The initial rate for a reaction is equal to the slope of

Consider the simple reaction aA 8n products. You run this reaction and wish to determine its order. What if you made a graph of reaction rate versus time? Could you use this to determine the order? Sketch plots of rate versus time for the reaction assuming that the order is zero, first, or second order. Sketch these plots on the same graph and compare them. Defend your answer.

There are many conditions that need to be met in order to result in a chemical reaction between molecules. What if all collisions between molecules resulted in a chemical reaction? How would life be different?

Many modern refrigerators have an internal temperature of 458F. What if refrigerators were set at 558F in the factory? How would this affect our lives?

Define the term stability from both a kinetic and a thermodynamic perspective. Give examples to show the differences in these concepts

Describe at least two experiments you could perform to determine a rate law.

Make a graph of [A] versus time for zero-, first-, and second-order reactions. From these graphs, compare successive half-lives.

How does temperature affect k, the rate constant? Explain.

Consider the following statements: In general, the rate of a chemical reaction increases at first. After that the rate of the reaction decreases because its rate is dependent on the concentration of reactants, and these are decreasing. Indicate everything that is correct in these statements, and indicate everything that is incorrect. Correct the incorrect statements, and explain

For the reaction A 1 B 88n C, explain at least two ways in which the rate law could be zero order in chemical A.

A friend of yours states, A balanced equation tells us how chemicals interact. Therefore, we can determine the rate law directly from the balanced equation. What do you tell your friend?

The rate constant (k) depends on which of the following? (There may be more than one answer.) a. the concentration of the reactants b. the nature of the reactants c. the temperature d. the order of the reaction Explain

Provide a conceptual rationale for the differences in the half-lives of zero-, first-, and second-order reactions.

Define reaction rate. Distinguish between the initial rate, average rate, and instantaneous rate of a chemical reaction. Which of these rates is usually fastest? The initial rate is the rate used by convention. Give a possible explanation as to why.

Consider the general reaction aA 1 bB 88n cC and the following average rate data over a specific time period Dt: 2DA Dt 5 0.0080 mol L21 s21 2DB Dt 5 0.0120 mol L21 s21 DC Dt 5 0.0160 mol L21 s21 Determine a set of possible coefficients to balance this general reaction.

Consider the reaction 4PH3(g) 88n P4(g) 1 6H2(g) If, in a certain experiment, over a specific time period, 0.0048 mole of PH3 is consumed in a 2.0-L container during each second of the reaction, what are the rates of production of P4 and H2 in this experiment?

In the Haber process for the production of ammonia, N2(g) 1 3H2(g) 88n 2NH3(g) what is the relationship between the rate of production of ammonia and the rate of consumption of hydrogen?

What are the units for each of the following if concentrations are expressed in moles per liter and time in seconds? a. rate of a chemical reaction b. rate constant for a zero-order rate law c. rate constant for a first-order rate law d. rate constant for a second-order rate law e. rate constant for a third-order rate law

The rate law for the reaction Cl2(g) 1 CHCl3(g) 88n HCl(g) 1 CCl4(g) is Rate 5 k[Cl2]1/2[CHCl3] What are the units for k assuming time in seconds?

The hydroxyl radical (OH) is an important oxidizing agent in the atmosphere. At 298 K the rate constant for the reaction of OH with benzene is 1.24 3 10212 cm3 molecule21 s21. Calculate the value of the rate constant in L mol21 s21.

At 408C, H2O2(aq) will decompose according to the following reaction: 2H2O2 1aq2 h 2H2O1l2 1 O2 1g2 The following data were collected for the concentration of H2O2 at various times. Time (s) [H2O2] (mol/L) 0 1.000 2.16 3 104 0.500 4.32 3 104 0.250 a. Calculate the average rate of decomposition of H2O2 between 0 and 2.16 3 104 s. Use this rate to calculate the average rate of production of O2(g) over the same time period. b. What are these rates for the time period 2.16 3 104 s to 4.32 3 104 s?

The reaction 2NO(g) 1 Cl2(g) 88n 2NOCl(g) was studied at 2108C. The following results were obtained, where Rate 5 2d3Cl2 4 dt [NO]0 (mol/L) [Cl2]0 (mol/L) Initial Rate (mol L21 min21) 0.10 0.10 0.18 0.10 0.20 0.36 0.20 0.20 1.45 a. What is the rate law? b. What is the value of the rate constant?

The reaction I 2 1aq2 1 OCl2 1aq2 h IO2 1aq2 1 Cl2 1aq2 was studied, and the following data were obtained: [I2]0 (mol/L) [OCl2]0 (mol/L) Initial Rate (mol L21 s21) 0.12 0.18 7.91 3 1022 0.060 0.18 3.95 3 1022 0.030 0.090 9.88 3 1023 0.24 0.090 7.91 3 1022 a. What is the rate law? b. Calculate the value of the rate constant. c. Calculate the initial rate for an experiment where both I2 and OCl2 are initially present at 0.15 mol/L.

The following data were obtained for the gas-phase decomposition of dinitrogen pentoxide, 2N2O5(g) 88n 4NO2(g) 1 O2(g) [N2O5]0 (mol/L) Initial Rate (mol L21 s21) 0.0750 8.90 3 1024 0.190 2.26 3 1023 0.275 3.26 3 1023 0.410 4.85 3 1023 where Rate 5 2d3N2O5 4 dt Write the rate law and calculate the value of the rate constant. 21. The decomposition of nitrosyl chloride was studied: 2NOCl(g) 34 2NO(g) 1 Cl2(g) The following data were obtained, where Rate 5 2d3NOCl4 dt [NOCl]0 (molecules/cm3) Initial Rate (molecules cm23 s21) 3.0 3 1016 5.98 3 104 2.0 3 1016 2.66 3 104 1.0 3 1016 6.64 3 103 4.0 3 1016 1.06 3 105 a. What is the rate law? b. Calculate the rate constant. c. Calculate the rate constant for the concentrations given in moles per liter.

The rate of the reaction between hemoglobin (Hb) and carbon monoxide (CO) was studied at 208C. The following data were collected, with all concentration units in mmol/L. (A hemoglobin concentration of 2.21 mmol/L is equal to 2.21 3 1026 mol/L.) [Hb]0 (mmol/L) [CO]0 (mmol/L) Initial Rate (mmol L21 s21) 2.21 1.00 0.619 4.42 1.00 1.24 4.42 3.00 3.71 a. Determine the orders of this reaction with respect to Hb and CO. b. Determine the rate law. c. Calculate the value of the rate constant. d. What would be the initial rate for an experiment with [Hb]0 5 3.36 mmol/L and [CO]0 5 2.40 mmol/L?

The following data were obtained for the reaction 2ClO2(aq) 1 2OH2(aq) 88n ClO3 2(aq) 1 ClO2 2(aq) 1 H2O(l) where Rate 5 2 d3ClO2 4 dt [ClO2]0 (mol/L) [OH2]0 (mol/L) Initial Rate (mol L21 s21) 0.0500 0.100 5.75 3 1022 0.100 0.100 2.30 3 1021 0.100 0.0500 1.15 3 1021 a. Determine the rate law and the value of the rate constant. b. What would be the initial rate for an experiment with [ClO2]0 5 0.175 mol/L and [OH2]0 5 0.0844 mol/L?

The reaction 2NO(g) 1 O2(g) 88n 2NO2(g) was studied, and the following data were obtained, where Rate 5 2d3O2 4 dt [NO]0 (molecules/cm3) [O2]0 (molecules/cm3) Initial Rate (molecules cm23 s21) 1.00 3 1018 1.00 3 1018 2.00 3 1016 3.00 3 1018 1.00 3 1018 1.80 3 1017 2.50 3 1018 2.50 3 1018 3.13 3 1017 What would be the initial rate for an experiment where [NO]0 5 6.21 3 1018 molecules/cm3 and [O2]0 5 7.36 3 1018 molecules/cm3?

The reaction H2SeO3(aq) 1 6I2(aq) 1 4H1(aq) 88n Se(s) 1 2I3 2(aq) 1 3H2O(l) was studied at 08C, and the following data were obtained: [H2SeO3]0 (mol/L) [H1]0 (mol/L) [I2]0 (mol/L) Initial Rate (mol L21 s21) 1.0 3 1024 2.0 3 1022 2.0 3 1022 1.66 3 1027 2.0 3 1024 2.0 3 1022 2.0 3 1022 3.33 3 1027 3.0 3 1024 2.0 3 1022 2.0 3 1022 4.99 3 1027 1.0 3 1024 4.0 3 1022 2.0 3 1022 6.66 3 1027 1.0 3 1024 1.0 3 1022 2.0 3 1022 0.42 3 1027 1.0 3 1024 2.0 3 1022 4.0 3 1022 13.2 3 1027 1.0 3 1024 1.0 3 1022 4.0 3 1022 3.36 3 1027 These relationships hold only if there is an insignificant amount of I3 2 present. What is the rate law and the value of the rate constant? aAssume that rate 5 2 d3H2SeO3 4 dt .b

The initial rate of a reaction doubles as the concentration of one of the reactants is quadrupled. What is the order of this reactant? If a reactant has a 21 order, what happens to the initial rate when the concentration of that reactant increases by a factor of two?

A study was made of the effect of the hydroxide concentration on the rate of the reaction I2(aq) 1 OCl2(aq) 88n IO2(aq) 1 Cl2(aq) The following data were obtained: [I2]0 (mol/L) [OCl2]0 (mol/L) [OH2]0 (mol/L) Initial Rate (mol L21 s21) 0.0013 0.012 0.10 9.4 3 1023 0.0026 0.012 0.10 18.7 3 1023 0.0013 0.0060 0.10 4.7 3 1023 0.0013 0.018 0.10 14.0 3 1023 0.0013 0.012 0.050 18.7 3 1023 0.0013 0.012 0.20 4.7 3 1023 0.0013 0.018 0.20 7.0 3 1023 Determine the rate law and the value of the rate constant for this reaction.

The initial rate for a reaction is equal to the slope of the tangent line at t < 0 in a plot of [A] versus time. From calculus, Initial rate 5 2d3A4 dt Therefore, the differential rate law for a reaction is Rate 5 2d3A4 dt 5 k3A4 n Assuming you have some calculus in your background, derive the zero-, first-, and second-order integrated rate laws using the differential rate law.

If the half-life for a reaction is 20. seconds, what would be the second half-life, assuming the reaction is either zero, first, or second order?

A certain reaction has the following general form: aA 88n bB At a particular temperature and [A]0 5 2.80 3 1023 M, concentration versus time data were collected for this reaction, and a plot of 1/[A] versus time resulted in a straight line with a slope value of 13.60 3 1022 L mol21 s21. a. Determine the rate law, the integrated rate law, and the value of the rate constant for this reaction. b. Calculate the half-life for this reaction. c. How much time is required for the concentration of A to decrease to 7.00 3 1024 M?

A certain reaction has the following general form: aA 88n bB At a particular temperature and [A]0 5 2.00 3 1022 M, concentration versus time data were collected for this reaction, and a plot of ln[A] versus time resulted in a straight line with a slope value of 22.97 3 1022 min21. a. Determine the rate law, the integrated rate law, and the value of the rate constant for this reaction. b. Calculate the half-life for this reaction. c. How much time is required for the concentration of A to decrease to 2.50 3 1023 M?

The decomposition of ethanol (C2H5OH) on an alumina (Al2O3) surface, C2H5OH(g) 88n C2H4(g) 1 H2O(g) was studied at 600 K. Concentration versus time data were collected for this reaction, and a plot of [A] versus time resulted in a straight line with a slope value of 24.00 3 1025 mol L21 s21. a. Determine the rate law, the integrated rate law, and the value of the rate constant for this reaction. b. If the initial concentration of C2H5OH was 1.25 3 1022 M, calculate the half-life for this reaction. c. How much time is required for all of the 1.25 3 1022 M C2H5OH to decompose?

The decomposition of hydrogen peroxide was studied at a particular temperature. The following data were obtained, where Rate 5 2d3H2O2 4 dt Time (s) [H2O2] (mol/L) 0 1.00 120 6 1 0.91 300 6 1 0.78 600 6 1 0.59 1200 6 1 0.37 1800 6 1 0.22 2400 6 1 0.13 3000 6 1 0.082 3600 6 1 0.050 Determine the integrated rate law, the differential rate law, and the value of the rate constant. Calculate the [H2O2] at 4000. s after the start of the reaction.

The dimerization of butadiene was studied at 500. K: 2C4H6(g) 88n C8H12(g) The following data were obtained, where Rate 5 2d3C4H6 4 dt Time (s) [C4H6] (mol/L) 195 1.6 3 1022 604 1.5 3 1022 1246 1.3 3 1022 2180 1.1 3 1022 6210 0.68 3 1022 Determine the forms of the integrated rate law, the differential rate law, and the value of the rate constant for this reaction.

The rate of the reaction NO2(g) 1 CO(g) 88n NO(g) 1 CO2(g) depends only on the concentration of nitrogen dioxide at temperatures below 2258C. At a temperature below 2258C, the following data were collected: Time (s) [NO2] (mol/L) 0 0.500 1.20 3 103 0.444 3.00 3 103 0.381 4.50 3 103 0.340 9.00 3 103 0.250 1.80 3 104 0.174Determine the integrated rate law, the differential rate law, and the value of the rate constant at this temperature. Calculate [NO2] at 2.70 3 104 s after the start of the reaction

The rate of the reaction O(g) 1 NO2(g) 88n NO(g) 1 O2(g) was studied at a certain temperature. This reaction is one step of the nitric oxidecatalyzed destruction of ozone in the upper atmosphere. a. In one experiment, NO2 was in large excess at a concentration of 1.0 3 1013 molecules/cm3 with the following data collected: Time (s) [O] (atoms/cm3) 0 5.0 3 109 1.0 3 1022 1.9 3 109 2.0 3 1022 6.8 3 108 3.0 3 1022 2.5 3 108 What is the order of the reaction with respect to oxygen atoms? b. The reaction is known to be first order with respect to NO2. Determine the overall rate law and the value of the rate constant

At 500 K in the presence of a copper surface, ethanol decomposes according to the equation C2H5OH(g) 88n CH3CHO(g) 1 H2(g) The pressure of C2H5OH was measured as a function of time, and the following data were obtained: Time (s) PC2H5OH (torr) 0 250. 100. 237 200. 224 300. 211 400. 198 500. 185 Since the pressure of a gas is directly proportional to the concentration of the gas, we can express the rate law for a gaseous reaction in terms of partial pressures. Using the preceding data, deduce the rate law, the integrated rate law, and the value of the rate constant, all in terms of pressure units in atm and time in seconds. Predict the pressure of C2H5OH after 900. s from the start of the reaction. (Hint: To determine the order of the reaction with respect to C2H5OH, compare how the pressure of C2H5OH decreases with each time listing.)

Experimental data for the reaction A 88n 2B 1 C have been plotted in the following three different ways (with concentration units in mol/L): 0 0.05 0.04 0.03 0.02 0.01 0 2 Time (s) [A] 4 6 0 2 4 6 3.0 3.5 4.0 4.5 5.0 Time (s) ln[A] 0 100 80 60 40 20 0 2 Time (s) 1/[A] 4 6 a. What is the order of the reaction with respect to A, and what is the initial concentration of A? b. What is the concentration of A after 9 s? c. What are the first three half-lives for this experiment?

The reaction NO(g) 1 O3(g) 88n NO2(g) 1 O2(g) was studied by performing two experiments. In the first experiment (results shown in following table), the rate of disappearance of NO was followed in a large excess of O3. (The [O3] remains effectively constant at 1.0 3 1014 molecules/cm3.) Time (ms) [NO] (molecules/cm3) 0 6.0 3 108 100 6 1 5.0 3 108 500 6 1 2.4 3 108 700 6 1 1.7 3 108 1000 6 1 9.9 3 107 In the second experiment, [NO] was held constant at 2.0 3 1014 molecules/cm3. The data for the disappearance of O3 were as follows: Time (ms) [O3] (molecules/cm3) 0 1.0 3 1010 50 6 1 8.4 3 109 100 6 1 7.0 3 109 200 6 1 4.9 3 109 300 6 1 3.4 3 109a. What is the order with respect to each reactant? b. What is the overall rate law? c. What is the value of the rate constant obtained from each set of experiments? Rate 5 k9[NO]x Rate 5 k0[O3]y d. What is the value of the rate constant for the overall rate law? Rate 5 k[NO]x[O3]y

Determine the forms of the integrated and the differential rate laws for the decomposition of benzene diazonium chloride, C6H5N2Cl(aq) 88n C6H5Cl(l) 1 N2(g) from the following data, which were collected at 50.8C and 1.00 atm: Time (s) N2 Evolved (mL) 6 19.3 9 26.0 14 36.0 22 45.0 30. 50.4 ` 58.3 The total solution volume was 40.0 mL

You and a coworker have developed a molecule that has shown potential as cobra antivenom (AV). This antivenom works by binding to the venom (V), thereby rendering it nontoxic. This reaction can be desrcibed by the rate law Rate 5 k[AV]1[V]1 You have been given the following data from your coworker: [V]0 5 0.20 M [AV]0 5 1.0 3 1024 M A plot of ln[AV] versus time gives a straight line with a slope of 20.32 s21. What is the value of the rate constant (k) for this reaction?

Consider the following representation of the reaction 2NO2(g) n 2NO(g) 1 O2(g). Time (a) time = 0 minutes (b) time = 10 minutes (c) time = ? minutes Determine the time for the final representation below if the reaction is a. first order b. second order c. zero order 43. The rate law for the decomposition of phosphine (PH3) is Rate 5 2d3PH3 4 dt 5 k3PH3 4 It takes 120. s for the concentration of 1.00 M PH3 to decrease to 0.250 M. How much time is required for 2.00 M PH3 to decrease to a concentration of 0.350 M?

The radioactive isotope 32P decays by first-order kinetics and has a half-life of 14.3 days. How long does it take for 95.0% of a given sample of 32P to decay?

Consider the following initial rate data for the decomposition of compound AB to give A and B: [AB]0 (mol/L) Initial Rate (mol L21 s21) 0.200 3.20 3 1023 0.400 1.28 3 1022 0.600 2.88 3 1022 Determine the half-life for the decomposition reaction initially having 1.00 M AB present.

The rate law for the reaction 2NOBr(g) 88n 2NO(g) 1 Br2(g) at some temperature is Rate 5 2d3NOBr4 dt 5 k3NOBr4 2 a. If the half-life for this reaction is 2.00 s when [NOBr]0 5 0.900 M, calculate the value of k for this reaction. b. How much time is required for the concentration of NOBr to decrease to 0.100 M?

A first-order reaction is 75.0% complete in 320. s. a. What are the first and second half-lives for this reaction? b. How long does it take for 90.0% completion?

For the reaction A n products, successive half-lives are observed to be 10.0, 20.0, and 40.0 min for an experiment in which [A]0 5 0.10 M. Calculate the concentration of A at the following times. a. 80.0 min b. 30.0 min

DDT (molar mass 5 354.49 g/mol) was a widely used insecticide that was banned from use in the United States in 1973. This ban was brought about due to the persistence of DDT in many different ecosystems, leading to high accumulations of the substance in many birds of prey. The insecticide was shown to cause a thinning of egg shells, pushing many birds toward extinction. If a 20-L drum of DDT was spilled into a pond, resulting in a DDT concentration of 8.75 3 1025 M, how long would it take for the levels of DDT to reach a concentration of 1.41 3 1027 M (a level that is generally assumed safe in mammals)? Assume the decomposition of DDT is a first-order process with a half-life of 56.0 days

Sulfuryl chloride undergoes first-order decomposition at 320.8C with a half-life of 8.75 h. SO2Cl2 1g2 h SO2 1g2 1 Cl2 1g2 What is the value of the rate constant, k, in s21? If the initial pressure of SO2Cl2 is 791 torr and the decomposition occurs in a 1.25-L container, how many molecules of SO2Cl2 remain after 12.5 h?

The decomposition of hydrogen iodide on finely divided gold at 1508C is zero order with respect to HI. The rate defined below is constant at 1.20 3 1024 mol/L ? s. 2HI(g) 88n H2(g) 1 I2(g) Rate 5 2d 3HI4 dt 5 k 5 1.20 3 1024 mol/L ? s a. If the initial HI concentration was 0.250 mol/L, calculate the concentration of HI at 25 minutes after the start of the reaction. b. How long will it take for all of the 0.250 M HI to decompose?

Consider two reaction vessels, one containing A and the other containing B, with equal concentrations at t 5 0. If both substances decompose by first-order kinectics, where kA 5 4.50 3 1024 s21 kB 5 3.70 3 1023 s21 how much time must pass to reach a condition such that [A] 5 4.00[B]?

Theophylline is a phamaceutical drug that is sometimes used to help with lung function. You observe a case where the initial lab results indicate that the concentration of theophylline in a patients body decreased from 2.0 3 1023 M to 1.0 3 1023 M in 24 hours. In another 12 hours, the drug concentration was found to be 5.0 3 1024 M. What is the value of the rate constant for the metabolism of this drug in the body?

Consider the hypothetical reaction A 1 B 1 2C 88n 2D 1 3E where the rate law is Rate 5 2d3A4 dt 5 k3A4 3B4 2 An experiment is carried out where [A]0 5 1.0 3 1022 M, [B]0 5 3.0 M, and [C]0 5 2.0 M. The reaction is started, and after 8.0 seconds, the concentration of A is 3.8 3 1023 M. a. Calculate the value of k for this reaction. b. Calculate the half-life for this experiment. c. Calculate the concentration of A after 13.0 seconds. d. Calculate the concentration of C after 13.0 seconds.

Consider the reaction 3A 1 B 1 C 88n D 1 E where the rate law is defined as 2d3A4 dt 5 k3A4 2 3B4 3C4 An experiment is carried out where [B]0 5 [C]0 5 1.00 M and [A]0 5 1.00 3 1024 M. a. If after 3.00 minutes [A] 5 3.26 3 1025 M, calculate the value of k. b. Calculate the half-life for this experiment. c. Calculate the concentration of B and the concentration of A after 10.0 minutes.

Define each of the following. a. elementary step b. molecularity c. reaction mechanism d. intermediate e. rate-determining step

Define what is meant by unimolecular and bimolecular steps. Why are termolecular steps infrequently seen in chemical reactions?

What two requirements must be met to call a mechanism plausible? Why say a plausible mechanism instead of the correct mechanism? Is it true that most reactions occur by a one-step mechanism? Explain.

Write the rate laws for the following elementary reactions. a. CH3NC(g) 88n CH3CN(g) b. O3(g) 1 NO(g) 88n O2(g) 1 NO2(g) c. O3(g) 88n O2(g) 1 O(g) d. O3(g) 1 O(g) 88n 2O2(g) e. 6 14C 88n 7 14N 1 b particle (nuclear decay)

A possible mechanism for the decomposition of hydrogen peroxide is H2O2 88n 2OH H2O2 1 OH 88n H2O 1 HO2 HO2 1 OH 88n H2O 1 O2Using your results fom Exercise 33, specify which step is the rate-determining step. What is the overall balanced equation for the reaction?

A proposed mechanism for a reaction is C4H9Br 88n C4H9 1 1 Br2 Slow C4H9 1 1 H2O 88n C4H9OH2 1 Fast C4H9OH2 1 1 H2O 88n C4H9OH 1 H3O1 Fast Write the rate law expected for this mechanism. What is the overall balanced equation for the reaction? What are the intermediates in the proposed mechanism?

Is the mechanism NO 1 Cl2 88n NOCl2 NOCl2 1 NO 88n 2NOCl consistent with the results you obtained in Exercise 18? If so, which step is the rate-determining step?

The reaction 2NO(g) 1 O2(g) 88n 2NO2(g) exhibits the rate law Rate 5 k[NO]2[O2] Which of the following mechanisms is consistent with this rate law? a. NO 1 O2 88n NO2 1 O Slow O 1 NO 88n NO2 Fast b. NO 1 O2 34 NO3 Fast equilibrium NO3 1 NO 88n 2NO2 Slow c. 2NO 88n N2O2 Slow N2O2 1 O2 88n N2O4 Fast N2O4 88n 2NO2 Fast d. 2NO 34 N2O2 Fast equilibrium N2O2 88n NO2 1 O Slow O 1 NO 88n NO2 Fast

The gas-phase reaction between Br2 and H2 to form HBr is assumed to proceed by the following mechanism: Br2 3:4 2Br Br 1 H2 3:4 HBr 1 H H 1 Br2 88n HBr 1 Br 2Br 88n Br2 a. Under what conditions does the rate law have the form rate 5 k9[Br2]? b. Under what conditions does the rate law have the form rate 5 k0[H2][Br2]1/2? c. Give expressions for k9 and k0 in terms of the rate constants used to define the mechanism.

The reaction 5Br2(aq) 1 BrO3 2(aq) 1 6H1(aq) 88n 3Br2(l) 1 3H2O(l) is expected to obey the mechanism BrO3 2(aq) 1 H1(aq) 3:4 HBrO3(aq) Fast equilibrium HBrO3(aq) 1 H1(aq) 3:4 H2BrO3 1(aq) Fast equilibrium Br2(aq) 1 H2BrO3 1(aq) 88n (BrOBrO2)(aq) 1 H2O(l) Slow (BrOBrO2)(aq) 1 4H1(aq) 1 4Br2(aq) 88n products Fast Write the rate law for this reaction.

The rate law for the reaction BrO3 2(aq) 1 3SO3 22(aq) 88n Br2(aq) 1 3SO4 22(aq) is Rate 5 k[BrO3 2][SO3 22][H1] The first step in a proposed mechanism is SO3 22(aq) 1 H1(aq) 88n HSO3 2(aq) Fast The second step is rate determining. Write a possible second step for the mechanism.

The reaction I2(aq) 1 OCl2(aq) 88n IO2(aq) 1 Cl2(aq) is believed to occur by the following mechanism: OCl2 1 H2O 3:4 HOCl 1 OH2 Fast equilibrium I2 1 HOCl 88n HOI 1 Cl2 Slow HOI 1 OH2 88n H2O 1 IO2 Fast Write the rate law for this reaction. Note: Since the reaction is in aqueous solution, the effective concentration of water remains constant. Thus the rate of the forward reaction in the first step can be written as Rate 5 k[H2O][OCl2] 5 k1[OCl2]

In the gas phase, the production of phosgene from chlorine and carbon monoxide is assumed to proceed by the following mechanism: Cl2 3:4 2Cl Fast equilibrium Cl 1 CO 3:4 COCl Fast equilibrium COCl 1 Cl2 88n COCl2 1 Cl Slow 2Cl 88n Cl2 Fast Overall reaction: CO 1 Cl2 88n COCl2 a. Write the rate law for this reaction. b. Which species are intermediates?

The following mechanism is proposed for the reduction of NO3 2 by MoCl6 22: MoCl6 22 3:4 MoCl5 2 1 Cl2 NO3 2 1 MoCl5 2 88n OMoCl5 2 1 NO2 2 a. What is the intermediate? b. Derive an expression for the rate law (rate 5 d[NO2 2]/dt) for the overall reaction using the steady-state approximation

The following mechanism has been proposed to account for the rate law of the decomposition of ozone to O2(g): O3 1 M 3:4 O2 1 O 1 M O 1 O3 88n 2O2 Apply the steady-state hypothesis to the concentration of atomic oxygen, and derive the rate law for the decomposition of ozone. (M stands for an atom or molecule that can exchange kinetic energy with the particles undergoing the chemical reaction.)

Consider the hypothetical reaction B 88n E 1 F which is assumed to occur by the mechanism B 1 B 3:4 B* 1 B B* 88n E 1 F where B* represents a B molecule with enough energy to surmount the reaction energy barrier. a. Derive the rate law for the production of E using the steady-state approximation. b. Assume that this reaction is known to be first order. Under what conditions does your derived rate law (from part a) agree with this observation? c. Explain how a chemical reaction can be first order, since even in a simple case (B 88n E 1 F) molecules must collide to build up enough energy to get over the energy barrier. Why arent all reactions at least second order? In other words, explain the physical significance of the result from part b.

How is the rate of a reaction affected by each of the following. a. activation energy b. temperature c. frequency of collisions d. orientation of collisions

The central idea of the collision model is that molecules must collide in order to react. Give two reasons why not all collisions of reactant molecules result in product formation.

Each of the statements given below is false. Explain why. a. The activation energy of a reaction depends on the overall energy change (DE) for the reaction. b. The rate law for a reaction can be deduced from examination of the overall balanced equation for the reaction. c. Most reactions occur by one-step mechanisms

Hydrogen reacts explosively with oxygen. However, a mixture of H2 and O2 can exist indefinitely at room temperature. Explain why H2 and O2 do not react under these conditions.

Consider the following potential energy plots Reaction coordinate E 1 2 3 4 5 a. Rank the reactions from fastest to slowest, and explain your answer. If any reactions have equal rates, explain why. b. Label the reactions as endothermic or exothermic, and supply your answer. c. Rank the exothermic reactions from greatest to least change in potential energy, and support your answer.

The graph below shows the number of collisions with a particular energy for two different temperatures. T1 T2 0 0 Ea Energy Number of collisions a. Which is greater, T2 or T1? How can you tell? b. What does this graph tell us about the temperature dependence of the rate of a chemical reaction? Explain your answer

Which of the following reactions would you expect to have the larger rate at room temperature? Why? (Hint: Think of which would have the lower activation energy.) 2Ce41(aq) 1 Hg2 21(aq) 88n 2Ce31(aq) 1 2Hg21(aq) H3O1(aq) 1 OH2(aq) 88n 2H2O(l)

The activation energy for the decomposition of HI(g) to H2(g) and I2(g) is 186 kJ/mol. The rate constant at 555 K is 3.52 3 1027 L mol21 s21. What is the rate constant at 645 K?

The decomposition of iodoethane in the gas phase proceeds according to the following equation: C2H5I(g) 88n C2H4(g) 1 HI(g) At 660. K, k 5 7.2 3 1024 s21; at 720. K, k 5 1.7 3 1022 s21. What is the rate constant for this firstorder decomposition at 3258C? If the initial pressure of iodoethane is 894 torr at 2458C, what is the pressure of iodoethane after three half-lives?

A certain reaction has an activation energy of 54.0 kJ/mol. As the temperature is increased from 228C to a higher temperature, the rate constant increases by a factor of 7.00. Calculate the higher temperature.

Chemists commonly use a rule of thumb that an increase of 10 K in temperature doubles the rate of a reaction. What must the activation energy be for this statement to be true for a temperature increase from 258C to 358C?

The reaction (CH3)3CBr 1 OH2 88n (CH3)3COH 1 Br2 in a certain solvent is first order with respect to (CH3)3CBr and zero order with respect to OH2. In several experiments the rate constant k was determined at different temperatures. A plot of ln(k) versus 1/T was constructed that resulted in a straight line with a slope of 21.10 3 104 K and a y intercept of 33.5. Assume that k has units of s21. a. Determine the activation energy for this reaction. b. Determine the value of the frequency factor A. c. Calculate the value of k at 258C.

The rate constant for the gas-phase decomposition of N2O5, N2O5 88n 2NO2 1 1 2O2 has the following temperature dependence: T (K) k (s21) 338 4.9 3 1023 318 5.0 3 1024 298 3.5 3 1025 Make the appropriate graph using these data, and determine the activation energy for this reaction

Experimental values for the temperature dependence of the rate constant for the gas-phase reaction NO(g) 1 O3(g) 88n NO2(g) 1 O2(g) are as follows: T (K) k (L mol21 s21) 195 1.08 3 109 230. 2.95 3 109 260. 5.42 3 109 298 12.0 3 109 369 35.5 3 109 Make the appropriate graph using these data, and determine the activation energy for this reaction

Draw a rough sketch of the energy profile for each of the following cases. a. DE 5 110 kJ/mol, Ea 5 25 kJ/mol b. DE 5 210 kJ/mol, Ea 5 50 kJ/mol c. DE 5 250 kJ/mol, Ea 5 50 kJ/mol Which reaction will have the greatest rate at 298 K? Assume the frequency factor A is the same for all three reactions

For the following reaction profiles, indicate a. the positions of reactants and products. b. the activation energy. c. DE for the reaction. Reaction coordinate E Reaction coordinate E d. The second reaction profile is representative of a reaction that occurs by a two-step mechanism. Which point on the plot represents the energy of the intermediate in the two-step reaction? Which step in the mechanism is rate determining, the first or the second step? Explain.

The activation energy for the reaction NO2(g) 1 CO(g) 88n NO(g) 1 CO2(g) is 125 kJ/mol, and DE for the reaction is 2216 kJ/mol. What is the activation energy for the reverse reaction [NO(g) 1 CO2(g) 88n NO2(g) 1 CO(g)]?

The activation energy for the reaction A2(g) 1 B2(g) 88n 2AB(g) is 167 kJ/mol, and DE for the reaction is 128 kJ/mol. What is the activation energy for the decomposition of AB?

Why does a catalyst increase the rate of a reaction? What is the difference between a homogeneous and a heterogeneous catalyst? Would a given reaction necessarily have the same rate law for both a catalyzed and an uncatalyzed pathway? Explain

Consider the following potential energy plots for a chemical reaction when answering the questions below. Reactants Products E2 Reaction progress Energy E1 a. Which plot (red or blue) is the catalyzed pathway? How do you know? b. What does DE1 represent? c. What does DE2 represent? d. Is the reaction endothermic or exothermic?

Would the slope of a ln(k) versus 1/T (K) plot for a catalyzed reaction be more or less negative than the slope of a ln(k) versus 1/T (K) plot for the uncatalyzed reaction? Assume that both rate laws are first order. Explain.

The decomposition of NH3 to N2 and H2 was studied on two surfaces: Surface Ea (kJ/mol) W 163 Os 197 Without a catalyst, the activation energy is 335 kJ/mol. a. Which surface is the better heterogeneous catalyst for the decomposition of NH3? Why? b. How many times faster is the reaction at 298 K on the W surface compared with the reaction with no catalyst present? Assume that the frequency factor A is the same for each reaction. c. The decomposition reaction on the two surfaces obeys a rate law of the form Rate 5 k 3NH3 4 3H2 4 How can you explain the inverse dependence of the rate on the H2 concentration?

One pathway for the destruction of ozone in the upper atmosphere is O3(g) 1 NO(g) 88n NO2(g) 1 O2(g) Slow NO2(g) 1 O(g) 88n NO(g) 1 O2(g) Fast Overall reaction: O3(g) 1 O(g) 88n 2O2(g) a. Which species is a catalyst? b. Which species is an intermediate? c. Ea for the uncatalyzed reaction O3(g) 1 O(g) 88n 2O2(g) is 14.0 kJ. Ea for the same reaction when catalyzed is 11.9 kJ. What is the ratio of the rate constant for the catalyzed reaction to that for the uncatalyzed reaction at 258C? Assume the frequency factor A is the same for each reaction.

One of the concerns about the use of Freons is that they will migrate to the upper atmosphere, where chlorine atoms can be generated by the reaction CCl2F2 88n CF2Cl 1 Cl Freon-12 Chlorine atoms can also act as a catalyst for the destruction of ozone. The activation energy for the reaction Cl 1 O3 88n ClO 1 O2 is 2.1 kJ/mol. Which is the more effective catalyst for the destruction of ozone, Cl or NO? (See Exercise 94.)

Assuming that the mechanism for the hydrogenation of C2H4 given in Section 15.9 is correct, would you predict that the product of the reaction of C2H4 with D2 would be CH2DOCH2D or CHD2OCH3?

For enzyme-catalyzed reactions that follow the mechanism E 1 S 34 E ? S E ? S 34 E 1 P a graph of the rate as a function of [S], the concentration of the substrate, has the following general appearance: Rate [S] Note that at high substrate concentrations the rate no longer changes with [S]. Suggest a reason for this.

Hydrogen peroxide decomposes to water and oxygen gas with the aid of a catalyst (MnO2). The activation energy of the uncatalyzed reaction is 70.0 kJ/mol. When the catalyst is added, the activation energy at 20.8C is 42.0 kJ/mol. Theoretically, to what temperature (8C) would one have to heat the hydrogen peroxide solution so that the rate of the uncatalyzed reaction is equal to the rate of the catalyzed reaction at 20.8C? Assume the frequency factor A is constant, and assume the initial concentrations are the same.

The activation energy for a reaction is changed from 184 kJ/mol to 59.0 kJ/mol at 600. K by the introduction of a catalyst. If the uncatalyzed reaction takes about 2400 years to occur, about how long will the catalyzed reaction take? Assume the frequency factor A is constant, and assume the initial concentrations are the same.

The rate law for a reaction can be determined only from experiment and not from the balanced equation. Two experimental procedures were outlined in this chapter. What are these two procedures? Explain how each method is used to determine rate laws.

The type of rate law for a reaction, either the differential rate law or the integrated rate law, is usually determined by which data are easiest to collect. Explain.

a. Using the free energy profile for a simple one-step reaction, show that at equilibrium K 5 kf/kr, where kf and kr are the rate constants for the forward and reverse reactions. Hint: Use the relationship DG8 5 2RT ln(K), and represent kf and kr using the Arrhenius equation (k 5 Ae2Ea/RT). Reaction coordinate G Reactants Ea (forward) G Ea (reverse) Products b. Why is the following statement false? A catalyst can increase the rate of a forward reaction but not the rate of the reverse reaction.

The decomposition of many substances on the surface of a heterogeneous catalyst shows the following behavior: Rate Concentration of reactant How do you account for the rate law changing from first order to zero order in the concentration of reactant?

Two isomers (A and B) of a given compound dimerize as follows: 2A 88n A2 2B 88n B2 Both processes are known to be second order in the reactant, and k1 is known to be 0.250 L mol21 s21 at 258C. In a particular experiment A, and B were placed in separate containers at 258C, where [A]0 5 1.00 3 1022 M and [B]0 5 2.50 3 1022 M. After each reaction had progressed for 3.00 min, [A] 5 3.00[B]. In this case the rate laws are defined as follows: Rate 5 2d3A4 dt 5 k1 3A4 2 Rate 5 2d3B4 dt 5 k2 3B4 2 a. Calculate the concentration of A2 after 3.00 min. b. Calculate the value of k2. c. Calculate the half-life for the experiment involving A

The thermal degradation of silk was studied by Kuruppillai, Hersh, and Tucker (Historic Textile and Paper Materials, ACS Advances in Chemistry Series, No. 212, 1986) by measuring the tensile strength of silk fibers at various times of exposure to elevated temperature. The loss of tensile strength follows first-order kinetics, 2ds dt 5 ks where s is the strength of the fiber retained after heating and k is the first-order rate constant. The effects of adding a deacidifying agent and an antioxidant to the silk were studied, and the following data were obtained: Strength Retained (%) Heating Time (days) Untreated Deacidifying Agent Antioxidant 0.00 100.0 100.1 114.6 1.00 67.9 60.8 65.2 2.00 38.9 26.8 28.1 3.00 16.1 11.3 6.00 6.8 a. Determine the first-order rate constants for the thermal degradation of silk for each of the three experiments. b. Does either of the two additives appear to retard the degradation of silk? c. Calculate the half-life for the thermal degradation of silk for each of the three experiments.

Sulfuryl chloride (SO2Cl2) decomposes to sulfur dioxide (SO2) and chlorine (Cl2) by reaction in the gas phase. The following data were obtained when a sample containing 5.00 3 1022 mole of sulfuryl chloride was heated to 600 K 6 1 K in a 5.00 3 1021 L container. Time (h) 0.00 1.00 2.00 4.00 8.00 16.00 Pressure (atm) 4.93 5.60 6.34 7.33 8.56 9.52 Define the rate as 2d[SO2Cl2]/dt. a. Determine the value of the rate constant for the decomposition of sulfuryl chloride at 600 K. b. What is the half-life of the reaction? c. What would be the pressure in the vessel after 0.500 h and after 12.0 h? d. What fraction of the sulfuryl chloride remains after 20.0 h?

One reason suggested for the instability of long chains of silicon atoms is that the decomposition involves the following transition state: A A O O O SiH4 + SiH2 H H H Si H A A O H H Si H H A A H Si H A A H Si H The activation energy for such a process is 210 kJ/mol, which is less than either the SiSi or the SiH bond energy. Why would a similar mechanism not be expected to play a very important role in the decomposition of long chains of carbon atoms as seen in organic compounds?

The following results were obtained at 600 K for the decomposition of ethanol on an alumina (Al2O3) surface, C2H5OH(g) 88n C2H4(g) 1 H2O(g) t (s) PTotal (torr) 0 250. 10. 265 20. 280. 30. 295 40. 310. 50. 325 a. Predict PTotal in torr at t 5 80. s. b. What is the value of the rate constant, and what are its units? c. What is the order of the reaction? d. Calculate PTotal at t 5 300. s.

At 620. K butadiene dimerizes at a moderate rate. The following data were obtained in an experiment involving this reaction: t (s) [C4H6] (mol/L) 0 0.01000 1000. 0.00629 2000. 0.00459 3000. 0.00361 a. Determine the order of the reaction in butadiene. b. In how many seconds is the dimerization 1.0% complete? c. In how many seconds is the dimerization 2.0% complete? d. What is the half-life for the reaction if the initial concentration of butadiene is 0.0200 M? e. Use the results from this problem and Exercise 34 to calculate the activation energy for the dimerization of butadiene.

The decomposition of NO2(g) occurs by the following bimolecular elementary reaction: 2NO2(g) 88n 2NO(g) 1 O2(g) The rate constant at 273 K is 2.3 3 10212 L mol21 s21, and the activation energy is 111 kJ/mol. How long will it take for the concentration of NO2(g) to decrease from an initial partial pressure of 2.5 atm to 1.5 atm at 500. K? Assume ideal gas behavior.

The activation energy for a certain uncatalyzed biochemical reaction is 50.0 kJ/mol. In the presence of a catalyst at 378C, the rate constant for the reaction increases by a factor of 2.50 3 103 as compared with the uncatalyzed reaction. Assuming that the frequency factor A is the same for both the catalyzed and uncatalyzed reactions, calculate the activation energy for the catalyzed reaction.

For the reaction 2N2O5(g) 88n 4NO2(g) 1 O2(g) the following data were collected, where Rate 5 2d3N2O5 4 dt t (s) T 5 338 K [N2O5] T 5 318 K [N2O5] 0 1.00 3 1021 M 1.00 3 1021 M 100. 6.14 3 1022 M 9.54 3 1022 M 300. 2.33 3 1022 M 8.63 3 1022 M 600. 5.41 3 1023 M 7.43 3 1022 M 900. 1.26 3 1023 M 6.39 3 1022 M Calculate Ea for this reaction.

Enzymes are kinetically important for many of the complex reactions necessary for plant and animal life to exist. However, only a tiny amount of any particular enzyme is required for these complex reactions to occur. Explain

Iodomethane (CH3I) is a commonly used reagent in organic chemistry. When used properly, this reagent allows chemists to introduce methyl groups in many different useful applications. The chemical does pose a risk as a carcinogen, possibly owing to iodomethanes ability to react with portions of the DNA strand (if they were to come in contact). Consider the following hypothetical initial rates data: [DNA]0 (mmol/L) [CH3I]0 (mmol/L) Initial Rate (mmol/L ? s) 0.100 0.100 3.20 3 1024 0.100 0.200 6.40 3 1024 0.200 0.200 1.28 3 1023 Which of the following could be a possible mechanism to explain the initial rate data? Mechanism I DNA 1 CH3I h DNAiCH3 1 1 I 2 Mechanism II CH3I h CH3 1 1 I 2 Slow DNA 1 CH3 1 h DNAiCH3 1 Fast

Experiments during a recent summer on a number of fireflies (small beetles, Lampyridae photinus) showed that the average interval between flashes of individual insects was 16.3 s at 21.08C and 13.0 s at 27.88C. a. What is the apparent activation energy of the reaction that controls the flashing? b. What would be the average interval between flashes of an individual firefly at 30.08C? c. Compare the observed intervals and the one you calculated in part b to the rule of thumb that the Celsius temperature is 54 minus twice the interval between flashes.

The compound NO2Cl is thought to decompose to NO2 and Cl2 by the following mechanism: NO2Cl 3:4 NO2 1 Cl NO2Cl 1 Cl 88n NO2 1 Cl2 Derive the rate law for the production of Cl2 using the steady-state approximation.

Many biochemical reactions are catalyzed by large protein molecules called enzymes. A typical mechanism for the conversion of a biochemical substrate (S) to product (P) catalyzed by an enzyme (E) involves the following steps: E 1 S 3:4 ES ES 88n P The rate-determining step is the decomposition of the intermediate enzymesubstrate complex (ES) to products (P). Under these conditions, show that the overall rate of product formation is Rate 5 d3P4 dt 5 k1k2 3E4 T3S4 k21 1 k2 1 k1 3S4 where [E]T equals the total enzyme concentration: [E]T 5 [E] 1 [ES]

The thiosulfate ion (S2O3 22) is oxidized by iodine as follows: 2S2O3 22 1aq2 1 I2 1aq2 h S4O6 22 1aq2 1 2I2 1aq2 In a certain experiment, 7.05 3 1023 mol/L of S2O3 22 is consumed in the first 11.0 seconds of the reaction. Calculate the rate of consumption of S2O3 22. Calculate the rate of production of iodide ion.

The reaction A1aq2 1 B1aq2 h products1aq2 was studied, and the following data were obtained: [A]0 (mol/L) [B]0 (mol/L) Initial Rate (mol L21 s21) 0.12 0.18 3.46 3 1022 0.060 0.12 1.15 3 1022 0.030 0.090 4.32 3 1023 0.24 0.090 3.46 3 1022 What is the order of the reaction with respect to A? What is the order of the reaction with respect to B? What is the value of the rate constant for the reaction?

A certain substance, initially present at 0.0800 M, decomposes by zero-order kinetics with a rate constant of 2.50 3 1022 mol L21 s21. Calculate the time (in seconds) required for the system to reach a concentration of 0.0210 M.

A reaction of the form aA h Products gives a plot of ln[A] versus time (in seconds), which is a straight line with a slope of 27.35 3 1023. Assuming [A]0 5 0.0100 M, calculate the time (in seconds) required for the reaction to reach 22.9% completion.

A certain reaction has the form aA h Products At a particular temperature, concentration versus time data were collected. A plot of 1[A] versus time (in seconds) gave a straight line with a slope of 6.90 3 1022. What is the differential rate law for this reaction? What is the integrated rate law for this reaction? What is the value of the rate constant for this reaction? If [A]0 for this reaction is 0.100 M, what is the first half-life (in seconds)? If the original concentration (at t 5 0) is 0.100 M, what is the second half-life (in seconds)?

Which of the following statement(s) is(are) true? a. The half-life for a zero-order reaction increases as the reaction proceeds. b. A catalyst does not change the value of the rate constant. c. The half-life for a reaction, aA 8n products, that is first order in A increases with increasing [A]0. d. The half-life for a second-order reaction increases as the reaction proceeds.

Consider the hypothetical reaction A2 1g2 1 B2 1g2 88n 2AB1g2 , where the rate law is: 2D3A2 4 Dt 5 k3A2 4 3B2 4 The value of the rate constant at 3028C is 2.45 3 1024 L mol21 s21, and at 5088C the rate constant is 0.891 L mol21 s21. What is the activation energy for this reaction? What is the value of the rate constant for this reaction at 3758C?

Experiments have shown that the average frequency of chirping by a snowy tree cricket (Oecanthus fultoni) depends on temperature as shown in the table. Chirping Rate (per min) Temperature (8C) 178 25.0 126 20.3 100. 17.3 What is the apparent activation energy of the process that controls the chirping? What is the rate of chirping expected at a temperature of 7.58C?

Consider the following reaction: CH3X 1 Y 88n CH3Y 1 X At 258C the following two experiments were run, yielding the following data: Experiment 1: [Y]0 5 3.0 M [CH3X] Time (h) 7.08 3 1023 M 1.0 4.52 3 1023 M 1.5 2.23 3 1023 M 2.3 4.76 3 1024 M 4.0 8.44 3 1025 M 5.7 2.75 3 1025 M 7.0 Experiment 2: [Y]0 5 4.5 M [CH3X] Time (h) 4.50 3 1023 M 0 1.70 3 1023 M 1.0 4.19 3 1024 M 2.5 1.11 3 1024 M 4.0 2.81 3 1025 M 5.5 Experiments were also run at 858C. The value of the rate constant at 858C was found to be 7.88 3 108 (with the time in units of hours), where [CH3X]0 5 1.0 3 1022 M and [Y]0 5 3.0 M. a. Determine the rate law and the value of k for this reaction at 258C. b. Determine the half-life at 858C. c. Determine Ea for the reaction. d. Given that the COX bond energy is known to be about 325 kJ/mol, suggest a mechanism that explains the results in parts a and c.

The following data were collected in two studies of the reaction 2A 1 B 88n C 1 D where Rate 5 2d3A4 dt Time (s) Experiment 1 [A] (M) 3 1022 Experiment 2 [A] (M) 3 1022 0 10.0 10.0 20. 6.67 5.00 40. 5.00 3.33 60. 4.00 2.50 80. 3.33 2.00 100. 2.86 1.67 120. 2.50 1.43 In experiment 1, [B]0 5 5.0 M. In experiment 2, [B]0 5 10.0 M. a. Why is [B] much greater than [A]? b. Give the rate law and value for k for this reaction c. Which of the following mechanisms could be correct for this reaction? Justify your choice. i. A 1 B 34 E (fast equilibrium) E 1 B 88n C 1 D (slow) ii. A 1 B 34 E (fast equilibrium) E 1 A 88n C 1 D (slow) iii. A 1 A 88n E (slow) E 1 B 88n C 1 D (fast)

Consider a reaction of the type aA n products, in which the rate law is found to be rate 5 k[A]3 (termolecular reactions are improbable but possible). If the first half-life of the reaction is found to be 40. s, what is the time for the second half-life? Hint: Using your calculus knowledge, derive the integrated rate law from the differential rate law for a termolecular reaction: Rate 5 2d3A4 dt 5 k3A4 3

For the reaction 2A 1 B 88n products a friend proposes the following mechanism: A 1 B 34 M A 1 M 88n products a. Assuming that the second step is the rate-determining step and the first step is a fast equilibrium step, determine the rate law. Represent the rate constant in terms of k1, k21, and k2. b. Using the steady-state approximation, determine the rate law. c. Under what conditions of [A] and [B] do you get the same rate law in parts a and b?

Consider the hypothetical reaction A 1 B 1 2C 88n 2D 1 3E In a study of this reaction, three experiments were run at the same temperature. The rate is defined as 2d[B]/dt. Experiment 1: [A]0 5 2.0 M [B]0 5 1.0 3 1023 M [C]0 5 1.0 M [B] (mol/L) Time (s) 2.7 3 1024 1.0 3 105 1.6 3 1024 2.0 3 105 1.1 3 1024 3.0 3 105 8.5 3 1025 4.0 3 105 6.9 3 1025 5.0 3 105 5.8 3 1025 6.0 3 105 Experiment 2: [A]0 5 1.0 3 1022 M [B]0 5 3.0 M [C]0 5 1.0 M [A] (mol/L) Time (s) 8.9 3 1023 1.0 7.1 3 1023 3.0 5.5 3 1023 5.0 3.8 3 1023 8.0 2.9 3 1023 10.0 2.0 3 1023 13.0 Experiment 3: [A]0 5 10.0 M [B]0 5 5.0 M [C]0 5 5.0 3 1021 M [C] (mol/L) Time (s) 0.43 1.0 3 1022 0.36 2.0 3 1022 0.29 3.0 3 1022 0.22 4.0 3 1022 0.15 5.0 3 1022 0.08 6.0 3 1022 Write the rate law for this reaction, and calculate the rate constant

A reaction represented by the equation 3O2(g) 88n 2O3(g) was studied at a specific temperature, and the following data were collected: Time (s) Total Pressure (atm) 0 1.000 46.89 0.9500 98.82 0.9033 137.9 0.8733 200.0 0.8333 286.9 0.7900 337.9 0.7700 511.3 0.7233 a. Determine the rate law for this reaction. b. Determine the value of the rate constant (including units). c. Calculate the time it would take for the total pressure to be 0.7133 atm.

The gas-phase decomposition 2N2O5 n 4NO2 1 O2 is first order but not unimolecular. A possible mechanism is M 1 N2O5 3:4 NO3 1 NO2 1 M NO3 1 NO2 88n NO 1 O2 1 NO2 NO3 1 NO 88n 2NO2 Apply the steady-state approximation to the concentrations of the intermediates NO3 and NO, and derive the rate law for the decomposition of N2O5.

You are studying the kinetics of the reaction H2(g) 1 F2(g) n 2HF(g) and you wish to determine a mechanism for the reaction. You run the reaction twice by keeping one reactant at a much higher pressure than the other reactant (this lower-pressure reactant begins at 1.000 atm). Unfortunately, you neglect to record which reactant was at the higher pressure, and you forget it later. Your data for the first experiment are as follows: Pressure of HF (atm) Time (min) 0 0 0.300 30.0 0.600 65.8 0.900 110.4 1.200 169.1 1.500 255.9 When you run the second experiment (in which the higher-pressure reactant is run at a much higher pressure), you determine the values of the apparent rate constants to be the same. It also turns out that you find data taken from another person in the lab. This individual found that the reaction proceeds 40.0 times faster at 558C than at 358C. You also know, from the energylevel diagram, that there are three steps to the mechanism, and the first step has the highest activation energy. You look up the bond energies of the species involved and they are (in kJ/mol): HOH (432), FOF (154), and HOF (565). a. Sketch an energy-level diagram (qualitative) that is consistent with the one described.

Hydrogen peroxide and the iodide ion react in acidic solution as follows: H2O2(aq) 1 3I2(aq) 1 2H1(aq) 88n I3 2(aq) 1 2H2O(l) The kinetics of this reaction were studied by following the decay of the concentration of H2O2 and constructing plots of ln[H2O2] versus time. All the plots were linear and all solutions had [H2O2]0 5 8.0 3 1024 mol/L. The slopes of these straight lines depended on the initial concentrations of I2 and H1. The results follow: [I2]0 (mol/L) [H1]0 (mol/L) Slope (min21) 0.1000 0.0400 20.120 0.3000 0.0400 20.360 0.4000 0.0400 20.480 0.0750 0.0200 20.0760 0.0750 0.0800 20.118 0.0750 0.1600 20.174 The rate law for this reaction has the form Rate 5 2d3H2O2 4 dt 5 1k1 1 k2 3H1 4 2 3I 2 4 m 3H2O2 4 n a. Specify the orders of this reaction with respect to [H2O2] and [I2]. b. Calculate the values of the rate constants k1 and k2. c. What reason could there be for the two-term dependence of the rate on [H1]?