Solved: Change of Concentration with Time (Section)(a)

An automotive fuel injector dispenses a fine spray of gasoline into the automobile cylinder, as shown in the bottom drawing here. When an injector gets clogged, as shown in the top drawing, the spray is not as fine or even and the performance of the car declines. How is this observation related to chemical kinetics? [Section 14.1]

Consider the following graph of the concentration of a substance X over time. Is each of the following statements true or false? (a) X is a product of the reaction. (b) The rate of the reaction remains the same as time progresses. (c) The average rate between points 1 and 2 is greater than the average rate between points 1 and 3. (d) As time progresses, the curve will eventually turn downward toward the x-axis. [Section 14.2] Time 1 2 3 [X]

You study the rate of a reaction, measuring both the concentration of the reactant and the concentration of the product as a function of time, and obtain the following results: Time B A Concentration (a) Which chemical equation is consistent with these data: (i) A B, (ii) B A, (iii) A 2 B, (iv) B 2 A? (b) Write equivalent expressions for the rate of the reaction in terms of the appearance or disappearance of the two substances. [Section 14.2]

Suppose that for the reaction K + L M, you monitor the production of M over time, and then plot the following graph from your data: 0 5 10 15 20 25 30 t, min [M] (a) Is the reaction occurring at a constant rate from t = 0 to t = 15 min? (b) Is the reaction completed at t = 15 min? (c) Suppose the reaction as plotted here were started with 0.20 mol K and 0.40 mol L. After 30 min, an additional 0.20 mol K are added to the reaction mixture. Which of the following correctly describes how the plot would look from t = 30 min to t = 60 min? (i) [M] would remain at the same constant value it has at t = 30 min, (ii) [M] would increase with the same slope as t = 0 to 15 min, until t = 45 min at which point the plot becomes horizontal again, or (iii) [M] decreases and reaches 0 at t = 45 min. [Section 14.2]

The following diagrams represent mixtures of NO(g) and O21g2. These two substances react as follows: 2 NO1g2 + O21g2 2 NO21g2 It has been determined experimentally that the rate is second order in NO and first order in O2. Based on this fact, which of the following mixtures will have the fastest initial rate? [Section 14.3] (1) (2) (3)

A friend studies a first-order reaction and obtains the following three graphs for experiments done at two different temperatures. (a) Which two graphs represent experiments done at the same temperature? What accounts for the difference in these two graphs? In what way are they the same? (b) Which two graphs represent experiments done with the same starting concentration but at different temperatures? Which graph probably represents the lower temperature? How do you know? [Section 14.4] Time 1 2 3 ln [A]

(a) Given the following diagrams at t = 0 min and t = 30 min, what is the half-life of the reaction if it follows first-order kinetics? t = 0 min t = 30 min

(b) After four half-life periods for a first-order reaction, what fraction of reactant remains? [Section 14.4]

Which of the following linear plots do you expect for a reaction A products if the kinetics are (a) zero order, (b) first order, or (c) second order? [Section 14.4]

The following diagram shows a reaction profile. Label the components indicated by the boxes. [Section 14.5] (4) Reaction progress Energy (3)

The accompanying graph shows plots of ln k versus 1>T for two different reactions. The plots have been extrapolated to the y-intercepts. Which reaction (red or blue) has (a) the larger value for Ea, and (b) the larger value for the frequency factor, A? [Section 14.5] 1/T ln k

The following graph shows two different reaction pathways for the same overall reaction at the same temperature. Is each of the following statements true or false? (a) The rate is faster for the red path than for the blue path. (b) For both paths, the rate of the reverse reaction is slower than the rate of the forward reaction. (c) The energy change E is the same for both paths. [Section 14.6] Reaction progress Potential energy

Consider the diagram that follows, which represents two steps in an overall reaction. The red spheres are oxygen, the blue ones nitrogen, and the green ones fluorine. (a) Write the chemical equation for each step in the reaction. (b) Write the equation for the overall reaction. (c) Identify the intermediate in the mechanism. (d) Write the rate law for the overall reaction if the first step is the slow, rate- determining step. [Section 14.6] + + +

Based on the following reaction profile, how many intermediates are formed in the reaction A C? How many transition states are there? Which step, A B or B C, is the faster? For the reaction A C, is E positive, negative, or zero? [Section 14.6] Potential energy Reaction progress A B C

Draw a possible transition state for the bimolecular reaction depicted here. (The blue spheres are nitrogen atoms, and the red ones are oxygen atoms.) Use dashed lines to represent the bonds that are in the process of being broken or made in the transition state. [Section 14.6] + +

The following diagram represents an imaginary two-step mechanism. Let the red spheres represent element A, the green ones element B, and the blue ones element C. (a) Write the equation for the net reaction that is occurring. (b) Identify the intermediate. (c) Identify the catalyst. [Sections 14.6 and 14.7]

Draw a graph showing the reaction pathway for an overall exothermic reaction with two intermediates that are produced at different rates. On your graph indicate the reactants, products, intermediates, transition states, and activation energies. [Sections 14.6 and 14.7]

(a) What is meant by the term reaction rate?

(b) Name three factors that can affect the rate of a chemical reaction.

(c) Is the rate of disappearance of reactants always the same as the rate of appearance of products?

(a) What are the units usually used to express the rates of reactions occurring in solution?

(b) From your everyday experience, give two examples of the effects of temperature on the rates of reactions.

(c) What is the difference between average rate and instantaneous rate?

Consider the following hypothetical aqueous reaction: A1aq2 S B1aq2. A flask is charged with 0.065 mol of A in a total volume of 100.0 mL. The following data are collected: Time (min) 0 10 20 30 40 Moles of A 0.065 0.051 0.042 0.036 0.031 (a) Calculate the number of moles of B at each time in the table, assuming that there are no molecules of B at time zero, and that A cleanly converts to B with no intermediates. (b) Calculate the average rate of disappearance of A for each 10-min interval in units of M>s. (c) Between t = 10 min and t = 30 min, what is the average rate of appearance of B in units of M>s? Assume that the volume of the solution is constant

A flask is charged with 0.100 mol of A and allowed to react to form B according to the hypothetical gas-phase reaction A1g2 B1g2. The following data are collected: Time (s) 0 40 80 120 160 Moles of A 0.100 0.067 0.045 0.030 0.020 (a) Calculate the number of moles of B at each time in the table, assuming that A is cleanly converted to B with no intermediates. (b) Calculate the average rate of disappearance of A for each 40-s interval in units of mol>s. (c) Which of the following would be needed to calculate the rate in units of concentration per time: (i) the pressure of the gas at each time, (ii) the volume of the reaction flask, (iii) the temperature, or (iv) the molecular weight of A?

The isomerization of methyl isonitrile 1CH3NC2 to acetonitrile 1CH3CN2 was studied in the gas phase at 215 C, and the following data were obtained: Time (s) 3Ch3nC4 1M2 0 0.0165 2000 0.0110 5000 0.00591 8000 0.00314 12,000 0.00137 15,000 0.00074 (a) Calculate the average rate of reaction, in M>s, for the time interval between each measurement. (b) Calculate the average rate of reaction over the entire time of the data from t = 0 to t = 15,000 s. (c) Which is greater, the average rate between t = 2000 and t = 12,000 s, or between t = 8000 and t = 15,000 s? (d) Graph 3CH3NC4 versus time and determine the instantaneous rates in M>s at t = 5000 s and t = 8000 s.

The rate of disappearance of HCl was measured for the following reaction: CH3OH1aq2 + HCl1aq2 CH3Cl1aq2 + H2O1l2 The following data were collected: Time (min) [HCl] (M) 0.0 1.85 54.0 1.58 107.0 1.36 215.0 1.02 430.0 0.580 (a) Calculate the average rate of reaction, in M>s, for the time interval between each measurement. (b) Calculate the average rate of reaction for the entire time for the data from t = 0.0 min to t = 430.0 min. (c) Which is greater, the average rate between t = 54.0 and t = 215.0 min, or between t = 107.0 and t = 430.0 min? (d) Graph [HCl] versus time and determine the instantaneous rates in M>min and M>s at t = 75.0 min and t = 250 min.

For each of the following gas-phase reactions, indicate how the rate of disappearance of each reactant is related to the rate of appearance of each product: (a) H2O21g2 H21g2 + O21g2 (b) 2 N2O1g2 2 N21g2 + O21g2 (c) N21g2 + 3 H21g2 2 NH31g2 (d) C2H5NH21g2 C2H41g2 + NH31g2

For each of the following gas-phase reactions, write the rate expression in terms of the appearance of each product and disappearance of each reactant: (a) 2 H2O1g2 2 H21g2 + O21g2 (b) 2 SO21g2 + O21g2 2 SO31g2 (c) 2 NO1g2 + 2 H21g2 N21g2 + 2 H2O1g2 (d) N21g2 + 2 H21g2 N2H41g2

( a ) Consider the combustion of H21g2: 2 H21g2 + O21g2 2 H2O1g2. If hydrogen is burning at the rate of 0.48 mol>s, what is the rate of consumption of oxygen? What is the rate of formation of water vapor?

(b) The reaction 2 NO1g2 + Cl21g2 2 NOCl1g2 is carried out in a closed vessel. If the partial pressure of NO is decreasing at the rate of 56 torr/min, what is the rate of change of the total pressure of the vessel?

(a) Consider the combustion of ethylene, C2H41g2 + 3 O21g2 2 CO21g2 + 2 H2O1g2. If the concentration of C2H4 is decreasing at the rate of 0.036 M>s, what are the rates of change in the concentrations of CO2 and H2O?

(b) The rate of decrease in N2H4 partial pressure in a closed reaction vessel from the reaction N2H41g2 + H21g2 2 NH31g2 is 74 torr per hour. What are the rates of change of NH3 partial pressure and total pressure in the vessel?

A reaction A + B C obeys the following rate law: Rate = k3B4 2 . (a) If [A] is doubled, how will the rate change? Will the rate constant change? (b) What are the reaction orders for A and B? What is the overall reaction order? (c) What are the units of the rate constant?

Consider a hypothetical reaction between A, B, and C that is first order in A, zero order in B, and second order in C. (a) Write the rate law for the reaction. (b) How does the rate change when [A] is doubled and the other reactant concentrations are held constant? (c) How does the rate change when [B] is tripled and the other reactant concentrations are held constant? (d) How does the rate change when [C] is tripled and the other reactant concentrations are held constant? (e) By what factor does the rate change when the concentrations of all three reactants are tripled? (f) By what factor does the rate change when the concentrations of all three reactants are cut in half?

The decomposition reaction of N2O5 in carbon tetrachloride is 2 N2O5 4 NO2 + O2. The rate law is first order in N2O5. At 64 C the rate constant is 4.82 * 10-3 s -1 . (a) Write the rate law for the reaction. (b) What is the rate of reaction when 3N2O54 = 0.0240 M? (c) What happens to the rate when the concentration of N2O5 is doubled to 0.0480 M? (d) What happens to the rate when the concentration of N2O5 is halved to 0.0120 M?

Consider the following reaction: 2 NO1g2 + 2 H21g2 N21g2 + 2 H2O1g2 (a) The rate law for this reaction is first order in H2 and second order in NO. Write the rate law. (b) If the rate constant for this reaction at 1000 K is 6.0 * 104 M -2 s -1 , what is the reaction rate when 3NO4 = 0.035 M and 3H24 = 0.015 M? (c) What is the reaction rate at 1000 K when the concentration of NO is increased to 0.10 M, while the concentration of H2 is 0.010 M? (d) What is the reaction rate at 1000 K if [NO] is decreased to 0.010 M and 3H24 is increased to 0.030 M?

Consider the following reaction: 2 NO1g2 + 2 H21g2 N21g2 + 2 H2O1g2 (a) The rate law for this reaction is first order in H2 and second order in NO. Write the rate law. (b) If the rate constant for this reaction at 1000 K is 6.0 * 104 M -2 s -1 , what is the reaction rate when 3NO4 = 0.035 M and 3H24 = 0.015 M? (c) What is the reaction rate at 1000 K when the concentration of NO is increased to 0.10 M, while the concentration of H2 is 0.010 M? (d) What is the reaction rate at 1000 K if [NO] is decreased to 0.010 M and 3H24 is increased to 0.030 M?

The reaction between ethyl bromide 1C2H5Br2 and hydroxide ion in ethyl alcohol at 330 K, C2H5Br1alc2 + OH- 1alc2 C2H5OH1l2 + Br - 1alc2, is first order each in ethyl bromide and hydroxide ion. When 3C2H5Br4 is 0.0477 M and 3OH- 4 is 0.100 M, the rate of disappearance of ethyl bromide is 1.7 * 10-7 M>s. (a) What is the value of the rate constant? (b) What are the units of the rate constant? (c) How would the rate of disappearance of ethyl bromide change if the solution were diluted by adding an equal volume of pure ethyl alcohol to the solution?

The iodide ion reacts with hypochlorite ion (the active ingredient in chlorine bleaches) in the following way: OCl - + I - OI - + Cl - . This rapid reaction gives the following rate data: 3oCl 4 1M2 3i 4 1M2 initial Rate 1M,s2 1.5 * 10-3 1.5 * 10-3 1.36 * 10-4 3.0 * 10-3 1.5 * 10-3 2.72 * 10-4 1.5 * 10-3 3.0 * 10-3 2.72 * 10-4 (a) Write the rate law for this reaction. (b) Calculate the rate constant with proper units. (c) Calculate the rate when 3OCl -4 = 2.0 * 10-3 M and 3I - 4 = 5.0 * 10 - 4 M.

The reaction 2 ClO21aq2 + 2 OH- 1aq2 ClO3 - 1aq2 + ClO2 - 1aq2 + H2O1l2 was studied with the following results: Experiment 1Clo22 1M2 3oh4 1M2 initial Rate 1M,s2 1 0.060 0.030 0.0248 2 0.020 0.030 0.00276 3 0.020 0.090 0.00828 (a) Determine the rate law for the reaction. (b) Calculate the rate constant with proper units. (c) Calculate the rate when 3ClO24 = 0.100 M and 3OH- 4 = 0.050 M.

The following data were measured for the reaction BF31g2 + NH31g2 F3BNH31g2: Experiment 3BF34 1m2 3nh34 1M2 initial Rate 1M,s2 1 0.250 0.250 0.2130 2 0.250 0.125 0.1065 3 0.200 0.100 0.0682 4 0.350 0.100 0.1193 5 0.175 0.100 0.0596 (a) What is the rate law for the reaction? (b) What is the overall order of the reaction? (c) Calculate the rate constant with proper units? (d) What is the rate when 3BF34 = 0.100 M and 3NH34 = 0.500 M?

The following data were collected for the rate of disappearance of NO in the reaction 2 NO1g2 + O21g2 2 NO21g2: Experiment 3no4 1M2 3o2 4 1M2 initial Rate 1M,s2 1 0.0126 0.0125 1.41 * 10-2 2 0.0252 0.0125 5.64 * 10-2 3 0.0252 0.0250 1.13 * 10-1 (a) What is the rate law for the reaction? (b) What are the units of the rate constant? (c) What is the average value of the rate constant calculated from the three data sets? (d) What is the rate of disappearance of NO when 3NO4 = 0.0750 M and 3O24 = 0.0100 M ? (e) What is the rate of disappearance of O2 at the concentrations given in part (d)?

Consider the gas-phase reaction between nitric oxide and bromine at 273 C: 2 NO1g2 + Br21g2 2 NOBr1g2. The following data for the initial rate of appearance of NOBr were obtained: Experiment 3no4 1m2 3Br24 1M2 initial Rate 1M,s2 1 0.10 0.20 24 2 0.25 0.20 150 3 0.10 0.50 60 4 0.35 0.50 735 (a) Determine the rate law. (b) Calculate the average value of the rate constant for the appearance of NOBr from the four data sets. (c) How is the rate of appearance of NOBr related to the rate of disappearance of Br2? (d) What is the rate of disappearance of Br2 when 3NO4 = 0.075 M and 3Br24 = 0.25 M ?

Consider the reaction of peroxydisulfate ion 1S2O8 2-2 with iodide ion 1I - 2 in aqueous solution: S2O8 2 - 1aq2 + 3 I - 1aq2 2 SO4 2 - 1aq2 + I3 - 1aq2 At a particular temperature the initial rate of disappearance of S2O8 2 - varies with reactant concentrations in the following manner: Experiment 3s2o8 24 1M2 3i 4 1M2 initial Rate 1M,s2 1 0.018 0.036 2.6 * 10-6 2 0.027 0.036 3.9 * 10-6 3 0.036 0.054 7.8 * 10-6 4 0.050 0.072 1.4 * 10-5 (a) Determine the rate law for the reaction and state the units of the rate constant. (b) What is the average value of the rate constant for the disappearance of S2O8 2 - based on the four sets of data? (c) How is the rate of disappearance of S2O8 2 - related to the rate of disappearance of I - ? (d) What is the rate of disappearance of I - when 3S2O8 2-4 = 0.025 M and 3I - 4 = 0.050 M ?

(a) Define the following symbols that are encountered in rate equations for the generic reaction A S B: 3A40, t1>2 3A4t, k.

(b) What quantity, when graphed versus time, will yield a straight line for a first-order reaction? (c) How can you calculate the rate constant for a first-order reaction from the graph you made in part (b)?

(a) For a generic second-order reaction A B, what quantity, when graphed versus time, will yield a straight line?

(b) What is the slope of the straight line from part (a)?

(c) How do the half-lives of first-order and second-order reactions differ?

(a) The gas-phase decomposition of SO2Cl2, SO2Cl21g2 SO21g2 + Cl21g2, is first order in SO2Cl2. At 600 K the halflife for this process is 2.3 * 105 s. What is the rate constant at this temperature?

(b) At 320 C the rate constant is 2.2 * 10-5 s -1 . What is the half-life at this temperature?

Molecular iodine, I21g2, dissociates into iodine atoms at 625 K with a first-order rate constant of 0.271 s -1 . (a) What is the half-life for this reaction? (b) If you start with 0.050 M I2 at this temperature, how much will remain after 5.12 s assuming that the iodine atoms do not recombine to form I2?

As described in Exercise 14.41, the decomposition of sulfuryl chloride 1SO2Cl22 is a first-order process. The rate constant for the decomposition at 660 K is 4.5 * 10-2 s -1 . (a) If we begin with an initial SO2Cl2 pressure of 450 torr, what is the partial pressure of this substance after 60 s? (b) At what time will the partial pressure of SO2Cl2 decline to one-tenth its initial value?

The first-order rate constant for the decomposition of N2O5, 2 N2O51g2 4 NO21g2 + O21g2, at 70 C is 6.82 * 10-3 s -1 . Suppose we start with 0.0250 mol of N2O51g2 in a volume of 2.0 L. (a) How many moles of N2O5 will remain after 5.0 min? (b) How many minutes will it take for the quantity of N2O5 to drop to 0.010 mol? (c) What is the half-life of N2O5 at 70 C ?

The reaction SO2Cl21g2 SO21g2 + Cl21g2 is first order in SO2Cl2. Using the following kinetic data, determine the magnitude and units of the first-order rate constant: Time (s) Pressure so2Cl2 (atm) 0 1.000 2500 0.947 5000 0.895 7500 0.848 10,000 0.803

From the following data for the first-order gas-phase isomerization of CH3NC at 215 C, calculate the first-order rate constant and half-life for the reaction: Time (s) Pressure Ch3nC (torr) 0 502 2000 335 5000 180 8000 95.5 12,000 41.7 15,000 22.4

Consider the data presented in Exercise 14.19. (a) By using appropriate graphs, determine whether the reaction is first order or second order. (b) What is the rate constant for the reaction? (c) What is the half-life for the reaction?

Consider the data presented in Exercise 14.20. (a) Determine whether the reaction is first order or second order. (b) What is the rate constant? (c) What is the half-life?

The gas-phase decomposition of NO2, 2 NO21g2 2 NO1g2 + O21g2, is studied at 383 C, giving the following data: Time (s) 3no24 (M) 0.0 0.100 5.0 0.017 10.0 0.0090 15.0 0.0062 20.0 0.0047 (a) Is the reaction first order or second order with respect to the concentration of NO2? (b) What is the rate constant? (c) Predict the reaction rates at the beginning of the reaction for initial concentrations of 0.200 M, 0.100 M, and 0.050 M NO2.

Sucrose 1C12H22O112, commonly known as table sugar, reacts in dilute acid solutions to form two simpler sugars, glucose and fructose, both of which have the formula C6H22O6. At 23 C and in 0.5 M HCl, the following data were obtained for the disappearance of sucrose: Time (min) 3C12h22o114 1M2 0 0.316 39 0.274 80 0.238 140 0.190 210 0.146 (a) Is the reaction first order or second order with respect to 3C12H22O114? (b) What is the rate constant? (c) Using this rate constant, calculate the concentration of sucrose at 39, 80, 140, and 210 min if the initial sucrose concentration was 0.316 M and the reaction were zero order in sucrose.

(a) What factors determine whether a collision between two molecules will lead to a chemical reaction?

(b) According to the collision model, why does temperature affect the value of the rate constant?

(c) Does the rate constant for a reaction generally increase or decrease with an increase in reaction temperature?

(a) In which of the following reactions would you expect the orientation factor to be least important in leading to reaction: NO + O NO2 or H + Cl HCl?

(b) How does the kinetic-molecular theory help us understand the temperature dependence of chemical reactions?

Calculate the fraction of atoms in a sample of argon gas at 400 K that has an energy of 10.0 kJ or greater.

(a) The activation energy for the isomerization of methyl isonitrile (Figure 14.7) is 160 kJ>mol. Calculate the fraction of methyl isonitrile molecules that has an energy of 160.0 kJ or greater at 500 K

(b) Calculate this fraction for a temperature of 520 K. What is the ratio of the fraction at 520 K to that at 500 K?

The gas-phase reaction Cl1g2 + HBr1g2 HCl1g2 + Br1g2 has an overall energy change of -66 kJ. The activation energy for the reaction is 7 kJ. (a) Sketch the energy profile for the reaction, and label Ea and E. (b) What is the activation energy for the reverse reaction?

For the elementary process N2O51g2 NO21g2 + NO31g2 the activation energy 1Ea2 and overall E are 154 kJ>mol and 136 kJ>mol, respectively. (a) Sketch the energy profile for this reaction, and label Ea and E. (b) What is the activation energy for the reverse reaction?

Indicate whether each statement is true or false. (a) If you compare two reactions with similar collision factors, the one with the larger activation energy will be faster. (b) A reaction that has a small rate constant must have a small frequency factor. (c) Increasing the reaction temperature increases the fraction of successful collisions between reactants.

Indicate whether each statement is true or false. (a) If you compare two reactions with similar collision factors, the one with the larger activation energy will be faster. (b) A reaction that has a small rate constant must have a small frequency factor. (c) Increasing the reaction temperature increases the fraction of successful collisions between reactants.

Based on their activation energies and energy changes and assuming that all collision factors are the same, which of the following reactions would be fastest and which would be slowest? (a) Ea = 45 kJ>mol; E = -25 kJ>mol (b) Ea = 35 kJ>mol; E = -10 kJ>mol (c) Ea = 55 kJ>mol; E = 10 kJ>mol

Which of the reactions in Exercise 14.61 will be fastest in the reverse direction? Which will be slowest?

(a) A certain first-order reaction has a rate constant of 2.75 * 10-2 s -1 at 20 C. What is the value of k at 60 C if Ea = 75.5 kJ>mol ?

(b) Another first-order reaction also has a rate constant of 2.75 * 10-2 s -1 at 20 C What is the value of k at 60 C if Ea = 125 kJ>mol ?

(c) What assumptions do you need to make in order to calculate answers for parts (a) and (b)?

Understanding the high-temperature behavior of nitrogen oxides is essential for controlling pollution generated in automobile engines. The decomposition of nitric oxide (NO) to N2 and O2 is second order with a rate constant of 0.0796 M-1 s -1 at 737 C and 0.0815 M-1 s -1 at 947 C. Calculate the activation energy for the reaction.

The rate of the reaction CH3COOC2H51aq2 + OH- 1aq2 CH3COO- 1aq2 + C2H5OH1aq2 was measured at several temperatures, and the following data were collected: Temperature 1C2 k 1M1 s12 15 0.0521 25 0.101 35 0.184 45 0.332 Calculate the value of Ea by constructing an appropriate graph.

The temperature dependence of the rate constant for a reaction is tabulated as follows: Temperature (K) k 1M 1 s12 600 0.028 650 0.22 700 1.3 750 6.0 800 23 Calculate Ea and A.

(a) What is meant by the term elementary reaction?

(b) What is the difference between a unimolecular and a bimolecular elementary reaction?

(c) What is a reaction mechanism?

(d) What is meant by the term rate-determining step?

(a) What is meant by the term molecularity?

(b) Why are termolecular elementary reactions so rare?

(c) What is an intermediate in a mechanism?

(d) What are the differences between an intermediate and a transition state?

What is the molecularity of each of the following elementary reactions? Write the rate law for each. (a) Cl21g2 2 Cl1g2 (b) OCl - 1aq2 + H2O1l2 HOCl1aq2 + OH- 1aq2 (c) NO1g2 + Cl21g2 NOCl21g2

What is the molecularity of each of the following elementary reactions? Write the rate law for each. (a) 2 NO1g2 N2O21g2 CH2 (b) H2C CH21g2 CH2CHCH31g2 (c) SO31g2 SO21g2 + O1g2

(a) Based on the following reaction profile, how many intermediates are formed in the reaction A D?

(b) How many transition states are there?

(c) Which step is the fastest?

(d) For the reaction A D, is E positive, negative, or zero? Potential energy Reaction progress A B C D

Consider the following energy profile. Reaction progess Potential energy (a) How many elementary reactions are in the reaction mechanism? (b) How many intermediates are formed in the reaction? (c) Which step is rate limiting? (d) For the overall reaction, is E positive, negative, or zero?

The following mechanism has been proposed for the gasphase reaction of H2 with ICl: H21g2 + ICl1g2 HI1g2 + HCl1g2 HI1g2 + ICl1g2 I21g2 + HCl1g2 (a) Write the balanced equation for the overall reaction. (b) Identify any intermediates in the mechanism. (c) If the first step is slow and the second one is fast, which rate law do you expect to be observed for the overall reaction?

The decomposition of hydrogen peroxide is catalyzed by iodide ion. The catalyzed reaction is thought to proceed by a two-step mechanism: H2O21aq2 + I - 1aq2 H2O1l2 + IO- 1aq2 1slow2 IO- 1aq2 + H2O21aq2 H2O1l2 + O21g2 + I - 1aq2 1fast2 (a) Write the chemical equation for the overall process. (b) Identify the intermediate, if any, in the mechanism. (c) Assuming that the first step of the mechanism is rate determining, predict the rate law for the overall process.

The reaction 2 NO1g2 + Cl21g2 2 NOCl1g2 was performed and the following data obtained under conditions of constant 3Cl24: Time (under conditions of constant [Cl2]) 1/[NO] (a) Is the following mechanism consistent with the data? NO1g2 + Cl21g2 NOCl21g2 1fast2 NOCl21g2 + NO1g2 2 NOCl1g2 1slow2 (b) Does the linear plot guarantee that the overall rate law is second order?

You have studied the gas-phase oxidation of HBr by O2: 4 HBr1g2 + O21g2 2 H2O1g2 + 2 Br21g2 You find the reaction to be first order with respect to HBr and first order with respect to O2. You propose the following mechanism: HBr1g2 + O21g2 HOOBr1g2 HOOBr1g2 + HBr1g2 2 HOBr1g2 HOBr1g2 + HBr1g2 H2O1g2 + Br21g2 (a) Confirm that the elementary reactions add to give the overall reaction. (b) Based on the experimentally determined rate law, which step is rate determining? (c) What are the intermediates in this mechanism? (d) If you are unable to detect HOBr or HOOBr among the products, does this disprove your mechanism?

(a) What is a catalyst?

(b) What is the difference between a homogeneous and a heterogeneous catalyst?

(c) Do catalysts affect the overall enthalpy change for a reaction, the activation energy, or both?

(a) Most commercial heterogeneous catalysts are extremely finely divided solid materials. Why is particle size important?

(b) What role does adsorption play in the action of a heterogeneous catalyst?

In Figure 14.22, we saw that Br - 1aq2 catalyzes the decomposition of H2O21aq2 into H2O1l2 and O21g2. Suppose that some KBr1s2 is added to an aqueous solution of hydrogen peroxide. Make a sketch of 3Br - 1aq24 versus time from the addition of the solid to the end of the reaction

In solution, chemical species as simple as H+ and OH- can serve as catalysts for reactions. Imagine you could measure the 3H+4 of a solution containing an acid-catalyzed reaction as it occurs. Assume the reactants and products themselves are neither acids nor bases. Sketch the 3H+4 concentration profile you would measure as a function of time for the reaction, assuming t = 0 is when you add a drop of acid to the reaction

The oxidation of SO2 to SO3 is accelerated by NO2. The reaction proceeds according to: NO21g2 + SO21g2 NO1g2 + SO31g2 2 NO1g2 + O21g2 2 NO21g2 (a) Show that, with appropriate coefficients, the two reactions can be summed to give the overall oxidation of SO2 by O2 to give SO3. (b) Do we consider NO2 a catalyst or an intermediate in this reaction? (c) Is this an example of homogeneous catalysis or heterogeneous catalysis?

The addition of NO accelerates the decomposition of N2O, possibly by the following mechanism: NO1g2 + N2O1g2 N21g2 + NO21g2 2 NO21g2 2 NO1g2 + O21g2 (a) What is the chemical equation for the overall reaction? Show how the two steps can be added to give the overall equation. (b) Is NO serving as a catalyst or an intermediate in this reaction? (c) If experiments show that during the decomposition of N2O, NO2 does not accumulate in measurable quantities, does this rule out the proposed mechanism?

Many metallic catalysts, particularly the precious-metal ones, are often deposited as very thin films on a substance of high surface area per unit mass, such as alumina 1Al2O32 or silica 1SiO22. (a) Why is this an effective way of utilizing the catalyst material compared to having powdered metals? (b) How does the surface area affect the rate of reaction?

(a) If you were going to build a system to check the effectiveness of automobile catalytic converters on cars, what substances would you want to look for in the car exhaust?

(b) Automobile catalytic converters have to work at high temperatures, as hot exhaust gases stream through them. In what ways could this be an advantage? In what ways a disadvantage?

(c) Why is the rate of flow of exhaust gases over a catalytic converter important?

When D2 reacts with ethylene 1C2H42 in the presence of a finely divided catalyst, ethane with two deuteriums, CH2DCH2D, is formed. (Deuterium, D, is an isotope of hydrogen of mass 2). Very little ethane forms in which two deuteriums are bound to one carbon (for example, CH3CHD2). Use the sequence of steps involved in the reaction (Figure 14.24) to explain why this is so.

Heterogeneous catalysts that perform hydrogenation reactions, as illustrated in Figure 14.24, are subject to poisoning, which shuts down their catalytic ability. Compounds of sulfur are often poisons. Suggest a mechanism by which such compounds might act as poisons

The enzyme carbonic anhydrase catalyzes the reaction CO21g2 + H2O1l2 HCO3 - 1aq2 + H+1aq2. In water, without the enzyme, the reaction proceeds with a rate constant of 0.039 s -1 at 25 C. In the presence of the enzyme in water, the reaction proceeds with a rate constant of 1.0 * 106 s -1 at 25 C. Assuming the collision factor is the same for both situations, calculate the difference in activation energies for the uncatalyzed versus enzyme-catalyzed reaction.

The enzyme urease catalyzes the reaction of urea, 1NH2CONH22, with water to produce carbon dioxide and ammonia. In water, without the enzyme, the reaction proceeds with a first-order rate constant of 4.15 * 10-5 s -1 at 100 C. In the presence of the enzyme in water, the reaction proceeds with a rate constant of 3.4 * 104 s -1 at 21 C. (a) Write out the balanced equation for the reaction catalyzed by urease. (b) If the rate of the catalyzed reaction were the same at 100 C as it is at 21 C, what would be the difference in the activation energy between the catalyzed and uncatalyzed reactions? (c) In actuality, what would you expect for the rate of the catalyzed reaction at 100 C as compared to that at 21 C? (d) On the basis of parts (c) and (d), what can you conclude about the difference in activation energies for the catalyzed and uncatalyzed reactions?

The activation energy of an uncatalyzed reaction is 95 kJ>mol. The addition of a catalyst lowers the activation energy to 55 kJ>mol. Assuming that the collision factor remains the same, by what factor will the catalyst increase the rate of the reaction at (a) 25 C, (b) 125 C?

Suppose that a certain biologically important reaction is quite slow at physiological temperature 137 C2 in the absence of a catalyst. Assuming that the collision factor remains the same, by how much must an enzyme lower the activation energy of the reaction to achieve a 1 * 105 @fold increase in the reaction rate?

Consider the reaction A + B C + D. Is each of the following statements true or false? (a) The rate law for the reaction must be Rate = k3A43B4. (b) If the reaction is an elementary reaction, the rate law is second order. (c) If the reaction is an elementary reaction, the rate law of the reverse reaction is first order. (d) The activation energy for the reverse reaction must be greater than that for the forward reaction.

Hydrogen sulfide 1H2S2 is a common and troublesome pollutant in industrial wastewaters. One way to remove H2S is to treat the water with chlorine, in which case the following reaction occurs: H2S1aq2 + Cl21aq2 S1s2 + 2 H+1aq2 + 2 Cl - 1aq2 The rate of this reaction is first order in each reactant. The rate constant for the disappearance of H2S at 28 C is 3.5 * 10-2 M-1 s -1 . If at a given time the concentration of H2S is 2.0 * 10 - 4 M and that of Cl2 s 0.025 M, what is the rate of formation of Cl - ?

The reaction 2 NO1g2 + O21g2 2 NO21g2 is second order in NO and first order in O2. When 3NO4 = 0.040 M, and 3O24 = 0.035 M, the observed rate of disappearance of NO is 9.3 * 10-5 M>s. (a) What is the rate of disappearance of O2 at this moment? (b) What is the value of the rate constant? (c) What are the units of the rate constant? (d) What would happen to the rate if the concentration of NO were increased by a factor of 1.8?

You perform a series of experiments for the reaction A B + C and find that the rate law has the form rate = k3A4 x . Determine the value of x in each of the following cases: (a) There is no rate change when 3A40 is tripled. (b) The rate increases by a factor of 9 when 3A40 is tripled. (c) When 3A40 is doubled, the rate increases by a factor of 8.

Consider the following reaction between mercury(II) chloride and oxalate ion: 2 HgCl21aq2 + C2O4 2 - 1aq2 2 Cl - 1aq2 + 2 CO21g2 + Hg2Cl21s2 The initial rate of this reaction was determined for several concentrations of HgCl2 and C2O4 2 -, and the following rate data were obtained for the rate of disappearance of C2O4 2 - : Experiment 3hgCl24 1M2 3C2o4 2 4 1M2 Rate 1m,s2 1 0.164 0.15 3.2 * 10-5 2 0.164 0.45 2.9 * 10-4 3 0.082 0.45 1.4 * 10-4 4 0.246 0.15 4.8 * 10-5 (a) What is the rate law for this reaction? (b) What is the value of the rate constant with proper units? (c) What is the reaction rate when the initial concentration of HgCl2 is 0.100 M and that of 1C2O4 2-2 is 0.25 M if the temperature is the same as that used to obtain the data shown?

The following kinetic data are collected for the initial rates of a reaction 2 X + Z products: Experiment 3x401M2 3Z401M2 Rate 1M,s2 1 0.25 0.25 4.0 * 101 2 0.50 0.50 3.2 * 102 3 0.50 0.75 7.2 * 102 (a) What is the rate law for this reaction? (b) What is the value of the rate constant with proper units? (c) What is the reaction rate when the initial concentration of X is 0.75 M and that of Z is 1.25 M?

The reaction 2 NO2 2 NO + O2 has the rate constant k = 0.63 M - 1 s- 1 . (a) Based on the units for k, is the reaction first or second order in NO2? (b) If the initial concentration of NO2 is 0.100 M, how would you determine how long it would take for the concentration to decrease to 0.025 M?

Consider two reactions. Reaction (1) has a constant half-life, whereas reaction (2) has a half-life that gets longer as the reaction proceeds. What can you conclude about the rate laws of these reactions from these observations?

A first-order reaction A B has the rate constant k = 3.2 * 10-3 s -1 . If the initial concentration of A is 2.5 * 10-2 M, what is the rate of the reaction at t = 660 s?

(a) The reaction H2O21aq2 H2O1l2 + 1 2O21g2 is first order. Near room temperature, the rate constant equals 7.0 * 10-4 s -1 . Calculate the half-life at this temperature

(b) At 415 C, 1CH222O decomposes in the gas phase, 1CH222O1g2 CH41g2 + CO1g2. If the reaction is first order with a half-life of 56.3 min at this temperature, calculate the rate constant in s -1 .

Americium-241 is used in smoke detectors. It has a firstorder rate constant for radioactive decay of k = 1.6 * 10-3 yr -1 . By contrast, iodine-125, which is used to test for thyroid functioning, has a rate constant for radioactive decay of k = 0.011 day-1 . (a) What are the half-lives of these two isotopes? (b) Which one decays at a faster rate? (c) How much of a 1.00-mg sample of each isotope remains after 3 half-lives? (d) How much of a 1.00-mg sample of each isotope remains after 4 days?

Urea 1NH2CONH22 is the end product in protein metabolism in animals. The decomposition of urea in 0.1 M HCl occurs according to the reaction NH2CONH21aq2 + H+1aq2 + 2 H2O1l2 2 NH4 +1aq2 + HCO - 3 1aq2 The reaction is first order in urea and first order overall. When 3NH2CONH24 = 0.200 M, the rate at 61.05 C is 8.56 * 10-5 M>s. (a) What is the rate constant, k? (b) What is the concentration of urea in this solution after 4.00 * 103 s if the starting concentration is 0.500 M? (c) What is the halflife for this reaction at 61.05 C ?

The rate of a first-order reaction is followed by spectroscopy, monitoring the absorbance of a colored reactant at 520 nm. The reaction occurs in a 1.00-cm sample cell, and the only colored species in the reaction has an extinction coefficient of 5.60 * 103 M-1 cm-1 at 520 nm. (a) Calculate the initial concentration of the colored reactant if the absorbance is 0.605 at the beginning of the reaction. (b) The absorbance falls to 0.250 at 30.0 min. Calculate the rate constant in units of s- 1 . (c) Calculate the half-life of the reaction. (d) How long does it take for the absorbance to fall to 0.100?

A colored dye compound decomposes to give a colorless product. The original dye absorbs at 608 nm and has an extinction coefficient of 4.7 * 104 M-1 cm-1 at that wavelength. You perform the decomposition reaction in a 1-cm cuvette in a spectrometer and obtain the following data: Time (min) Absorbance at 608 nm 0 1.254 30 0.941 60 0.752 90 0.672 120 0.545 From these data, determine the rate law for the reaction dye product and determine the rate constant.

Cyclopentadiene 1C5H62 reacts with itself to form dicyclopentadiene 1C10H122. A 0.0400 M solution of C5H6 was monitored as a function of time as the reaction 2 C5H6 C10H12 proceeded. The following data were collected: Time (s) 3C5h64 1M2 0.0 0.0400 50.0 0.0300 100.0 0.0240 150.0 0.0240 200.0 0.0174 Plot 3C5H64 versus time, ln3C5H64 versus time, and 1>3C5H64 versus time. (a) What is the order of the reaction? (b) What is the value of the rate constant?

The first-order rate constant for reaction of a particular organic compound with water varies with temperature as follows: Temperature (K) Rate Constant 1s12 300 3.2 * 10-11 320 1.0 * 10-9 340 3.0 * 10-8 355 2.4 * 10-7 From these data, calculate the activation energy in units of kJ>mol.

At 28 C, raw milk sours in 4.0 h but takes 48 h to sour in a refrigerator at 5 C. Estimate the activation energy in kJ>mol for the reaction that leads to the souring of milk?

The following is a quote from an article in the August 18, 1998, issue of The New York Times about the breakdown of cellulose and starch: A drop of 18 degrees Fahrenheit [from 77 F to 59 F4 lowers the reaction rate six times; a 36-degree drop [from 77 F to 41F] produces a fortyfold decrease in the rate. (a) Calculate activation energies for the breakdown process based on the two estimates of the effect of temperature on rate. Are the values consistent? (b) Assuming the value of Ea calculated from the 36 drop and that the rate of breakdown is first order with a half-life at 25 C of 2.7 yr, calculate the half-life for breakdown at a temperature of -15 C

The following mechanism has been proposed for the reaction of NO with H2 to form N2O and H2O: NO1g2 + NO1g2 N2O21g2 N2O21g2 + H21g2 N2O1g2 + H2O1g2 (a) Show that the elementary reactions of the proposed mechanism add to provide a balanced equation for the reaction. (b) Write a rate law for each elementary reaction in the mechanism. (c) Identify any intermediates in the mechanism. (d) The observed rate law is rate = k3NO4 2 3H24. If the proposed mechanism is correct, what can we conclude about the relative speeds of the first and second reactions?

Ozone in the upper atmosphere can be destroyed by the following two-step mechanism: Cl1g2 + O31g2 ClO1g2 + O21g2 ClO1g2 + O1g2 Cl1g2 + O21g2 (a) What is the overall equation for this process? (b) What is the catalyst in the reaction? (c) What is the intermediate in the reaction?

Using Figure 14.23 as your basis, draw the energy profile for the bromide-catalyzed decomposition of hydrogen peroxide. (a) Label the curve with the activation energies for reactions [14.30] and [14.31]. (b) Notice from Figure 14.22 that when Br - 1aq2 is first added, Br2 accumulates to some extent during the reaction and the solution turns brown. What does this tell us about the relative rates of the reactions represented by Equations 14.30 and 14.31?

The following mechanism has been proposed for the gasphase reaction of chloroform 1CHCl32 and chlorine: Step 1: Cl21g2 k1 k - 1 2 Cl1g2 1fast2 Step 2: Cl1g2 + CHCl31g2 k2 HCl1g2 + CCl31g2 1slow2 Step 3: Cl1g2 + CCl31g2 k3 CCl4 1fast2 (a) What is the overall reaction? (b) What are the intermediates in the mechanism? (c) What is the molecularity of each of the elementary reactions? (d) What is the ratedetermining step? (e) What is the rate law predicted by this mechanism? (Hint: The overall reaction order is not an integer.)

Consider the hypothetical reaction 2 A + B 2 C + D. The following two-step mechanism is proposed for the reaction: Step 1: A + B C + X Step 2: A + X C + D X is an unstable intermediate. (a) What is the predicted rate law expression if Step 1 is rate determining? (b) What is the predicted rate law expression if Step 2 is rate determining? (c) Your result for part (b) might be considered surprising for which of the following reasons: (i) The concentration of a product is in the rate law. (ii) There is a negative reaction order in the rate law. (iii) Both reasons (i) and (ii). (iv) Neither reasons (i) nor (ii).

In a hydrocarbon solution, the gold compound 1CH323AuPH3 decomposes into ethane 1C2H62 and a different gold compound, 1CH32AuPH3. The following mechanism has been proposed for the decomposition of 1CH323AuPH3: Step 1: 1CH323 AuPH3 k1 k -1 1CH323Au + PH3 1fast2 Step 2: 1CH323 Au k2 C2H6 + 1CH32Au 1slow2 Step 3: 1CH32Au + PH3 k3 1CH32AuPH3 1fast2(a) What is the overall reaction? (b) What are the intermediates in the mechanism? (c) What is the molecularity of each of the elementary steps? (d) What is the rate-determining step? (e) What is the rate law predicted by this mechanism? (f) What would be the effect on the reaction rate of adding PH3 to the solution of 1CH323AuPH3?

Platinum nanoparticles of diameter 2 nm are important catalysts in carbon monoxide oxidation to carbon dioxide. Platinum crystallizes in a face-centered cubic arrangement with an edge length of 3.924 . (a) Estimate how many platinum atoms would fit into a 2.0-nm sphere; the volume of a sphere is 14>32pr 3 . Recall that 1 A = 1 * 10-10 m and 1 nm = 1 * 10-9 m. (b) Estimate how many platinum atoms are on the surface of a 2.0-nm Pt sphere, using the surface area of a sphere 14pr 2 2 and assuming that the footprint of one Pt atom can be estimated from its atomic diameter of 2.8 A . (c) Using your results from (a) and (b), calculate the percentage of Pt atoms that are on the surface of a 2.0-nm nanoparticle. (d) Repeat these calculations for a 5.0-nm platinum nanoparticle. (e) Which size of nanoparticle would you expect to be more catalytically active and why?

One of the many remarkable enzymes in the human body is carbonic anhydrase, which catalyzes the interconversion of carbon dioxide and water with bicarbonate ion and protons. If it were not for this enzyme, the body could not rid itself rapidly enough of the CO2 accumulated by cell metabolism. The enzyme catalyzes the dehydration (release to air) of up to 107 CO2 molecules per second. Which components of this description correspond to the terms enzyme, substrate, and turnover number?

Suppose that, in the absence of a catalyst, a certain biochemical reaction occurs x times per second at normal body temperature 137 C2. In order to be physiologically useful, the reaction needs to occur 5000 times faster than when it is uncatalyzed. By how many kJ>mol must an enzyme lower the activation energy of the reaction to make it useful?

Enzymes are often described as following the two-step mechanism: E + S ES 1fast2 ES E + P 1slow2 where E = enzyme, S = substrate, ES = enzyme9substrate complex, and P = product. (a) If an enzyme follows this mechanism, what rate law is expected for the reaction? (b) Molecules that can bind to the active site of an enzyme but are not converted into product are called enzyme inhibitors. Write an additional elementary step to add into the preceding mechanism to account for the reaction of E with I, an inhibitor.

Dinitrogen pentoxide 1N2O52 decomposes in chloroform as a solvent to yield NO2 and O2. The decomposition is first order with a rate constant at 45 C of 1.0 * 10-5 s -1 . Calculate the partial pressure of O2 produced from 1.00 L of 0.600 M N2O5 solution at 45 C over a period of 20.0 h if the gas is collected in a 10.0-L container. (Assume that the products do not dissolve in chloroform.)

The reaction between ethyl iodide and hydroxide ion in ethanol 1C2H5OH2 solution, C2H5I1alc2 + OH- 1alc2 C2H5OH1l2 + I - 1alc2, has an activation energy of 86.8 kJ>mol and a frequency factor of 2.10 * 1011 M-1 s -1 . (a) Predict the rate constant for the reaction at 35 C. (b) A solution of KOH in ethanol is made up by dissolving 0.335 g KOH in ethanol to form 250.0 mL of solution. Similarly, 1.453 g of C2H5I is dissolved in ethanol to form 250.0 mL of solution. Equal volumes of the two solutions are mixed. Assuming the reaction is first order in each reactant, what is the initial rate at 35 C? (c) Which reagent in the reaction is limiting, assuming the reaction proceeds to completion? (d) Assuming the frequency factor and activation energy do not change as a function of temperature, calculate the rate constant for the reaction at 50 C.

You obtain kinetic data for a reaction at a set of different temperatures. You plot ln k versus 1>T and obtain the following graph: 1/T ln k Suggest a molecular-level interpretation of these unusual data.

The gas-phase reaction of NO with F2 to form NOF and F has an activation energy of Ea = 6.3 kJ>mol. and a frequency factor of A = 6.0 * 108 M-1 s -1 . The reaction is believed to be bimolecular: NO1g2 + F21g2 NOF1g2 + F1g2 (a) Calculate the rate constant at 100 C. (b) Draw the Lewis structures for the NO and the NOF molecules, given that the chemical formula for NOF is misleading because the nitrogen atom is actually the central atom in the molecule. (c) Predict the shape for the NOF molecule. (d) Draw a possible transition state for the formation of NOF, using dashed lines to indicate the weak bonds that are beginning to form. (e) Suggest a reason for the low activation energy for the reaction.

The mechanism for the oxidation of HBr by O2 to form 2 H2O and Br2 is shown in Exercise 14.74. (a) Calculate the overall standard enthalpy change for the reaction process. (b) HBr does not react with O2 at a measurable rate at room temperature under ordinary conditions. What can you infer from this about the magnitude of the activation energy for the rate-determining step? (c) Draw a plausible Lewis structure for the intermediate HOOBr. To what familiar compound of hydrogen and oxygen does it appear similar?

The rates of many atmospheric reactions are accelerated by the absorption of light by one of the reactants. For example, consider the reaction between methane and chlorine to produce methyl chloride and hydrogen chloride: Reaction 1: CH41g2 + Cl21g2 CH3Cl1g2 + HCl1g2 .This reaction is very slow in the absence of light. However, Cl21g2 can absorb light to form Cl atoms: Reaction 2: Cl21g2 + hv 2 Cl1g2 Once the Cl atoms are generated, they can catalyze the reaction of CH4 and Cl2, according to the following proposed mechanism: Reaction 3: CH41g2 + Cl1g2 CH31g2 + HCl1g2 Reaction 4: CH31g2 + Cl21g2 CH3Cl1g2 + Cl1g2 The enthalpy changes and activation energies for these two reactions are tabulated as follows: Reaction h 1kJ,mol2 Ea 1kJ,mol2 3 +4 17 4 -109 4 (a) By using the bond enthalpy for Cl2 (Table 8.4), determine the longest wavelength of light that is energetic enough to cause reaction 2 to occur. In which portion of the electromagnetic spectrum is this light found? (b) By using the data tabulated here, sketch a quantitative energy profile for the catalyzed reaction represented by reactions 3 and 4. (c) By using bond enthalpies, estimate where the reactants, CH41g2 + Cl21g2, should be placed on your diagram in part (b). Use this result to estimate the value of Ea for the reaction CH41g2 + Cl21g2 CH31g2 + HCl1g2 + Cl1g2. (d) The species Cl(g) and CH31g2 in reactions 3 and 4 are radicals, that is, atoms or molecules with unpaired electrons. Draw a Lewis structure of CH3, and verify that it is a radical. (e) The sequence of reactions 3 and 4 comprises a radical chain mechanism. Why do you think this is called a chain reaction? Propose a reaction that will terminate the chain reaction.

Many primary amines, RNH2, where R is a carbon-containing fragment such as CH3, CH3CH2, and so on, undergo reactions where the transition state is tetrahedral. (a) Draw a hybrid orbital picture to visualize the bonding at the nitrogen in a primary amine (just use a C atom for R). (b) What kind of reactant with a primary amine can produce a tetrahedral intermediate?

Many primary amines, RNH2, where R is a carbon-containing fragment such as CH3, CH3CH2, and so on, undergo reactions where the transition state is tetrahedral. (a) Draw a hybrid orbital picture to visualize the bonding at the nitrogen in a primary amine (just use a C atom for R). (b) What kind of reactant with a primary amine can produce a tetrahedral intermediate?

As shown in Figure 14.24, the first step in the heterogeneous hydrogenation of ethylene is adsorption of the ethylene molecule on a metal surface. One proposed explanation for the sticking of ethylene to a metal surface is the interaction of the electrons in the CC p bond with vacant orbitals on the metal surface. (a) If this notion is correct, would ethane be expected to adsorb to a metal surface, and, if so, how strongly would ethane bind compared to ethylene? (b) Based on its Lewis structure, would you expect ammonia to adsorb to a metal surface using a similar explanation as for ethylene?

Problem 1DE Let’s explore the chemical Kinetics of our favorite hypothetical reaction: a A + b B ? c C + cf D. We shall assume that all the substances are soluble in water and that we carry out the reaction in aqueous solution. Substances A and C both absorb visible light, and the absorption maxima are 510 nm for A and for 640 nm for C. Substances B and D are colorless. You are provided with pure samples of all four substances and you know their chemical formulas. You are also provided appropriate instrumentation to obtain visible absorption spectra (see the Closer Look box on using spectroscopic methods in Section). Let’s design an experiment to ascertain the kinetics of our reaction, (a) What experiments could you design to determine the rate law and the rate constant for the reaction at room temperature? Would you need to know the values of the stoichiometric constants a and c in order to find the rate law? (b) Design an experiment to determine the activation energy for the reaction. What challenges might you face in actually carrying out this experiment? (c) You now want to test whether a particular water-soluble substance Q is a homogeneous catalyst for the reaction. What experiments can you carry out to test this notion? (d) If Q does indeed catalyze the reaction, what follow-up experiments might you undertake to learn more about the reaction profile for the reaction?

An automotive fuel injector dispenses a fine spray of gasoline into the automobile cylinder, as shown in the bottom drawing here. When an injector gets clogged, as shown in the top drawing, the spray is not as fine or even and the performance of the car declines. How is this observation related to chemical kinetics? [Section 14.1]

Consider the following graph of the concentration of a sub- stance X over time. Is each of the following statements true or false? (a) X is a product of the reaction. (b) The rate of the reaction remains the same as time progresses. (c) The average rate between points 1 and 2 is greater than the average rate between points 1 and 3. (d) As time progresses, the curve will eventually turn downward toward the x-axis. [Section 14.2]

You study the rate of a reaction, measuring both the concentration of the reactant and the concentration of the product as a function of time, and obtain the following results: 1. Which chemical equation is consistent with these data: (i) A B, (ii) B A, (iii) A 2 B, 2. Write equivalent expressions for the rate of the reaction in terms of the appearance or disappearance of the two substances. [Section 14.2]

Suppose that for the reaction K + L M, you monitor the production of M over time, and then plot the following graph from your data: 1. Is the reaction occurring at a constant rate from t = 0 to t = 15 min? 2. Is the reaction completed at t = 15 min? 3. Suppose the reaction as plotted here were started with 0.20 mol K and 0.40 mol L. After 30 min, an additional 0.20 mol K are added to the reaction mixture. Which of the following correctly describes how the plot would look from t = 30 min to t = 60 min? (i) [M] would remain at the same constant value it has at t = 30 min, (ii) [M] would increase with the same slope as t = 0 to 15 min, until t = 45 min at which point the plot becomes horizontal again, or (iii) [M] decreases and reaches 0 at t = 45 min. [Section 14.2]

The following diagrams represent mixtures of \(\mathrm{NO}(g)\) and \(\mathrm{O}_{2}(g)\). These two substances react as follows: \(2 \mathrm{NO}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{NO}_{2}(g)\). It has been determined experimentally that the rate is second order in NO and first order in \(\mathrm{O}_{2}\). Based on this fact, which of the following mixtures will have the fastest initial rate? [Section 14.3] Equation Transcription: Text Transcription: NO(g) O_{2}(g) 2 NO(g)+O_{2}(g){rightarrow}2 NO_{2}(g) NO O_2

A friend studies a first-order reaction and obtains the following three graphs for experiments done at two different temperatures. (a) Which two graphs represent experiments done at the same temperature? What accounts for the difference in these two graphs? In what way are they the same? (b) Which two graphs represent experiments done with the same starting concentration but at different temperatures? Which graph probably represents the lower temperature? How do you know? [Section 14.4]

(a) Given the following diagrams at \(t=0 \mathrm{~min}\) and \(t=30 \mathrm{~min}\), what is the half-life of the reaction if it follows first-order kinetics? (b) After four half-life periods for a first-order reaction, what fraction of reactant remains? [Section 14.4] Equation Transcription: Text Transcription: t=0 min t=30 min t=0 min t=30 min

Which of the following linear plots do you expect for a reaction A products if the kinetics are (a) zero order, (b) first order, or (c) second order? [Section 14.4]

The following diagram shows a reaction profile. Label the components indicated by the boxes. [Section 14.5]

The accompanying graph shows plots of ln k versus 1/T for two different reactions. The plots have been extrapolated to the y-intercepts. Which reaction (red or blue) has (a) the larger value for Ea, and (b) the larger value for the frequency factor, A? [Section 14.5]

The following graph shows two different reaction pathways for the same overall reaction at the same temperature. Is each of the following statements true or false? (a) The rate is faster for the red path than for the blue path. (b) For both paths, the rate of the reverse reaction is slower than the rate of the forward reaction. (c) The energy change \(\Delta E\) is the same for both paths. [Section 14.6] Equation Transcription: Text Transcription: {Delta}E

Consider the diagram that follows, which represents two steps in an overall reaction. The red spheres are oxygen, the blue ones nitrogen, and the green ones fluorine. (a) Write the chemical equation for each step in the reaction. (b) Write the equation for the overall reaction. (c) Identify the intermediate in the mechanism. (d) Write the rate law for the overall reaction if the first step is the slow, rate-determining step. [Section 14.6]

Based on the following reaction profile, how many intermediates are formed in the reaction \(\mathrm{A} \longrightarrow \mathrm{C}\)? How many transition states are there? Which step, \(\mathrm{A} \longrightarrow \mathrm{B}\) or \(\mathrm{B} \longrightarrow \mathrm{C}\), is the faster? For the reaction \(\mathrm{A} \longrightarrow \mathrm{C}\), is \(\Delta E\) positive, negative, or zero? [Section 14.6] Equation Transcription: A ? C A ? B B ? C A ? C Text Transcription: A {rightarrow} C A {rightarrow} B B {rightarrow} C A {rightarrow} C {Delta}E

Draw a possible transition state for the bimolecular reaction depicted here. (The blue spheres are nitrogen atoms, and the red ones are oxygen atoms.) Use dashed lines to represent the bonds that are in the process of being broken or made in the transition state. [Section 14.6]

Problem 15E Visualizing Concepts The following diagram represents an imaginary two-step mechanism. Let the red spheres represent element A. the green ones element B. and the blue ones element C. (a) Write the equation for the net reaction that is occurring, (b) Identify the intermediate, (c) Identify the catalyst. [Sections]

Problem 16E Visualizing Concepts Draw a graph showing the reaction pathway for an overall exothermic reaction with two intermediates that are produced at different rates. On your graph indicate the reactants, products, intermediates, transition states, and activation energies. [Sections]

Problem 17E Reaction Rates (Sections) (a) What is meant by the term reaction rate? (b) Name three factors that can affect the rate of a chemical reaction, (c) Is the rate of disappearance of reactants always the same as the rate of appearance of products?

Problem 18E Reaction Rates (Sections) (a) What are the units usually used to express the rates of reactions occurring in solution? (b) From your everyday experience, give two examples of the effects of temperature on the rates of reactions, (c) What is the difference between average rate and instantaneous rate?

Consider the following hypothetical aqueous reaction: \(\mathrm{A}(a q) \rightarrow \mathrm{B}(a q)\). A flask is charged with 0.065 mol of A in a total volume of 100.0 mL. The following data are collected: (a) Calculate the number of moles of B at each time in the table, assuming that there are no molecules of B at time zero, and that A cleanly converts to B with no intermediates. (b) Calculate the average rate of disappearance of A for each 10-min interval in units of \(M / s\). (c) Between \(t=10 \min\) and \(t=30 \min\), what is the average rate of appearance of B in units of \(M / s\)? Assume that the volume of the solution is constant. Equation Transcription: Text Transcription: A(aq){rightarrow}B(aq) M/s t=10 min t=30 min M/s

A flask is charged with 0.100 mol of A and allowed to react to form B according to the hypothetical gas-phase reaction \(\mathrm{A}(a q) \rightarrow \mathrm{B}(a q)\). The following data are collected: (a) Calculate the number of moles of B at each time in the table, assuming that A is cleanly converted to B with no intermediates. (b) Calculate the average rate of disappearance of A for each 40-s interval in units of mol/s. (c) Which of the following would be needed to calculate the rate in units of concentration per time: (i) the pressure of the gas at each time, (ii) the volume of the reaction flask, (iii) the temperature, or (iv) the molecular weight of A? Equation Transcription: Text Transcription: A(g)B(g) mol/s

The rate of disappearance of HCl was measured for the following reaction: \(\mathrm{CH}_{3} \mathrm{OH}(a q)+\mathrm{HCl}(a q) \longrightarrow \mathrm{CH}_{3} \mathrm{Cl}(a q)+\mathrm{H}_{2} \mathrm{O}(l)\) The following data were collected: (a) Calculate the average rate of reaction, in \({M} / \mathrm{s}\), for the time interval between each measurement. (b) Calculate the average rate of reaction for the entire time for the data from \(t=0.0 \mathrm{~min}\) to \(t=430.0 \mathrm{~min}\). (c) Which is greater, the average rate between \(t=54.0\) and \(t=215.0 \mathrm{~min}\), or between \(t=107.0\) and \(t=430.0 \mathrm{~min}\)? (d) Graph [HCl] versus time and determine the instantaneous rates in \({M} / \mathrm{min}\) and \({M} / \mathrm{s}\) at \(t=75.0 \mathrm{~min}\) and \(t=250 \mathrm{~min}\). Equation Transcription: Text Transcription: HCl CH3OH(aq)+HCl(aq)CH3Cl(aq)+H2O(l) M/s t=0.0 min t=430.0 min t=54.0 t=215.0 min t=107.0 t=430.0 min [HCl] M/min M/s t=75.0 min t=250 min

The isomerization of methyl isonitrile \(\left(\mathrm{CH}_{3} \mathrm{NC}\right)\) to acetonitrile (\left(\mathrm{CH}_{3} \mathrm{CN}\right)\) was studied in the gas phase at \(215\ ^{\circ} \mathrm{C}\), and the following data were obtained: Time (s) \(\left[\mathrm{CH}_{3} \mathrm{NC}\right](\mathrm{M})\) 0 0.0165 2000 0.0110 5000 0.00591 8000 0.00314 12,000 0.00137 15,000 0.00074 Calculate the average rate of reaction, in \(M/ \mathrm {s}\), for the time interval between each measurement. (b) Calculate the average rate of reaction over the entire time of the data from \(t=0\) to \(t=15,000\) s. (c) Which is greater, the average rate between \(t=2000\) and \(t=12,000\) s, or between \(t=8000\) and \(t=15,000\) s? (d) Graph \(\left[\mathrm{CH}_{3} \mathrm{NC}\right]\) versus time and determine the instantaneous rates in \(M/ \mathrm {s}\) at \(t=5000\) s and \(t=8000\) s. Equation Transcription: Text Transcription: (CH_{3}NC) (CH_{3}CN) 215 ^{o}C [CH_{3}NC](M) M/s t=0 t=15,000 t=2000 t=12,000 t=8000 t=15,000 [CH_{3}NC] M/s t=5000 t=8000

Problem 23E Reaction Rates (Sections) For each of the following gas-phase reactions, indicate how the rate of disappearance of each reactant is related to the rate of appearance of each product: (a) H2O2(g)?H2(g) + O2(g) (b) 2 N2O(g)?2 N2(g) + O2(g) (c) N2(g) + 3 H2(g)?2NH3(g) (d) C2H5NH2(g)?C2H4(g) + NH3(g)

Problem 24E Reaction Rates (Sections) For each of the following gas-phase reactions, write the rate expression in terms of the appearance of each product and disappearance of each reactant: (a) 2 H2O(g)?2 H2(g) + O2(g) (b) 2 SO2(g) + O2(g)?>2 SO3(g) (c) 2 NO(g) + 2 H2(g) ? N2(g) + 2 H2O(g) (d) N2(g) + 2 H2(g) ? N2H4(g)

Problem 25E Reaction Rates (Sections) (a) Consider the combust ion of H2(g): 2 H2(g) + O2(g) ? 2 H2O(g). If hydrogen is burning at the rate of 0.48 mol/s. what is the rate of consumption of oxygen? What is the rate of formation of water vapor? (b) The reaction 2 NO(g) + CI2(g)?2 NOCI(g) is carried out in a closed vessel. If the partial pressure of NO is decreasing at the rate of 56 torr/min. what is the rate of change of the total pressure of the vessel?

Problem 26E Reaction Rates (Sections) (a) Consider the combustion of ethylene. C2H4(g) + 3 O2(g)?2 CO2(g) + 2 H2O(g). If the concentration of C2H4 is decreasing at the rate of 0.036 Mls. what are the rates of change in the concentrations of CO2 and H2O? (b) The rate of decrease in N2H4 partial pressure in a closed reaction vessel from the reaction N2H4(g) + H2(g)?2 NH3(g) is 74 torr per hour. What are the rates of change of NH3 partial pressure and total pressure in the vessel?

Problem 27E Rate Laws (Section) A reaction A + B?C obeys the following rate law: Rate = K[B]2. (a) If [A] is doubled, how will the rate change? Will the rate constant change? (b) What are the reaction orders for A and B? What is the overall reaction order? (c) What are the units of the rate constant?

Problem 28E Rate Laws (Section) Consider a hypothetical reaction between A. B. and C that is first order in A zero order in B. and second order in C. (a) Write the rate law for the reaction, (b) How does the rate change when [A] is doubled and the other reactant concentrations are held constant? (c) How does the rate change when [B] is tripled and the other reactant concentrations are held constant? (d) How does the rate change when [C] is tripled and the other reactant concentrations are held constant? (e) By what factor does the rate change when the concentrations of all three reactants are tripled? (f) By what factor does the rate change when the concentrations of all three reactants are cut in half?

Problem 29E Rate Laws (Section) The decomposition reaction of N205 in carbon tetrachloride is 2 N205->4 N02 + 02. The rate law is first order in N205. At 64 °C the rate constant is 4.82 x 10-3 s-1. (a) Write the rate law for the reaction, (b) What is the rate of reaction when [N205] = 0.0240 M? (c) What happens to the rate when the concentration of N205 is doubled to 0.0480 M? (d) What happens to the rate when the concentration of N205 is halved to 0.0120 M?

Problem 30E Rate Laws (Section) Consider the following reaction: 2 NO(g) + 2 H2(g)?N2(g) + 2 H20(g) (a) The rate law for this reaction is first order in H2 and second order in NO. Write the rate law. (b) If the rate constant for this reaction at 1000 K is 6.0 x 104 M-2 s-1. what is the reaction rate when [NO] = 0.035 M and [H2] = 0.015 M? (c) What is the reaction rate at 1000 K when the concentration of NO is increased to 0.10 M, while the concentration of H2 is 0.010 M? (d) What is the reaction rate at 1000 K if [NO] is decreased to 0.010 M and [H2] is increased to 0.030 M?

Problem 31E Rate Laws (Section) Consider the following reaction: CH3Br(aq) + OH-(aq)?CH3OH(aq) + Br-(aq) The rate law for this reaction is first order in CH3Br and first order in OH-. When [CH3Br] is 5.0 x 10-3 M and [OH-] is 0.050 M, the reaction rate at 298 K is 0.0432 M/s. (a) What is the value of the rate constant? (b) What are the units of the rate constant? (c) What would happen to the rate if the concentration of OH- were tripled? (d) What would happen to the rate if the concentration of both reactants were tripled?

Problem 32E Rate Laws (Section) The reaction between ethyl bromide (C2H5Br) and hydroxide ion in ethyl alcohol at 330 K. C2H5Br(ale) + OH- (a/c)— C2H50H(/) + Br- (ale), is first order each in ethyl bromide and hydroxide ion. When [C2H5Br] is 0.0477 M and [OH- ] is 0.100 M, the rate of disappearance of ethyl bromide is 1.7 x 10-7 Mis. (a) What is the value of the rate constant? (b) What are the units of the rate constant? (c) How would the rate of disappearance of ethyl bromide change if the solution were diluted by adding an equal volume of pure ethyl alcohol to the solution?

The iodide ion reacts with hypochlorite ion (the active ingredient in chlorine bleaches) in the following way: \(\text { OCl }+I^{-} \rightarrow \mathrm{OI}^{-}+\mathrm{Cl}^{-}\). This rapid reaction gives the following rate data: \({\left[\mathrm{OCl}^{-}\right](\mathrm{M})}\) \({[\Gamma](M)}\) \((\mathrm{M} / \mathrm{s})\) \(1.5 \times 10^{-3}\) \(1.5 \times 10^{-3}\) \(1.36 \times 10^{-4}\) \(3.0 \times 10^{-3}\) \(1.5 \times 10^{-3}\) \(2.72 \times 10^{-4}\) \(1.5 \times 10^{-3}\) \(3.0 \times 10^{-3}\) \(2.72 \times 10^{-4}\) (a) Write the rate law for this reaction. (b) Calculate the rate constant with proper units. (c) Calculate the rate when \({\left[O C l^{-}\right]=2.0 \times 10^{-3} \mathrm{M} \text { and }[\Gamma]=5.0 \times 10^{-4} \mathrm{M}}\) Equation Transcription: Text Transcription: OCl-+I-OI-+Cl- [OCl-](M) 1.5 x 10-3 3.0 x 10-3 1.5 x 10-3 [ \Gamma ](M) 1.5 x 10-3 1.5 x 10-3 3.0 x 10-3 (M/s) 1.36 x 10-4 2.72 x 10-4 2.72 x 10-4 [OCl-] = 2.0 x 10-3M and [ \Gamma]=5.0 x 10-4M

The reaction \(2 \mathrm{ClO}_{2}(a q)+2 \mathrm{OH}^{-}(a q) \rightarrow \mathrm{ClO}_{3}^{-}(a q)+\mathrm{ClO}_{2}^{-}(a q)+\mathrm{H}_{2} \mathrm{O}(l)\) was studied with the following results: Experiment \(\mathrm{ClO}_{2}(\mathrm{M})\) \({\left[\mathrm{OH}^{-}\right](\mathrm{M})} \) Initial Rate \((\mathrm{M} / \mathrm{s})\) 1 0.060 0.030 0.0248 2 0.020 0.030 0.00276 3 0.020 0.090 0.00828 (a) Determine the rate law for the reaction. (b) Calculate the rate constant with proper units. (c) Calculate the rate when \({\left[\mathrm{ClO}_{2}\right]=0.100 \mathrm{M} \text { and }\left[\mathrm{OH}^{-}\right]=0.050 \mathrm{M}}\) Equation Transcription: Text Transcription: 2ClO2(aq)+2OH-(aq) \rightarrow ClO3-(aq)+ClO2-(aq)+H2O(l) ClO2(M) [OH-](M) (M/s) [ClO2]=0.100M and [OH-]=0.050M

The following data were measured for the reaction \(B F_{3}(g)+N H_{3}(g) \rightarrow F_{3} B N H_{3}(g)\) Experiment \({\left[B F_{3}\right](M)}\) \({\left[N H_{3}\right](M)}\) Initial Rate \((M / s)\) 1 2 3 4 5 (a) What is the rate law for the reaction? (b) What is the overall order of the reaction? (c) Calculate the rate constant with proper units? (d) What is the rate when \({\left[B F_{3}\right]=0.100 M \text { and }\left[N H_{3}\right]=0.500 M}\)? Equation Transcription: Text Transcription: B F_{3}(g)+N H_{3}(g) \rightarrow F_{3} B N H_{3}(g) [BF3](M) [NH3](M) (M/s) [BF3]=0.100 M and [NH3]=0.500M

The following data were collected for the rate of disappearance of \(\mathrm{NO}\) in the reaction \(2 \mathrm{NO}(g)+\mathrm{O}_{2}(g) \rightarrow 2 \mathrm{NO}_{2}(g)\) Experiment \({[\mathrm{NO}](\mathrm{M})}\) \({\left[\mathrm{O}_{2}\right](\mathrm{M})}\) Initial Rate \((\mathrm{M} / \mathrm{s})\) 1 0.0126 0.0125 \(1.14 \times 10^{-2}\) 2 0.0252 0.0125 \(5.64 \times 10^{-2}\) 3 0.0252 0.0250 \(1.13 \times 10^{-1}\) (a) What is the rate law for the reaction? (b) What are the units of the rate constant? (c) What is the average value of the rate constant calculated from the three data sets? (d) What is the rate of disappearance of \(\mathrm{NO}\) when \({[\mathrm{NO}]=0.0750 \mathrm{M} \text { and }\left[\mathrm{O}_{2}\right]=0.0100 \mathrm{M}}\)? is the rate of disappearance of \(\mathrm{O}_{2}\) at the concentrations given in part ? Equation Transcription: Text Transcription: NO 2NO(g)+O2(g) \rightarrow 2NO2(g) [NO](M) [O2](M) (M/s) 1.14 x 10-2 5.64 x 10-2 1.13 x 10-1 NO [NO]=0.0750M and [O2]=0.0100M O2

The following data were collected for the rate of disappearance of \(\mathrm{NO}\) in the reaction \(2 \mathrm{NO}(g)+\mathrm{O}_{2}(g) \rightarrow 2 \mathrm{NO}_{2}(g)\) Experiment \({[\mathrm{NO}](\mathrm{M})}\) \({\left[\mathrm{O}_{2}\right](\mathrm{M})}\) Initial Rate \((\mathrm{M} / \mathrm{s})\) 1 0.0126 0.0125 \(1.14 \times 10^{-2}\) 2 0.0252 0.0125 \(5.64 \times 10^{-2}\) 3 0.0252 0.0250 \(1.13 \times 10^{-1}\) (a) What is the rate law for the reaction? (b) What are the units of the rate constant? (c) What is the average value of the rate constant calculated from the three data sets? (d) What is the rate of disappearance of \(\mathrm{NO}\) when \({[\mathrm{NO}]=0.0750 \mathrm{M} \text { and }\left[\mathrm{O}_{2}\right]=0.0100 \mathrm{M}}\)? is the rate of disappearance of \(\mathrm{O}_{2}\) at the concentrations given in part ? Equation Transcription: Text Transcription: NO 2NO(g)+O2(g) \rightarrow 2NO2(g) [NO](M) [O2](M) (M/s) 1.14 x 10-2 5.64 x 10-2 1.13 x 10-1 NO [NO]=0.0750M and [O2]=0.0100M O2

4.38] Consider the reaction of peroxydisulfate ion \(\left(S_{2} O_{8}^{2-}\right)\) with iodide ion \(\left(I^{-}\right)\) in aqueous solution: \(S_{2} O_{8}^{2-}(a q)+3 I^{-}(a q) \rightarrow 2 S O_{4}^{2-}(a q)+I_{3}(a q)\) At a particular temperature the initial rate of disappearance of \(S_{2} O_{8}^{2-}\) varies with reactant concentrations in the following manner: Experiment \({\left[S_{2} O_{8}^{2-}\right](M)}\) \({\left[I^{-}\right](M)}\) Initial Rate \((M / s)\) 1 0.018 \(2.6 \times 10^{-6}\) 2 0.027 \(3.9 \times 10^{-6}\) 3 0.036 \(7.8 \times 10^{-6}\) 4 0.050 \(1.4 \times 10^{-5}\) (a) Determine the rate law for the reaction and state the units of the rate constant. (b) What is the average value of the rate constant for the disappearance of \(S_{2} O_{8}^{2-}\) based on the four sets of data? (c) How is the rate of disappearance of \(S_{2} O_{8}^{2-}\) related to the rate of disappearance of \(I^{-}\) ? (d) What is the rate of disappearance of \(I^{-}\) when \({\left[S_{2} O_{8}^{2-}\right]=0.025 M \text { and }\left[I^{-}\right]=0.050 M}\)? Equation Transcription: Text Transcription: (S2O82-) (I-) S2O82-(aq)+3I-(aq) \rightarrow 2SO42-(aq)+I3-(aq) S2O82- [S2O82-](M) [I-](M) (M/s) 2.6 x 10-6 3.9 x 10-6 7.8 x 10-6 1.4 x 10-5 S2O82- S2O82- I- I- [S2O82-]=0.025M and [I-]=0.050M

Problem 39E Change of Concentration with Time (Section) (a) Define the following symbols that are encountered in rate equations for the generic reaction AS B: [A]0, t [A]t, k. (b) What quantity, when graphed versus time, will yield a straight line for a first-order reaction? (c) How can you calculate the rate constant for a first-order reaction from the graph you made in part (b)?

Problem 40E Change of Concentration with Time (Section) (a) For a generic second-order reaction A— B, what quantity, when graphed versus time, will yield a straight line? (b) What is the slope of the straight line from part (a)? (c) How do the half-lives of first-order and second-order reactions differ?

Problem 41E Change of Concentration with Time (Section) (a) The gas-phase decomposition of SO2CI2. SO2CI2(g)? SO2(g) + CI2(g). is first order in SO2CI2. At 600 K the halflife for this process is 2.3 x 105 s. What is the rate constant at this temperature? (b) At 320 °C the rate constant is 2.2 x 10-5 s-1. What is the half-life at this temperature?

Problem 42E Change of Concentration with Time (Section) Molecular iodine. I2(g). dissociates into iodine atoms at 625 K with a first-order rate constant of 0.271 s-1. (a) What is the half-life for this reaction? (b) If you start with 0.050 M I2 at this temperature, how much will remain after 5.12 s assuming that the iodine atoms do not recombine to form I2?

Problem 43E Change of Concentration with Time (Section) As described in Exercise, the decomposition of sulfuryl chloride (SO2CI2) is a first-order process. The rate constant for the decomposition at 660 K is 4.5 x 10-2 s-1. (a) If we begin with an initial SO2CI2 pressure of 450 torr, what is the partial pressure of this substance after 60 s? (b) At what time will the partial pressure of SO2CI2 decline to one-tenth its initial value? Exercise Change of Concentration with Time (Section) (a) The gas-phase decomposition of S02CI2. SO2CI2(g)? SO2(g) + CI2(g), is first order in SO2CI2. At 600 K the half life for this process is 2.3 x 105 s. What is the rate constant at this temperature? (b) At 320 CC the rate constant is 2.2 x 10-5 s-1. What is the half-life at this temperature?

Problem 44E Change of Concentration with Time (Section) The first-order rate constant for the decomposition of N2O5. 2 N2O5(g)?4 NO2(g) + O2(g), at 70 °C is 6.82 x 10-3 s-1. Suppose we start with 0.0250 mol of N2O5(g) in a volume of 2.0 L. (a) How many moles of N205 will remain after 5.0 min? (b) How many minutes will it take for the quantity of N2O5 to drop to 0.010 mol? (c) What is the half-life of N2O5 at 70 °C ?

The reaction \(\mathrm{SO}_{2} \mathrm{Cl}_{2}(g) \rightarrow \mathrm{SO}_{2}(g)+\mathrm{Cl}_{2}(g)\) is first order in \(\mathrm{SO}_{2} \mathrm{Cl}_{2}\). Using the following kinetic data, determine the magnitude and units of the first-order rate constant: Time (s) Pressure \(\mathrm{SO}_{2} \mathrm{Cl}_{2}\) (atm) 0 2500 5000 7500 10,000 Equation Transcription: Text Transcription: SO2Cl2(g) \rightarrow SO2(g)+Cl2(g) SO2Cl2 SO2Cl2

From the following data for the first-order gas-phase isomerization of \(\mathrm{CH}_{3} \mathrm{NC} \text { at } 215^{\circ} \mathrm{C}\), calculate the first-order rate constant and half-life for the reaction: Equation Transcription: Text Transcription: CH3NC at 215°C

Consider the data presented in Exercise 14.19. (a) By using appropriate graphs, determine whether the reaction is first order or second order. (b) What is the rate constant for the reaction? (c) What is the half-life for the reaction?

Consider the data presented in Exercise 14.20. (a) Determine whether the reaction is first order or second order. (b) What is the rate constant? (c) What is the half-life?

Consider the data presented in Exercise 14.20. (a) Determine whether the reaction is first order or second order. (b) What is the rate constant? (c) What is the half-life?

Sucrose \(\left(C_{12} H_{22} O_{11}\right)\), commonly known as table sugar, reacts in dilute acid solutions to form two simpler sugars, glucose and fructose, both of which have the formula \(C_{6} H_{22} O_{6} \text { at } 23^{\circ} C\) and in \(0.5 M H C l\), the following data were obtained for the disappearance of sucrose: Time \({\left[C_{12} H_{22} O_{11}\right](M)}\) 0 39 80 140 210 (a) Is the reaction first order or second order with respect to \({\left[C_{12} H_{22} O_{11}\right]}\)? What is the rate constant? (c) Using this rate constant, calculate the concentration of sucrose at \(39,80,140 \text { and } 210 \mathrm{~min}\) if the initial sucrose concentration was \(0.316 M\) and the reaction were zero order in sucrose. Equation Transcription: Text Transcription: (C12H22O11) C6H22O6 at 23°C 0.5MHCl [C12H22O11](M) [C12H22O11] 39, 80, 140 and 210 min 0.316M

Problem 51E Temperature and Rate (Section) (a) What factors determine whether a collision between two molecules will lead to a chemical reaction? (b) According to the collision model, why does temperature affect the value of the rate constant? (c) Does the rate constant for a reaction generally increase or decrease with an increase in reaction temperature?

Problem 53E Temperature and Rate (Section) Calculate the fraction of atoms in a sample of argon gas at 400 K that has an energy of 10.0 kJ or greater.

Problem 52E Temperature and Rate (Section) (a) In which of the following reactions would you expect the orientation factor to be least important in leading to reaction: NO + O?NO2 or H + CI?HCI? (b) How does the kinetic-molecular theory help us understand the temperature dependence of chemical reactions?

(a) The activation energy for the isomerization of methyl isonitrile (Figure 14.7) is \(160 \mathrm{~kJ}>\mathrm{mol}\). Calculate the fraction of methyl isonitrile molecules that has an energy of \(160.0 \mathrm{~kJ}\) or greater at \(500 \mathrm{~K}\). (b) Calculate this fraction for a temperature of \(520 \mathrm{~K}\). What is the ratio of the fraction at \(520 \mathrm{~K}\) to that at \(500 \mathrm{~K}\)? Equation Transcription: Text Transcription: 160 kJ>mol 160.0 kJ 500 K 520 K 520 K 500 K

Problem 55E Temperature and Rate (Section) The gas-phase reaction Cl(g) + HBr(g)?HCI(g) + Br(g) has an overall energy change of -66 kJ. The activation energy for the reaction is 7 kJ. (a) Sketch the energy profile for the reaction, and label Ea and AE. (b) What is the activation energy for the reverse reaction?

Problem 57E Temperature and Rate (Section) Indicate whether each statement is true or false. (a) If you compare two reactions with similar collision factors, the one with the larger activation energy will be faster. (b) A reaction that has a small rate constant must have a small frequency factor. (c) Increasing the reaction temperature increases the fraction of successful collisions between reactants.

Problem 58E Temperature and Rate (Section) Indicate whether each statement is true or false. (a) If you measure the rate constant for a reaction at different temperatures, you can calculate the overall enthalpy change for the reaction. (b) Exothermic reactions are faster than endothermic reactions. (c) If you double the temperature for a reaction, you cut the activation energy in half.

Problem 59E Temperature and Rate (Section) Based on their activation energies and energy changes and assuming that all collision factors are the same, which of the following reactions would be fastest and which would be slowest? (a) Ea = 45 kJ/mol: ????E = -25 kJ/mol (b) Ea = 35 kJ/mol: ????E = -10 kJ/mol (c) Ea = 55 kJ/mol: ????E= 10 kJ/mol

Temperature and Rate (Section) Which of the reactions in Exercise will be fastest in the reverse direction? Which will be slowest? Temperature and Rate (Section) (a) A certain first-order reaction has a rate constant of at . What is the value of k at if ? (b) Another first-order reaction also has a rate constant of at What is the value of k at if ? (c) What assumptions do you need to make in order to calculate answers for parts (a) and (b)?

Temperature and Rate (Section) (a) A certain first-order reaction has a rate constant of at 20 °C. What is the value of k at if ? (b) Another first-order reaction also has a rate constant of at 20 °C What is the value of k at 60 °C if Ea = 125 kJ/mol ? (c) What assumptions do you need to make in order to calculate answers for parts (a) and (b)?

Temperature and Rate (Section) Understanding the high-temperature behavior of nitrogen oxides is essential for controlling pollution generated in automobile engines. The decomposition of nitric oxide (NO) to and is second order with a rate constant of at 737 C and at 947 °C. Calculate the activation energy for the reaction.

The rate of the reaction \(\mathrm{CH}_{3} \mathrm{COOC}_{2} \mathrm{H}_{5}(a q)+\mathrm{OH}(a q) \rightarrow \mathrm{CH}_{3} \mathrm{COO}^{-}(a q)+\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(a q)\) was measured at several temperatures, and the following data were collected: Temperature \(\left({ }^{\circ} \mathrm{C}\right) \) \(k\left(M^{-1} s^{-1}\right)\) 15 25 35 45 Calculate the value of \(E_{a}\) by constructing an appropriate graph. Equation Transcription: Text Transcription: CH_3COOC_2H_5(aq)+OH-(aq) \rightarrow CH_3COO-(aq)+C_2H_5OH(aq) (°C) k(M-1s-1) E_a

The temperature dependence of the rate constant for a reaction is tabulated as follows: Calculate \(E_{a} \text { and } A\) Equation Transcription: Text Transcription: E_a and A

Reaction Mechanisms (Section) (a) What is meant by the term elementary reaction? (b) What is the difference between a unimolecular and a bimolecular elementary reaction? (c) What is a reaction mechanism? (d) What is meant by the term rate-determining step?

Reaction Mechanisms (Section) What is the molecularity of each of the following elementary reactions? Write the rate law for each. (a) (b) (c)

Reaction Mechanisms (Section) (a) What is meant by the term molecularity? (b) Why are termolecular elementary reactions so rare? (c) What is an intermediate in a mechanism? (d) What are the differences between an intermediate and a transition state?

What is the molecularity of each of the following elementary reactions? Write the rate law for each. (a) \(2 \mathrm{NO}(g) \rightarrow \mathrm{N}_{2} \mathrm{O}_{2}(g)\) (b) (c) \(\mathrm{SO}_{3}(g) \rightarrow \mathrm{SO}_{2}(g)+\mathrm{O}(g)\) Equation Transcription: Text Transcription: 2 NO(g) \rightarrow N_2O_2(g) SO_3(g) \rightarrow SO_2(g)+O(g)

(a) Based on the following reaction profile, how many intermediates are formed in the reaction \(A \rightarrow D\)? (b) How many transition states are there? (c) Which step is the fastest? (d) For the reaction \(A \rightarrow D, \text { is } \Delta E\) positive, negative, or zero? Equation Transcription: Text Transcription: A \rightarrow D A \rightarrow D, is \Delta E

Consider the following energy profile. (a) How many elementary reactions are in the reaction mechanism? (b) How many intermediates are formed in the reaction? (c) Which step is rate limiting? (d) For the overall reaction, is \(\Delta E\) positive, negative, or zero? Equation Transcription: Text Transcription: \Delta E

Strong Acids and Bases (Section) Calculate the concentration of an aqueous solution of that has a pH of 10.05.

Problem 72E Reaction Mechanisms (Section) The decomposition of hydrogen peroxide is catalyzed by iodide ion. The catalyzed reaction is thought to proceed by a two-step mechanism: H2O2(aq) + I - (aq)?H2O(l) + IO- (aq) (slow) IO- (aq) + H2O2(aq)?H20(I) + O2(g) + I - (ag) (fast) (a) Write the chemical equation for the overall process, (b) Identify the intermediate, if any, in the mechanism, (c) Assuming that the first step of the mechanism is rate determining, predict the rate law for the overall process.

The reaction \(2 \mathrm{NO}(\mathrm{g})+\mathrm{Cl}_{2}(\mathrm{~g}) \rightarrow 2 \mathrm{NOCl}(\mathrm{g})\) was performed and the following data obtained under conditions of constant \({\left[\mathrm{Cl}_{2}\right]}\): (a) Is the following mechanism consistent with the data? \(\mathrm{NO}(\mathrm{g})+\mathrm{Cl}_{2}(\mathrm{~g}) \rightarrow \mathrm{NOCl}_{2}(\mathrm{~g})\) (fast) \(\mathrm{NOCl}_{2}(\mathrm{~g})+\mathrm{NO}(\mathrm{g}) \rightarrow 2 \mathrm{NOCl}(\mathrm{g})\) (slow) (b) Does the linear plot guarantee that the overall rate law is second order? Equation Transcription: Text Transcription: 2NO(g)+Cl2(g) \rightarrow 2 NOCl(g) [Cl2] NO(g)+Cl2(g) \rightarrow NOCl2(g) NOCl2(g)+NO(g) \rightarrow 2 NOCl(g)

Weak Acids (Section) Lactic acid has one acidic hydrogen. A 0.10 M solution of lactic acid has a pH of 2.44. Calculate Ka.

Problem 75E Catalysis (Section) (a) What is a catalyst? (b) What is the difference between a homogeneous and a heterogeneous catalyst? (c) Do catalysts affect the overall enthalpy change for a reaction, the activation energy, or both?

(a) Most commercial heterogeneous catalysts are extremely finely divided solid materials. Why is particle size important? (b) What role does adsorption play in the action of a heterogeneous catalyst?

In Figure 14.22, we saw that \(\mathrm{Br}^{-}(a q)\) catalyzes the decomposition of \(\mathrm{H}_{2} \mathrm{O}_{2}(a q) \text { into } \mathrm{H}_{2} \mathrm{O}(l) \text { and } \mathrm{O}_{2}(g)\). Suppose that some \(\mathrm{KBr}(s)\) is added to an aqueous solution of hydrogen peroxide. Make a sketch of \({\left[\mathrm{Br}^{-}(a q)\right]}\) versus time from the addition of the solid to the end of the reaction. Equation Transcription: Text Transcription: Br-(aq) H2O2(aq) into H2O(l) and O2(g) KBr(s) [Br-(aq)]

In solution, chemical species as simple as and can serve as catalysts for reactions. Imagine you could measure the of a solution containing an acid-catalyzed reaction as it occurs. Assume the reactants and products themselves are neither acids nor bases. Sketch the concentration profile you would measure as a function of time for the reaction, assuming t = 0 is when you add a drop of acid to the reaction.

Problem 79E Catalysis (Section) The oxidation of S02 to S03 is accelerated by N02. The reaction proceeds according to: NO2(g) + SO2(g)—? NO (g) + SO3(g) 2 NO(g) + O2(g)—?2 NO2(g) (a) Show that, with appropriate coefficients, the two reactions can be summed to give the overall oxidation of SO2 by O2 to give SO3. (b) Do we consider NO2 a catalyst or an intermediate in this reaction? (c) Is this an example of homogeneous catalysis or heterogeneous catalysis?

Step 1 of 4 (a) The given two chemical reactions are as follows; ..................(1) .............(2) To obtain a chemical equation for the overall equation, multiply equation (1) with 2 and then add to equation (2). ____________________________________________________________________ ________________________________________________________________________ Cancel the terms that appear on both sides of equation (3). Thus, chemical equation for the overall equation is as follows: ____________________________________________________________________________ Step 3 of 4 (b) A catalyst is a substance that changes the speed of a chemical reaction without itself undergoing any permanent chemical change in the process. So, it is consumed in one elementary step but is regenerated in the subsequent step. In the given mechanism, NO is considered as a catalyst but not as intermediate because it is consumed in the first step but reproduced in the second step. ____________________________________________________________________________ Step 4 of 4 (c) An intermediate is a substance that is formed in one elementary step and is consumed in the next. So, we can consider as intermediate in the given mechanism. This means the amount of formed in step 1 is consumed quickly in step 2 before the process of accumulation. Step 2 is fast and we can apply the same mechanism. Therefore,, if does not accumulate in measurable quantities, the proposed mechanism is not ruled out due to the fast step 2 . ____________________________________________________________________________

Many metallic catalysts, particularly the precious-metal ones, are often deposited as very thin films on a substance of high surface area per unit mass, such as alumina ( ) or silica ( ). (a) Why is this an effective way of utilizing the catalyst material compared to having powdered metals? (b) How does the surface area affect the rate of reaction?

(a) If you were going to build a system to check the effectiveness of automobile catalytic converters on cars, what substances would you want to look for in the car exhaust? (b) Automobile catalytic converters have to work at high temperatures, as hot exhaust gases stream through them. In what ways could this be an advantage? In what ways a disadvantage? (c) Why is the rate of flow of exhaust gases over a catalytic converter important?

When \(D_{2}\) reacts with ethylene \(\left(C_{2} H_{4}\right)\) in the presence of a finely divided catalyst, ethane with two deuteriums, \(C H_{2} D-C H_{2} D\), is formed. (Deuterium, D, is an isotope of hydrogen of mass 2). Very little ethane forms in which two deuteriums are bound to one carbon (for example, \(C H_{3}-C H D_{2}\)). Use the sequence of steps involved in the reaction (Figure 14.24) to explain why this is so. Equation Transcription: Text Transcription: D2 (C2H4) CH2D-CH2D CH3-CHD2

Heterogeneous catalysts that perform hydrogenation reactions, as illustrated in Figure 14.24, are subject to “poisoning,” which shuts down their catalytic ability. Compounds of sulfur are often poisons. Suggest a mechanism by which such compounds might act as poisons.

Problem 85E Catalysis (Section) The enzyme carbonic anhydrase catalyzes the reaction CO2(g) + H2O(I)?HCO3 - (aq) + H+ (aq). In water, without the enzyme, the reaction proceeds with a rate constant of 0.039 s-1 at 25 °C. In the presence of the enzyme in water, the reaction proceeds with a rate constant of 1.0 x 106 s-1 at 25 °C. Assuming the collision factor is the same for both situations, calculate the difference in activation energies for the uncatalyzed versus enzyme-catalyzed reaction.

Problem 87E Catalysis (Section) The activation energy of an uncatalyzed reaction is 95 kJ/mol. The addition of a catalyst lowers the activation energy to 55 kJ/mol. Assuming that the collision factor remains the same, by what factor will the catalyst increase the rate of the reaction at (a) 25 °C. (b) 125 °C?

Problem 86E Catalysis (Section) The enzyme urease catalyzes the reaction of urea. (NH2CONH2), with water to produce carbon dioxide and ammonia. In water, without the enzyme, the reaction proceeds with a first-order rate constant of 4.15 x 10-5 s-1 at 100 eC. In the presence of the enzyme in water, the reaction proceeds with a rate constant of 3.4 x 104 s-1 at 21 °C. (a) Write out the balanced equation for the reaction catalyzed by urease, (b) If the rate of the catalyzed reaction were the same at 100 °C as it is at 21 °C, what would be the difference in the activation energy between the catalyzed and uncatalyzed reactions? (c) In actuality, what would you expect for the rate of the catalyzed reaction at 100 °C as compared to that at 21 CC? (d) On the basis of parts (c) and (d), what can you conclude about the difference in activation energies for the catalyzed and uncatalyzed reactions?

Catalysis (Section) Suppose that a certain biologically important reaction is quite slow at physiological temperature (37 °C) in the absence of a catalyst. Assuming that the collision factor remains the same, by how much must an enzyme lower the activation energy of the reaction to achieve a fold increase in the reaction rate?

Consider the reaction . Is each of the following statements true or false? (a) The rate law for the reaction must be Rate = k[A][B]. (b) If the reaction is an elementary reaction, the rate law is second order, (c) If the reaction is an elementary reaction, the rate law of the reverse reaction is first order, (d) The activation energy for the reverse reaction must be greater than that for the forward reaction.

Problem 90AE Hydrogen sutfide (H2S) is a common and troublesome pollutant in industrial wastewaters. One way to remove H2S is to treat the water with chlorine, in which case the following reaction occurs: H2S{aq) + CI2(ag)?S(s) + 2 H+(aq) + 2 Cl- (aq) The rate of this reaction is first order in each reactant. The rate constant for the disappearance of H2S at 28 °C is 3.5 x 10-2 M-1 s-1. If at a given time the concentration of H2S is 2.0 x 10- 4 M and that of CI2 s 0.025 M. what is the rate of formation of Cl- ?

Problem 91AE The reaction 2 NO(g) + O2(g)?2 NO2(g) is second order in NO and first order in O2. When [NO] = 0.040 M, and [O2] = 0.035 M. the observed rate of disappearance of NO is 9.3 x 10-5 Mis. (a) What is the rate of disappearance of 02 at this moment? (b) What is the value of the rate constant? (c) What are the units of the rate constant? (d) What would happen to the rate if the concentration of NO were increased by a factor of 1.8?

Consider the following reaction between mercury(II) chloride and oxalate ion: \(2 \mathrm{HgCl}_{2}(a q)+\mathrm{C}_{2} \mathrm{O}_{4}^{2-}(a q) \rightarrow 2 \mathrm{Cl}^{-}(a q)+2 \mathrm{CO}_{2}(g)+\mathrm{Hg}_{2} \mathrm{Cl}_{2}(s)\) The initial rate of this reaction was determined for several concentrations of \(\mathrm{HgCl}_{2} \text { and } \mathrm{C}_{2} \mathrm{O}_{4}^{2-}\), and the following rate data were obtained for the rate of disappearance of \(\mathrm{C}_{2} \mathrm{O}_{4}^{2-}\); (a) What is the rate law for this reaction? (b) What is the value of the rate constant with proper units? (c) What is the reaction rate when the initial concentration of \(\mathrm{HgCl}_{2} \text { is } 0.100 \mathrm{M}\) and that of \(\left(\mathrm{C}_{2} \mathrm{O}_{4}^{2-}\right) \text { is } 0.25 \mathrm{M}\) if the temperature is the same as that used to obtain the data shown? Equation Transcription: Text Transcription: 2 HgCl2(aq)+C2O42-(aq) \rightarrow 2 Cl-(aq)+2 CO2(g)+Hg2Cl2(s) HgCl2 and C2O42- C2O42- HgCl2 is 0.100 M (C2O42-) is 0.25 M

Problem 92AE You perform a series of experiments for the reaction A?B + C and find that the rate law has the form rate = k[A]x. Determine the value of x in each of the following cases: (a) There is no rate change when [A]0 is tripled, (b) The rate increases by a factor of 9 when [A]0 is tripled, (c) When [A]0 is doubled, the rate increases by a factor of 8.

The following kinetic data are collected for the initial rates of a reaction \(2 X+Z \rightarrow\) products: (a) What is the rate law for this reaction? (b) What is the value of the rate constant with proper units? (c) What is the reaction rate when the initial concentration of \(X \text { is } 0.75 \mathrm{M}\) and that of \(Z \text { is } 1.25 \mathrm{M}\)? Equation Transcription: Text Transcription: 2 X+Z \rightarrow X is 0.75 M Z is 1.25 M

Problem 95AE The reaction 2 NO2?2 NO + O2 has the rate constant k = 0.63 M-1 s-1. (a) Based on the units for k, is the reaction first or second order in NO2? (b) If the initial concentration of NO2 is 0.100 M, how would you determine how long it would take for the concentration to decrease to 0.025 M?

Problem 96AE Consider two reactions. Reaction (1) has a constant half-life, whereas reaction (2) has a half-life that gets longer as the reaction proceeds. What can you conclude about the rate laws of these reactions from these observations?

Problem 98AE (a) The reaction H2O2(aq)?H2O(I) + 1/2O2(g) is first order. Near room temperature, the rate constant equals 7.0 x 10-4 s-1. Calculate the half-life at this temperature, (b) At 415 °C. (CH2)20 decomposes in the gas phase. (CH2)2O(g)?CH4(g) + CO(g). If the reaction is first order with a half-life of 56.3 min at this temperature, calculate the rate constant in s-1.

Problem 97AE A first-order reaction A.B has the rate constant fc = 3.2 x 10-3 s-1. If the initial concentration of A is 2.5 x 10-2 M, what is the rate of the reaction at t = 660 s?

Problem 99AE Americium-241 is used in smoke detectors. It has a first-order rate constant for radioactive decay of k = 1.6 x 10-3 yr-1. By contrast, iodine-125, which is used to test for thyroid functioning, has a rate constant for radioactive decay of k = 0.011 day-1, (a) What are the half-lives of these two isotopes? (b) Which one decays at a faster rate? (c) How much of a 1.00-mg sample of each isotope remains after 3 half-lives? (d) How much of a 1.00-mg sample of each isotope remains after 4 days?

Problem 100AE Urea (NH2CONH2) is the end product in protein metabolism in animals. The decomposition of urea in 0.1 M HCI occurs according to the reaction NH2CONH2(ag) + H+(aq) + 2 H2O(I)?2 NH4 +(aq) + HCO 3 - (aq) The reaction is first order in urea and first order overall. When [NH2CONH2] = 0.200 M, the rate at 61.05 °C is 8.56 x 10-5 M/s. (a) What is the rate constant. K? (b) What is the concentration of urea in this solution after 4.00 x 103 s if the starting concentration is 0.500 M? (c) What is the halflife for this reaction at 61.05 °C ?

A colored dye compound decomposes to give a colorless product. The original dye absorbs at \(608 \mathrm{~nm}\) and has an extinction coefficient of \(4.7 \times 10^{4} M^{-1} \mathrm{~cm}^{-1}\) at that wavelength. You perform the decomposition reaction in a \(1-\mathrm{cm}\) cuvette in a spectrometer and obtain the following data: From these data, determine the rate law for the reaction \(" \text { dye } \rightarrow \text { product" }\) and determine the rate constant. Equation Transcription: Text Transcription: 608 nm 4.7 x 104 M-1 cm-1 1-cm "dye \rightarrow product"

Cyclopentadiene \(\left(\mathrm{C}_{5} \mathrm{H}_{6}\right)\) reacts with itself to form dicyclopentadiene \(\left(\mathrm{C}_{10} \mathrm{H}_{12}\right)\). A \(0.0400 \mathrm{M}\) solution of \(\mathrm{C}_{5} \mathrm{H}_{6}\) was monitored as a function of time as the reaction \(2 \mathrm{C}_{5} \mathrm{H}_{6} \rightarrow \mathrm{C}_{10} \mathrm{H}_{12}\) proceeded. The following data were collected: Plot \({\left[\mathrm{C}_{5} \mathrm{H}_{6}\right]}\) versus time, ln \({\left[\mathrm{C}_{5} \mathrm{H}_{6}\right]}\) versus time, and \(1 /\left[\mathrm{C}_{5} \mathrm{H}_{6}\right]\) versus time. (a) What is the order of the reaction? (b) What is the value of the rate constant? Equation Transcription: Text Transcription: (C_5H_6) (C_10H_12) 0.0400 M C_5H_6 2 C_5H_6 \rightarrow C_10H_12 [C_5H_6] [C_5H_6] 1/[C_5H_6]

The first-order rate constant for reaction of a particular organic compound with water varies with temperature as follows: From these data, calculate the activation energy in units of \(\mathrm{kJ} / \mathrm{mol}\). Equation Transcription: Text Transcription: kJ/mol

Problem 105AE At 28 °C. raw milk sours in 4.0 h but takes 48 h to sour in a refrigerator at 5 °C. Estimate the activation energy in kJ/mol for the reaction that leads to the souring of milk?

Problem 106AE The following is a quote from an article in the August 18. 1998. issue of The New York Times about the breakdown of cellulose and starch: _A drop of 18 degrees Fahrenheit [from 77 °F to 59 °F4 lowers the reaction rate six times: a 36-degree drop [from 77 °F to 41 °F] produces a fortyfold decrease in the rate.” (a) Calculate activation energies for the breakdown process based on the two estimates of the effect of temperature on rate. Are the values consistent? (b) Assuming the value of Ea calculated from the 36° drop and that the rate of breakdown is first order with a half-life at 25 °C of 2.7 yr, calculate the half-life for breakdown at a temperature of -15 °C.

Problem 107AE The following mechanism has been proposed for the reaction of NO with H2 to form N20 and H20: NO(g) + NO(g)—N2O2(g) N2O2(g) + H2(g)-»N2O(g) + H2O(g) (a) Show that the elementary reactions of the proposed mechanism add to provide a balanced equation for the reaction, (b) Write a rate law for each elementary reaction in the mechanism, (c) Identify any intermediates in the mechanism, (d) The observed rate law is rate = k[NO]2[H2]. If the proposed mechanism is correct, what can we conclude about the relative speeds of the first and second reactions?

Problem 108AE Ozone in the upper atmosphere can be destroyed by the following two-step mechanism: Cl(g) + O3(g)ClO(g) + O2(g) ClO(g) + O(g)Cl(g) + O2(g) (a) What is the overall equation for this process? (b) What is the catalyst in the reaction? (c) What is the intermediate in the reaction?

Using Figure 14.23 as your basis, draw the energy profile for the bromide-catalyzed decomposition of hydrogen peroxide. (a) Label the curve with the activation energies for reactions \({[14.30] \text { and [14.31] }}\). (b) Notice from Figure 14.22 that when \(B r^{-}(a q)\) is first added, \(B r_{2}\) accumulates to some extent during the reaction and the solution turns brown. What does this tell us about the relative rates of the reactions represented by Equations 14.30 and 14.31? Equation Transcription: Text Transcription: [14.30] and [14.31] Br^-(aq) Br_2

Problem 111AE Consider the hypothetical reaction 2 A + Q-*2 C + D. The following two-step mechanism is proposed for the reaction: Step 1: A + B?C + X Step 2: A + X?C + D X is an unstable intermediate, (a) What is the predicted rate law expression if Step 1 is rate determining? (b) What is the predicted rate law expression if Step 2 is rate determining? (c) Your result for part (b) might be considered surprising for which of the following reasons: (i) The concentration of a product is in the rate law (ii) There is a negative reaction order in the rate law (iii) Both reasons (i) and (ii). (iv) Neither reasons (i) nor (ii).

The following mechanism has been proposed for the gas-phase reaction of chloroform \(\left(\mathrm{CHCl}_{3}\right)\) and chlorine: \(step 1: \quad C l_{2}(g) \underset{k-1}{\stackrel{k}{\rightleftarrows}} 2 C l(g) (fast)\) \(step 2: \quad \mathrm{Cl}(g)+\mathrm{CHCl}_{3}(g)_{\rightarrow}^{k_{2}} \mathrm{HCl}(g)+\mathrm{CCl}_{3}(g)( slow )\) \(step 3: $\quad \mathrm{Cl}(\mathrm{g})+\mathrm{CCl}_{3}(\mathrm{~g}) \stackrel{k_{3}}{\rightarrow} \mathrm{CCl}_{4} \quad (fast)\) (a) What is the overall reaction? (b) What are the intermediates in the mechanism? (c) What is the molecularity of each of the elementary reactions? (d) What is the rate-determining step? (e) What is the rate law predicted by this mechanism? (Hint: The overall reaction order is not an integer.) Equation Transcription: Text Transcription: (CHCl3) step 1: \quad C l_2(g) \underset k-1\stackrelk \rightleftarrows 2 C l(g) (fast) step 2: \quad Cl(g)+CHCl_3(g)_\rightarrow^k_2 HCl(g)+CCl_3(g)( slow ) step 3: \quad Cl(g)+CCl_3(g) \stackrel{k_3 \rightarrow CCl_4 \quad (fast)

In a hydrocarbon solution, the gold compound \(\left(\mathrm{CH}_{3}\right)_{3} \mathrm{AuPH}_{3}\) decomposes into ethane \(\left(\mathrm{C}_{2} \mathrm{H}_{6}\right)\) and a different gold compound, \(\left(\mathrm{CH}_{3}\right) \mathrm{AuPH}_{3}\). The following mechanism has been proposed for the decomposition of \(\left(\mathrm{CH}_{3}\right) \mathrm{AuPH}_{3}\) \(Step 1: $\left(\mathrm{CH}_{3}\right)_{3} \mathrm{AuPH}_{3} \underset{k_{-1}}{\stackrel{k_{1}}{\rightleftharpoons}}\left(\mathrm{CH}_{3}\right)_{3} \mathrm{Au}+\mathrm{PH}_{3} \quad$ (fast)\) \(Step 2: $\left(\mathrm{CH}_{3}\right)_{3} \mathrm{Au} \stackrel{\mathrm{k}_{2}}{\longrightarrow} \mathrm{C}_{2} \mathrm{H}_{6}+\left(\mathrm{CH}_{3}\right) \mathrm{Au}$ (slow)\) \(Step 3: $\quad\left(\mathrm{CH}_{3}\right) \mathrm{Au}+\mathrm{PH}_{3} \stackrel{k_{3}}{\longrightarrow}\left(\mathrm{CH}_{3}\right) \mathrm{AuPH}_{3} \quad$ (fast)\) (a) What is the overall reaction? (b) What are the intermediates in the mechanism? (c) What is the molecularity of each of the elementary steps? (d) What is the rate-determining step? (e) What is the rate law predicted by this mechanism? (f) What would be the effect on the reaction rate of adding \(\mathrm{PH}_{3}\) to the solution of \(\left(\mathrm{CH}_{3}\right)_{3} \mathrm{AuPH}_{3}\)? Equation Transcription: Text Transcription: (CH3)3AuPH3 (C2H6) (CH3)AuPH3 (CH3)AuPH3 step 1: (CH3)3AuPH3 k-1k1 (CH3)3Au + PH3 (fast) step 2: (CH3)3Au k2 C2H6 + (CH3)Au (slow) step 3: (CH3)3Au + PH3 k3 (CH3)AuPH3 (fast) PH3 (CH3)3AuPH3

Problem 113AE Platinum nanoparticles of diameter -2 nm are important catalysts in carbon monoxide oxidation to carbon dioxide. Platinum crystallizes in a face-centered cubic arrangement with an edge length of 3.924 A. (a) Estimate how many platinum atoms would fit into a 2.0-nm sphere: the volume of a sphere is (4/3)tt/3. Recall that 1 Ae = 1 x 10-10 m and 1 nm = 1 x 10-9 m. (b) Estimate how many platinum atoms are on the surface of a 2.0-nm Pt sphere, using the surface area of a sphere (4nr2) and assuming that the "footprint* of one Pt atom can be estimated from its atomic diameter of 2.8 A. (c) Using your results from (a) and (b), calculate the percentage of Pt atoms that are on the surface of a 2.0-nm nanoparticle, (d) Repeat these calculations for a 5.0-nm platinum nanoparticle, (e) Which size of nanoparticle would you expect to be more catalytically active and why?

Problem 114AE One of the many remarkable enzymes in the human body is carbonic anhydrase. which catalyzes the interconversion of carbon dioxide and water with bicarbonate ion and protons. If it were not for this enzyme, the body could not rid itself rapidly enough of the 002 accumulated by cell metabolism. The enzyme catalyzes the dehydration (release to air) of up to 107 002 molecules per second. Which components of this description correspond to the terms enzyme, substrate, and turnover number?

Problem 115AE Suppose that, in the absence of a catalyst, a certain biochemical reaction occurs x times per second at normal body temperature (37 °C). In order to be physiologically useful, the reaction needs to occur 5000 times faster than when it is uncatalyzed. By how many kJ/mol must an enzyme lower the activation energy of the reaction to make it useful?

Problem 116AE Enzymes are often described as following the two-step mechanism: E + S ? ES (fast) ES ? E + P (slow) where E = enzyme, S = substrate. ES = enzyme9substrate complex, and P = product. (a) If an enzyme follows this mechanism, what rate law is expected for the reaction? (b) Molecules that can bind to the active site of an enzyme but are not converted into product are called enzyme inhibitors. Write an additional elementary step to add into the preceding mechanism to account for the reaction of E with I, an inhibitor.

Problem 117AE Dinitrogen pentoxide (N205) decomposes in chloroform as a solvent to yield N02 and 02. The decomposition is first order with a rate constant at 45 °C of 1.0 x 10-5 s-1. Calculate the partial pressure of 02 produced from 1.00 L of 0.600 M N205 solution at 45 °C over a period of 20.0 h if the gas is collected in a 10.0-L container. (Assume that the products do not dissolve in chloroform.)

Problem 118AE The reaction between ethyl iodide and hydroxide ion in ethanol (C2H5OH) solution. C2H5I(a/c) + OH- (a/c)? C2H5OH(/) + I - (ale), has an activation energy of 86.8 kJ/mol and a frequency factor of 2.10 x 1011 M-1 s-1. (a) Predict the rate constant for the reaction at 35 °C. (b) A solution of KOH in ethanol is made up by dissolving 0.335 g KOH in ethanol to form 250.0 mL of solution. Similarly. 1.453 g of C2H5I is dissolved in ethanol to form 250.0 mL of solution. Equal volumes of the two solutions are mixed. Assuming the reaction is first order in each reactant, what is the initial rate at 35 °C? (c) Which reagent in the reaction is limiting, assuming the reaction proceeds to completion? (d) Assuming the frequency factor and activation energy do not change as a function of temperature, calculate the rate constant for the reaction at 50 °C.

You obtain kinetic data for a reaction at a set of different temperatures. You plot ln k versus \(1 / T\) and obtain the following graph: Suggest a molecular-level interpretation of these unusual data. Equation Transcription: Text Transcription: 1/T

Problem 120IE Integrative Exercises The gas-phase reaction of NO with F2 to form NOF and F has an activation energy of Ea = 6.3 kJ/mol. and a frequency factor of A = 6.0 x 108 A4-1 s-1. The reaction is believed to be bimolecular: NO(g) + F2(g) ? NOF(g) + F(g) (a) Calculate the rate constant at 100 °C. (b) Draw the Lewis structures for the NO and the NOF molecules, given that the chemical formula for NOF is misleading because the nitrogen atom is actually the central atom in the molecule, (c) Predict the shape for the NOF molecule, (d) Draw a possible transition state for the formation of NOF, using dashed lines to indicate the weak bonds that are beginning to form, (e) Suggest a reason for the low activation energy for the reaction.

Problem 121IE The mechanism for the oxidation of HBr by 02 to form 2 H20 and Br2 is shown in Exercise, (a) Calculate the overall standard enthalpy change for the reaction process, (b) HBr does not react with 02 at a measurable rate at room temperature under ordinary conditions. What can you infer from this about the magnitude of the activation energy for the rate-determining step? (c) Draw a plausible Lewis structure for the intermediate HOOBr. To what familiar compound of hydrogen and oxygen does it appear similar? Reaction Mechanisms (Section) You have studied the gas-phase oxidation of HBr by 02: 4 HBr(g) + 02(g)—2 H20(g) + 2 Br2(g) You find the reaction to be first order with respect to HBr and first order with respect to 02. You propose the following mechanism: HBr(g) + 02(g)- HOOBr(g) HOOBr(g) + HBr(g)—2 HOBr(g) HOBr(g) + HBr(g)— H20(g) + Br2(g) (a) Confirm that the elementary reactions add to give the overall reaction, (b) Based on the experimentally determined rate law, which step is rate determining? (c) What are the intermediates in this mechanism? (d) If you are unable to detect HOBr or HOOBr among the products, does this disprove your mechanism?

The rates of many atmospheric reactions are accelerated by the absorption of light by one of the reactants. For example, consider the reaction between methane and chlorine to produce methyl chloride and hydrogen chloride: Reaction 1: \(\mathrm{CH}_{4}(g)+\mathrm{Cl}_{2}(g) \rightarrow \mathrm{CH}_{3} \mathrm{Cl}(g)+\mathrm{HCl}(g)\) This reaction is very slow in the absence of light. However, \(\mathrm{Cl}_{2}(g)\) can absorb light to form \(\mathrm{Cl}\) atoms: Reaction 2: \(\mathrm{Cl}_{2}(g)+h v \rightarrow 2 \mathrm{Cl}(g)\) Once the \(\mathrm{Cl}\) atoms are generated, they can catalyze the reaction of \(\mathrm{CH}_{4} \text { and } \mathrm{Cl}_{2}\), according to the following proposed mechanism: Reaction 3: \(\mathrm{CH}_{4}(g)+\mathrm{Cl}(g) \rightarrow \mathrm{CH}_{3}(g)+\mathrm{HCl}(g)\) Reaction 4: \(\mathrm{CH}_{3}(g)+\mathrm{Cl}_{2}(g) \rightarrow \mathrm{CH}_{3} \mathrm{Cl}(g)+\mathrm{Cl}(g)\) The enthalpy changes and activation energies for these two reactions are tabulated as follows: (a) By using the bond enthalpy for \(\mathrm{Cl}_{2}\) (Table 8.4), determine the longest wavelength of light that is energetic enough to cause reaction 2 to occur. In which portion of the electromagnetic spectrum is this light found? (b) By using the data tabulated here, sketch a quantitative energy profile for the catalyzed reaction represented by reactions 3 and 4. (c) By using bond enthalpies, estimate where the reactants, \(\mathrm{CH}_{4}(g)+\mathrm{Cl}_{2}(g)\), should be placed on your diagram in part (b). Use this result to estimate the value of \(\mathrm{E}_{a}\) for the reaction \(\mathrm{CH}_{4}(g)+\mathrm{Cl}_{2}(g) \rightarrow \mathrm{CH}_{3}(g)+\mathrm{HCl}(g)+\mathrm{Cl}(g)\). (d) The species \(\mathrm{Cl}(g) \text { and } \mathrm{CH}_{3}(g)\) in reactions 3 and 4 are radicals, that is, atoms or molecules with unpaired electrons. Draw a Lewis structure of \(\mathrm{CH}_{3}\), and verify that it is a radical. (e) The sequence of reactions 3 and 4 comprises a radical chain mechanism. Why do you think this is called a “chain reaction”? Propose a reaction that will terminate the chain reaction. Equation Transcription: Text Transcription: CH_4(g)+Cl2(g) \rightarrow CH_3Cl(g)+HCl(g) Cl_2(g) Cl Cl_2(g)+hv \rightarrow 2Cl(g) Cl CH_4 and Cl_2 CH_4(g)+Cl(g) \rightarrow CH_3(g)+HCl(g) CH_3(g)+Cl_2(g) \rightarrow CH_3Cl(g)+Cl(g) Cl_2 CH_4(g)+Cl_2(g) E_a CH_4(g)+Cl_2(g) \rightarrow CH_3(g)+HCl(g)+Cl(g) Cl(g) and CH_3(g) CH_3

Problem 123IE Many primary amines. RNH2. where R is a carbon-containing fragment such as CH3. CH3CH2. and so on. undergo reactions where the transition state is tetrahedral, (a) Draw a hybrid orbital picture to visualize the bonding at the nitrogen in a primary amine (just use a C atom for _R"). (b) What kind of reactant with a primary amine can produce a tetrahedral intermediate?

The \(\mathrm{NO}_{x}\) waste stream from automobile exhaust includes species such as \(\mathrm{NO} \text { and } \mathrm{NO}_{2}\). Catalysts that convert these species to \(\mathrm{~N}_{2}\). are desirable to reduce air pollution. (a) Draw the Lewis dot and VSEPR structures of \(\mathrm{NO}, \mathrm{NO}_{2} \text { and } \mathrm{N}_{2}\). (b) Using a resource such as Table 8.4, look up the energies of the bonds in these molecules. In what region of the electromagnetic spectrum are these energies? (c) Design a spectroscopic experiment to monitor the conversion of \(\mathrm{NO}_{x} \text { into } \mathrm{N}_{2}\) , describing what wavelengths of light need to be monitored as a function of time. Equation Transcription: Text Transcription: NO_x NO and NO_2 N_2 NO, NO_2 and N_2 NO_x into N_2

As shown in Figure 14.24, the first step in the heterogeneous hydrogenation of ethylene is adsorption of the ethylene molecule on a metal surface. One proposed explanation for the “sticking” of ethylene to a metal surface is the interaction of the electrons in the \(C \neg C \pi\) bond with vacant orbitals on the metal surface. (a) If this notion is correct, would ethane be expected to adsorb to a metal surface, and, if so, how strongly would ethane bind compared to ethylene? (b) Based on its Lewis structure, would you expect ammonia to adsorb to a metal surface using a similar explanation as for ethylene? Equation Transcription: Text Transcription: C \neg C \pi

Problem 56E Temperature and Rate (Section) For the elementary process N2O5(g)?NO2(g) + NO3(g) the activation energy (Ea) and overall AE are 154 kJ/mol and 136 kJ/mol, respectively, (a) Sketch the energy profile for this reaction, and label Ea and AE. (b) What is the activation energy for the reverse reaction?

Problem 101AE The rate of a first-order reaction is followed by spectroscopy, monitoring the absorbance of a colored reactant at 520 nm. The reaction occurs in a 1.00-cm sample cell, and the only colored species in the reaction has an extinction coefficient of 5.60 x 103 M-1 cm-1 at 520 nm. (a) Calculate the initial concentration of the colored reactant if the absorbance is 0.605 at the beginning of the reaction, (b) The absorbance falls to 0.250 at 30.0 min. Calculate the rate constant in units of s-1. (c) Calculate the half-life of the reaction, (d) How long does it take for the absorbance to fall to 0.100?