Sample Exercise 14.1 (p. 578) For the reaction pictured at the bottom of the previous page, calculate the average rate at which A disappears over the time interval from 20 s to 40 s. (1.2 x 10-2 M/s) Practice Exercise 1 (14.1) If the experiment on the previous page is run for 60 s, 0.16 mol A remain. Which of the following statement is or is not true? (i) After 60 s there are 0.84 mol B in the flask. (ii) The decrease in the number of moles of A from t 1 = 0 s to t 2 = 20 s is greater than that from t 1 = 40 s to t 2 = 60 s. (iii) The average rate for the reaction from t 1 = 40 s to t 2 = 60 s is 7.0 x 10-3 M/s. (a) Only one of the statements is true. (b) Statements (i) and (ii) are true. (c) Statements (i) and (iii) are true. (d) Statements (ii) and (iii) are true. (e) All three statements are true. Practice Exercise 2 (14.1) From the reaction pictured, calculate the average rate of appearance of B over the time interval from 0 to 40 s. (1.8 x 10-2 M/s) - 1 -
Average Rate vs. Instantaneous Rate Sample Exercise 14.2 (p. 580) Using the reaction graphed above, calculate the instantaneous rate of disappearance of C 4 H 9 Cl at t = 0 (the initial rate). (2.0 x 10-4 M/s) Practice Exercise 1 (14.2) Which of the following would be the instantaneous rate of the reaction in the previous figure at t = 1000 s? a) 1.2 x 10-4 M/s b) 8.8 x 10-5 M/s c) 6.3 x 10-5 M/s d) 2.7 x 10-5 M/s e) More than one of these. Practice Exercise 2 (14.2) For the reaction graphed above, calculate the instantaneous rate of disappearance of C 4 H 9 Cl at t = 300 s. (1.1 x 10-4 M/s) - 2 -
Reaction Rates and Stoichiometry Sample Exercise 14.3 (p. 581) a) How is the rate at which ozone disappears related to the rate at which oxygen appears in in the following equation? 2 O 3(g) 3 O 2(g) (- 1 [O 3 ] = 1 [O 2 ]) 2 t 3 t b) If the rate at which O 2 appears, [O 2 ]/ t, is 6.0 x 10-5 M/s at a particular instant, at what rate is O 3 disappearing at this same time, - [O 3 ]/ t? (4.0 x 10-5 M/s) Practice Exercise 1 (14.3) At a certain time in a reaction, substance A is disappearing at a rate of 4.0 x 10-2 M/s, substance B is appearing at a rate of 2.0 x 10-2 M/s, and substance C is appearing at a rate of 6.0 x 10-2 M/s. Which of the following could be the stoichiometry for the reaction being studied? a) 2A + B 3C b) A 2B + 3C c) 2A B + 3C d) 4A 2B + 3C e) A + 2B 3C - 3 -
Practice Exercise 2 (14.3) The decomposition of N 2 O 5 proceeds according to the following equation: 2 N 2 O 5(g) 4 NO 2(g) + O 2(g) If the rate of decomposition of N 2 O 5 at a particular instant in a reaction vessel is 4.2 x 10-7 M/s, what is the rate of appearance of a) NO 2 (8.4 x 10-7 M/s) b) O 2 (2.1 x 10-7 M/s) - 4 -
14.3 Concentration and Rate Sample Exercise 14.4 (p. 584) Consider a reaction A + B C for which rate = k[a][b] 2. Each of the following boxes represents a reaction mixture in which A is shown as red spheres and B as blue ones. Rank these mixtures in order of increasing rate of reaction. (2 < 1 < 3) Practice Exercise 1 (14.4) Suppose the rate law for the reaction in this Sample Exercise were rate = k[a] 2 [B]. What would be the ordering of the rates for the three mixtures shown above, from slowest to fastest? a) 1 < 2 < 3 b) 1 < 3 < 2 c) 3 < 2 < 1 d) 2 < 1 < 3 e) 3 < 1 < 2 Practice Exercise 2 (14.4) Assuming that the rate = k[a][b], rank the mixtures represented above in order of increasing rate. (2 = 3 < 1) - 5 -
Sample Exercise 14.5 (p. 585) a) What are the overall reaction orders for the reactions described in the following equations: i) 2 N 2 O 5(g) 4 NO 2(g) + O 2(g) Rate = k[n 2 O 5 ] ii) CHCl 3(g) + Cl 2(g) CCl 4(g) + HCl (g) Rate = k[chcl 3 ][Cl 2 ] 1/2 b) What are the units of the rate constant for the rate law for Equation (i)? Practice Exercise 1 (14.5) Which of the following are the units of the rate constant for (ii)? a) M -1/2 s -1 b) M -1/2 s -1/2 c) M 1/2 s -1 d) M -1/2 s -1 e) M -1/2 s -1/2 Practice Exercise 2 (14.5) a) What is the reaction order of the reactant H 2 in Equation (iii)? iii) H 2(g) + I 2(g) 2 HI Rate = k[h 2 ][I 2 ] (1) b) What are the units of the rate constant for Equation (iii)? (M -1 s -1 ) - 6 -
Sample Exercise 14.6 (p. 586) The initial rate of a reaction A + B C was measured for several different starting concentrations of A and B, and the results are as follows: Using these data, determine a) the rate law for the reaction (k[a] 2 ) b) the magnitude of the rate constant (4.0 x 10-3 M -1 s -1 ) c) the rate of the reaction when [A] = 0.050 M and [B] = 0.100 M. (1.0 x 10-5 M/s) - 7 -
Practice Exercise 1 (14.6) A certain reaction X + Y Z is described as being first order in [X] and third order overall. Which of the following statements is or are true? (i) The rate law for the reaction is: Rate = [X][Y] 2. (ii) If the concentration of X is increased by a factor of 1.5, the rate will increase by a factor of 2.25. (iii) If the concentration of Y is increased by a factor of 1.5, the rate will increase by a factor of 2.25. a) Only one statement is true. b) Statements (i) and (ii) are true. c) Statements (i) and (iii) are true. d) Statements (ii) and (iii) are true. e) All three statements are true. Practice Exercise 2 14.6 The following data were measured for the reaction of nitric oxide with hydrogen: 2 NO (g) + 2 H 2(g) N 2(g) + 2 H 2 O (g) a) Determine the rate law for this reaction. (k[no] 2 [H 2 ]) b) Calculate the rate constant. (1.2 M -2 s -1 ) c) Calculate the rate when [NO] = 0.050 M and [H 2 ] = 0.150 M. (4.5 x 10-4 M/s) - 8 -
14.4 The Change of Concentration with Time Sample Exercise 14.7 (p. 588) The first-order rate constant for the decomposition of a certain insecticide in water at 12 o C is 1.45 yr -1. A quantity of this insecticide is washed into a lake on June 1, leading to a concentration of 5.0 x 10-7 g/cm 3 of water. Assume that the average temperature of the lake is 12 o C. a) What is the concentration of the insecticide on June 1 of the following year? (1.2 x 10-7 g/cm 3 ) b) How long will it take for the concentration of the insecticide to drop to 3.0 x 10-7 g/cm 3? (0.35 yr) Practice Exercise 1 (14.7) At 25 o C, the decomposition of dinitrogen pentoxide, N 2 O 5(g), into NO 2(g) and O 2(g) follows first-order kinetics with k = 3.4 x 10-5 s -1. A sample of N 2 O 5 with an initial pressure of 760 torr decomposes at 25 o C until its partial pressure is 650 torr. How much time (in seconds) has elapsed? a) 5.3 x 10-6 b) 2000 c) 4600 d) 34,000 e) 190,000-9 -
Practice Exercise 2 (14.7) The decomposition of dimethyl ether, CH 3 OCH 3, at 510 o C is a first-order process with a rate constant of 6.8 x 10-4 s -1 : CH 3 OCH 3 (g) CH 4(g) + H 2(g) + CO (g) If the initial pressure of CH 3 OCH 3 is 135 torr, what is its partial pressure after 1420 s? (51 torr) Sample Exercise 14.8 (p. 590) The following data were obtained for the gas phase decomposition of nitrogen dioxide at 300 C: NO 2(g) NO (g) + 1/2 O 2(g) f Is the reaction first or second order in NO 2? (Hint: use data and plots below.) (2 nd order) - 10 -
Practice Exercise 1 (14.8) For a certain reaction A products, a plot of ln[a] versus time produces a straight line with a slope of -3.0 x 10-2 s -1. Which of the following statements is or are true? (i) The reaction follows first-order kinetics. (ii) The rate constant for the reaction is 3.0 x 10-2 s -1. (iii) The initial concentration of [A] was 1.0 M. a) Only one of the statements is true. b) Statements (i) and (ii) are true. c) Statements (i) and (iii) are true. d) Statements (ii) and (iii) are true. e) All three statements are true. Practice Exercise 2 (14.8) Consider again the decomposition of NO 2 discussed above. The reaction is second order in NO 2 with k = 0.543 M -1 s -l. If the initial concentration of NO 2 in a closed vessel is 0.0500 M, what is the remaining concentration after 0.500 hr? (1.0 x 10-3 M) - 11 -
Sample Exercise 14.9 (p. 590) From the figure below, estimate the half-life of C 4 H 9 Cl with water. (~340 s) Practice Exercise 1 (14.9) We noted in an earlier Practice Exercise that at 25 o C the decomposition of N 2 O 5(g) into NO 2(g) and O 2(g) follows first-order kinetics with k = 3.4 x 10-5 s -1. How long will it take for a sample originally containing 2.0 atm of N 2 O 5 to reach a partial pressure of 380 torr? a) 5.7 h b) 8.2 h c) 11 h d) 16 h e) 32 h Practice Exercise 2 (14.9) a) Calculate t 1/2 for the decomposition of the insecticide described in Sample Exercise 14.7. (0.478 yr = 1.51 x 10 7 s) b) How long does it take for the concentration of the insecticide to reach one-quarter of the initial value? (two half-lives = 2(0.478 yr) = 0.956 yr) - 12 -
14.5 Temperature and Rate Sample Exercise 14.10 (p. 597) Consider a series of reactions having the following energy profiles: Assuming that all three reactions have nearly the same frequency factors, rank the reactions from slowest to fastest. ( (2)< (3) < (1) ) Practice Exercise 1 (14.10) Which of the following statement is or are true? (i) The activation energies for the forward and reverse directions of a reaction can be different. (ii) Assuming that A is constant, ir both E a and T increase, then k will increase. (iii) For two different reactions, the one with the smaller value of E a will necessarily have the larger value for k. a) Only one of the statements is true. b) Statements (i) and (ii) are true. c) Statements (ii) and (iii) are ture. d) All three statements are true. Practice Exercise 2 (14.10) Imagine that these reactions are reversed. Rank these reverse reactions from slowest to fastest. ( (2) < (1) < (3) ) - 13 -
Sample Exercise 14.11 (p. 598) The following table shows the rate constants for the rearrangement of methyl isonitrile at various temperatures: a) From these data, calculate E a for the reaction. (160 kj/mol) (Hint: make a table of T, 1/T and ln k) b) What is the value of the rate constant at 430.0 K? (1.0 x 10-6 s -1 ) Practice Exercise 1 (14.11) Using the data in Sample Exercise 14.11, which of the following is the rate constant for the rearrangement of methyl isonitrile at 320 o C? a) 8.1 x 10-15 s -1 b) 2.2 x 10-13 s -1 c) 2.7 x 10-9 s -1 d) 2.3 x 10-1 s -1 e) 9.2 x 10 3 s -1 Practice Exercise 2 (14.11) Using the data in Sample Exercise 14.11, above, calculate the rate constant for the rearrangement of methyl isonitrile at 280 o C. (2.2 x 10-2 s -1 ) - 14 -
14.6 Reaction Mechanisms Sample Exercise 14.12 (p. 600) It has been proposed that the conversion of ozone into O 2 proceeds via two elementary steps: O 3(g) O 2(g) + O (g) O 3(g) + O (g) 2 O 2(g) a) Describe the molecularity of each step in this mechanism. b) Write the equation for the overall reaction. c) Identify the intermediate(s). Practice Exercise 1 (14.12) Consider the two-step reaction mechanism: A (g) + B (g) X (g) + Y (g) X (g) + C (g) Y (g) + Z (g) Which of the following statements about this mechanism is or are true? (i) Both of the steps in this mechanism are bimolecular. (ii) The overall reaction is A (g) + B (g) + C (g) Y (g) + Z (g) (iii) The substance X (g) is an intermediate in this mechanism. a) Only one of these statements is true. b) Statements (i) and (ii) are true. c) Statements (i) and (iii) are true. d) Statements (ii) and (iii) are true. Practice Exercise 2 (14.12) For the reaction Mo(CO) 6 + P(CH 3 ) 3 Mo(CO) 5 P(CH 3 ) 3 + CO the proposed mechanism is Mo(CO) 6 Mo(CO) 5 + CO Mo(CO) 5 + P(CH 3 ) 3 Mo(CO) 5 P(CH 3 ) 3 a) Is the proposed mechanism consistent with the equation for the overall reaction? b) Identify the intermediates. - 15 -
Sample Exercise 14.13 (p. 602) If the following reaction occurs in a single elementary step, predict the rate law: H 2(g) + Br 2(g) 2 HBr (g) Practice Exercise 1 (14.13) Consider the following reaction: 2A + B X + 2 Y. You are told that the first step in the mechanism of this reaction has the following rate law: Rate = k[a][b]. Which of the following could be the first step in the reation mechanism (note that substance Z is an intermediate)? a) A + A Y + Z b) A X + Z c) A + A + B X + Y + Y d) B X + Y e) A + B X + Z Practice Exercise 2 (14.13) Consider the following reaction: 2 NO (g) + Br 2(g) 2 NOBr (g). a) Write the rate law for the reaction, assuming it involves a single elementary step. b) Is a single-step mechanism likely for this reaction? Why or why not? Rate Laws for Multistep Mechanisms Sample Exercise 14.14 (p. 604) The decomposition of nitrous oxide, N 2 O, is believed to occur by a two-step mechanism: Step 1: N 2 O (g ) N 2(g) + O (g) (slow) Step 2: N 2 O (g) + O (g) N 2(g) + O 2(g) (fast) a) Write the equation for the overall reaction. b) Write the rate law for the overall reaction. - 16 -
Practice Exercise 1 (14.14) Let s consider a hypothetical reaction similar to that in Practice Exercise 1 of Sample Exercise 14.13: 2 C + D J + 2 K. You are told that the rate of this reaction is second order overall and second order in [C]. Could any of the following be a rate-determining first step in a reaction mechanism that is consistent with the observed rate law for the reaction (note that substance Z is an intermediate)? a) C + D K + Z b) C J + Z c) C + D J + Z d) D J + K e) None of these are consistent with the observed rate law. Practice Exercise 2 (14.14) Ozone reacts with nitrogen dioxide to produce dinitrogen pentoxide and oxygen: O 3(g) + 2 NO 2(g) N 2 O 5(g) + O 2(g) The reaction is believed to occur in two steps: O 3(g) + NO 2(g) NO 3(g) + O 2(g) NO 3(g) + NO 2(g) N 2 O 5(g) The experimental rate law is rate = k[o 3 ][NO 2 ]. What can you say about the relative rates of the two steps of the mechanism? Sample Exercise 14.15 (p. 606) Show that the following mechanism for the equation 2 NO (g) + Br 2(g) 2 NOBr (g) also produces a rate law consistent with the experimentally observed one: Step 1: NO(g) + NO(g) 1 k k 1 N 2 O 2(g) (fast equilibrium) Step 2: N 2 O 2(g) + Br 2(g) 2 NOBr(g) (slow) - 17 -
Practice Exercise 1 (14.15) Consider the following hypothetical reaction: 2 P + Q 2 R + S The following mechanism is proposed for this reaction: P + P T (fast) Q + T R + U (slow) U R + S (fast) Substances T and U are unstable intermediates. What rate law is predicted by this mechanism? a) Rate = k[p] 2 b) Rate = k [P][Q] c) Rate = k[p] 2 [Q] d) Rate = k[p][q] 2 e) Rate = k[u] Practice Exercise 2 (14.15) The first step of a mechanism involving the reaction of bromine is Br 2(g) k1 2 Br (g) (fast equilibrium) k 1 What is the expression relating the concentration of Br(g) to that of Br 2 (g)? - 18 -
Sample Integrative Exercise 14: Putting Concepts Together (p. 613) Formic acid (HCOOH) decomposes in the gas phase at elevated temperatures as follows: HCOOH (g) CO 2(g) + H 2(g) The decomposition reaction is determined to be first order. A graph of the partial pressure of HCOOH versus time for decomposition at 838 K is shown as the red curve in the figure below. When a small amount of solid ZnO is added to the reaction chamber, the partial pressure of acid versus time varies as shown by the blue curve in the figure below. - 19 -
a) Estimate the half-life and first-order rate constant for formic acid decomposition. b) What can you conclude from the effect of added ZnO on the decomposition of formic acid? c) The progress of the reaction was followed by measuring the partial pressure of formic acid vapor at selected times. Suppose that, instead, we had plotted the concentration of formic acid in units of mol/l. What effect would this have had on the calculated value of k? d) The pressure of formic acid vapor at the start of the reaction is 3.00 x 10 2 torr. Assuming constant temperature and ideal-gas behavior, what is the pressure in the system at the end of the reaction? If the volume of the reaction chamber is 436 cm 3, how many moles of gas occupy the reaction chamber at the end of the reaction? e) The standard heat of formation of formic acid vapor is H o f = -378.6 kj/mol. Calculate H o for the overall reaction. Assuming that the activation energy (E a ) for the reaction is 184 kj/mol, sketch an approximate energy profile for the reaction, and label E a, H o, and the transition state. - 20 -