas-phase decomposition of dinitrogen pentoxide are 2N2O5(g) - 4NO2(g) 1 O2(g) rate 5 k3N2O5 4 Which of the following can be considered valid mechanisms for the reaction? I One-step collision II 2N2O5(g) - 2NO3(g) 1 2NO2(g) [slow] 2NO3(g) - 2NO2(g) 1 2O(g) [fast] 2O(g) - O2(g) [fast] III N2O5(g) BA NO3(g) 1 NO2(g) [fast] NO2(g) 1 N2O5(g) - 3NO2(g) 1 O(g) [slow] NO3(g) 1 O(g) - NO2(g) 1 O2(g) [fast] IV 2N2O5(g) BA 2NO2(g) 1 N2O3(g) 1 3O(g) [fast] N2O3(g) 1 O(g) - 2NO2(g) [slow] 2O(g) - O2(g) [fast] V 2N2O5(g) - N4O10(g) [slow] N4O10(g) - 4NO2(g) 1 O2(g) [fast]

Nitrification is a biological process for removing NH3 from wastewater as NH4 1: NH4 1 1 2O2 - NO3 2 1 2H1 1 H2O The first-order rate constant is given as k1 5 0.47e0.095 (T5158C) where k1 is in day21 and T is in 8C. (a) If the initial concentration of NH3 is 3.0 mol/m3, how long will it take to reduce the concentration to 0.35 mol/m3 in the spring (T 5 208C)? (b) In the winter (T 5 108C)? (c) Using your answer to part (a), what is the rate of O2 consumption?

Carbon disulfide, a poisonous, flammable liquid, is an excellent solvent for phosphorus, sulfur, and some other nonmetals. A kinetic study of its gaseous decomposition reveals these data: Initial Rate Initial [CS2] Experiment (mol/Ls) (mol/L) 1 2.731027 0.100 2 2.231027 0.080 3 1.531027 0.055 4 1.231027 0.044 (a) Write the rate law for the decomposition of CS2. (b) Calculate the average value of the rate constant.

Like any catalyst, palladium, platinum, or nickel catalyzes both directions of a reaction: addition of hydrogen to (hydrogenation) 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 hydrogenation of fats that contain some cis- double bonds?

In a clock reaction, a dramatic color change occurs at a time determined by concentration and temperature. Consider the iodine clock reaction, whose overall equation is 2I2(aq) 1 S2O8 22(aq) - I2(aq) 1 2SO4 22(aq) As I2 forms, it is immediately consumed by its reaction with a fixed amount of added S2O3 22: I2(aq) 1 2S2O3 22(aq) - 2I2(aq) 1 S4O6 22(aq) Once the S2O3 22 is consumed, the excess I2 forms a blue-black product with starch present in solution: I2 1 starch - starchI2 (blue-black) The rate of the reaction is also influenced by the total concentration of ions, so KCl and (NH4)2SO4 are added to maintain a constant value. Use the data below, obtained at 238C, to determine: (a) The average rate for each trial (b) The order with respect to each reactant (c) The rate constant (d) The rate law for the overall reaction Expt 1 Expt 2 Expt 3 0.200 M KI (mL) 10.0 20.0 20.0 0.100 M Na2S2O8 (mL) 20.0 20.0 10.0 0.0050 M Na2S2O3 (mL) 10.0 10.0 10.0 0.200 M KCl (mL) 10.0 0.0 0.0 0.100 M (NH4)2SO4 (mL) 0.0 0.0 10.0 Time to color (s) 29.0 14.5 14.5

Heat transfer to and from a reaction flask is often a critical factor in controlling reaction rate. The heat transferred (q) depends on a heat transfer coefficient (h) for the flask material, the temperature difference (DT) across the flask wall, and the commonly wetted area (A) of the flask and bath, q 5 hADT. When an exothermic reaction is run at a given T, there is a bath temperature at which the reaction can no longer be controlled, and the reaction runs away suddenly. A similar problem is often seen when a reaction is scaled up from, say, a half-filled small flask to a half-filled large flask. Explain these behaviors.

The molecular scenes below represent the first-order reaction in which cyclopropane (red) is converted to propene (green): t = 0 min t = 20 min t = 60 min Determine (a) the half-life and (b) the rate constant.

The growth of Pseudomonas bacteria is modeled as a first-order process with k 5 0.035 min21 at 378C. The initial Pseudomonas population density is 1.03103 cells/L. (a) What is the population density after 2 h? (b) What is the time required for the population to go from 1.03103 to 2.03103 cells/L?

Consider the following organic reaction, in which one halogen replaces another in an alkyl halide: CH3CH2Br 1 KI - CH3CH2I 1 KBr In acetone, this particular reaction goes to completion because KI is soluble in acetone but KBr is not. In the mechanism, I2 approaches the carbon opposite to the Br (see Figure 16.20, p. 704, with I2 instead of OH2). After Br2 has been replaced by I 2 and precipitates as KBr, other I2 ions react with the ethyl iodide by the same mechanism. (a) If we designate the carbon 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 I, 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? (c) The deuterated reactant, CH3CHDBr (where D is deuterium, 2H), has two optical isomers because C-1 is chiral. If the reaction is run with one of the isomers, the ethyl iodide is not optically active. Explain.

Another radioisotope of iodine, 131I, is also used to study thyroid function (see Follow-up Problem 16.7A). A patient is given a sample that is 1.731024 M 131I. If the half-life is 8.04 days, what fraction of the radioactivity remains after 30. days?

The effect of substrate concentration on the first-order growth rate of a microbial population follows the Monod equation: m 5 mmaxS Ks 1 S where m is the first-order growth rate (s21), mmax is the maximum growth rate (s21), S is the substrate concentration (kg/m3), and Ks is the value of S that gives one-half of the maximum growth rate (in kg/m3). For mmax 5 1.531024 s21 and Ks 5 0.03 kg/m3: (a) Plot m vs. S for S between 0.0 and 1.0 kg/m3. (b) The initial population density is 5.03103 cells/m3. What is the density after 1.0 h, if the initial S is 0.30 kg/m3? (c) What is it if the initial S is 0.70 kg/m3?

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, 2D[A]/Dt (in mol/Ls), is shown, with each sphere representing 0.010 mol and the container volume at 0.50 L. I 3.5104 II 5.6104 III 5.6104 IV 4.9104 (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.

The mathematics of the first-order rate law can be applied to any situation in which a quantity decreases by a constant fraction per unit of time (or unit of any other variable). (a) As light moves through a solution, its intensity decreases per unit distance traveled in the solution. Show that ln a intensity of light leaving the solution intensity of light entering the solutionb 5 2fraction of light removed per unit of length 3 distance traveled in solution (b) The value of your savings declines under conditions of constant inflation. Show that ln a value remaining initial value b 5 2fraction lost per unit of time 3 savings time interval

Figure 16.25 (p. 714) shows key steps in the metalcatalyzed (M) hydrogenation of ethylene: C2H4(g) 1 H2(g) - C2H6(g) Use the following symbols to write a mechanism that gives the overall equation: H2(ads) adsorbed hydrogen molecules M-H hydrogen atoms bonded to metal atoms C2H4(ads) adsorbed ethylene molecules C2H5(ads) adsorbed ethyl radicals

Human liver enzymes catalyze the degradation of ingested toxins. By what factor is the rate of a detoxification changed if an enzyme lowers the Ea by 5 kJ/mol at 378C?

Acetone is one of the most important solvents in organic chemistry, used to dissolve everything from fats and waxes to airplane glue and nail polish. At high temperatures, it decomposes in a first-order process to methane and ketene (CH2CO). At 6008C, the rate constant is 8.731023 s21. (a) What is the half-life of the reaction? (b) How long does it take for 40.% of a sample of acetone to decompose? (c) How long does it take for 90.% of a sample of acetone to decompose?

A (green), B (blue), and C (red) are structural isomers. The molecular filmstrip depicts them undergoing a chemical change as time proceeds. 1 t = 0 2 3 4 5 t = (a) Write a mechanism for the reaction. (b) What role does C play?