Topic: Chemical Kinetics. (aq) + 6H + (aq) 3Br 2. O(l) If the rate of appearance of Br 2

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1 PHYSICAL CHEMISTRY by: SHAILENDRA KR. Classes at: - SCIENCE TUTORIALS; Opp. Khuda Baksh Library, Ashok Rajpath, Patna PIN POINT STUDY CIRCLE;House No. 5A/65, Opp. Mahual Kothi, Alpana Market, Patna Topic: Chemical Kinetics Meq. Approach 01. Consider the following reaction in aqueous solution, 5Br (aq) + BrO 3 (aq) + 6H + (aq) 3Br 2 (aq) + 3H 2 O(l) If the rate of appearance of Br 2 at a particular moment during the reaction is M s 1, what is the rate of disappearance (in M s 1 ) of Br at that moment? 02. Consider the following reaction at 25 C, (CH 3 ) 3 COH (l) + HCl (aq) (CH 3 ) 3 CCl(l) + H 2 O(l) The experimentally determined rate law for this reaction indicates that the reaction is first-order in (CH 3 ) 3 COH and that the reaction is first-order overall. Which of the following would produce an increase in the rate of this reaction? (a) increasing the concentration of (CH 3 ) 3 COH (b) increasing the concentration of HCl (c) decreasing the concentration of HCl (d) decreasing the concentration of (CH 3 ) 3 CCl (e) It is impossible to tell. 03. A certain first-order reaction has a rate constant, K, equal to 2.1 x 10 5 s 1 at 355 K. If the activation energy for this reaction is 135 kj/mol, calculate the value of the rate constant (in s 1 ) at 550 K. 04. Which of the following influences the rate of a chemical reaction performed in solution? (a) temperature (b) activation energy (c) presence of a catalyst (d) concentrations of reactants (e) All of the above influence the rate. 05. The two diagrams below represent snapshots of a very small portion of a first-order reaction in which A molecules are being converted to B molecules (A B): Which of the following diagrams represents a snapshot of a very small portion of this system at t = 3 min? Page No.: 1

2 (a) (b) (c) (d) (e) 06. Laughing gas, N 2 O, can be prepared from H 2 and NO: H 2 + 2NO N 2 O + H 2 O A study of initial concentration versus initial rate at a certain temperature yields the following data for this reaction: [H 2, M [NO, M initial rate, M s x x x x 10 6 Which of the following is the correct rate law for this reaction? (a) Rate = k[h 2 [NO 2 (b) Rate = k[h 2 [NO (c) Rate = k[no 2 (d) Rate = k[h 2 2 (e) Rate = k 07. Iodine-131, a radioactive isotope of iodine, is used medicinally as a radiotracer for the diagnosis and treatment of illnesses associated with the thyroid gland. The half-life of iodine-131 is 7.0 x 105 seconds. If a patient is given 0.45 g of iodine-131, calculate how long it would take (in seconds) for 90.0% of the iodine-131 to decay. Recall: radioactive decay is a first-order process. 08. Consider a reaction which is first-order in A and first-order in B, A + B Products Rate = k[a[b What are the relative rates of this reaction in the vessels shown below. Note: each vessel has the same volume. (a) III > I = IV > II (c) IV > II > III > I (e) III > I > IV > II (b) I > III > II > IV (d) II > IV > I > III Page No.: 2

3 09. The complex ion, [Cr(NH 3 )5Cl 2+, reacts with OH ion in aqueous solution, [Cr(NH 3 )5Cl 2+ (aq) + OH (aq) [Cr(NH 3 ) 5 (OH) 2+ (aq) + Cl (aq) The following data were obtained for this reaction at 25oC, time, min [Cr(NH 3 ) 5 Cl 2+, M The order of the reaction with respect to the [Cr(NH 3 )5Cl 2+ ion is: (a) zero order (b) first order (c) second order (d) third order (e) fourth order 10. A student determined the value of the rate constant, k, for a chemical reaction at several different temperatures. Which of the following graphs of the student's data would give a straight line? (a) k versus T (b) k versus (1/T) (c) ln k versus (1/T) (d) ln k versus T (e) ln k versus E a 11. In the experiment, "How Can Spectrophotometric Methods Be Used to Determine the Order of a Chemical Reaction", it is necessary to remove invalid data points towards the end of the reaction. Which of the following statements best explains why this is necessary? (a) The Spectronic 20 becomes unstable towards the end of the reaction. (b) Towards the end of the reaction, the temperature of the solution is significantly different than the initial temperature of the solution. (c) Towards the end of the reaction, the concentrations of the reactants are so high that it is difficult to measure them accurately. (d) Towards the end of the reaction, the concentrations of the products are sufficiently high that the reverse reaction competes with the forward reaction. (e) None of these. The next two questions are about this reaction: 2N 2!!!" #!! 4N The rate law for the above reaction is: (a) rate = k [N 2 2 (b) rate = [N 2 2 (c) rate = k [N 2 2 / [N 4 [ 1 (d) rate = k [N 2 x (e) rate = [N 2 x Page No.: 3

4 13. If the instantaneous rate of appearance of N is M/s at some moment in time, what is the rate of disappearance of N 2 in M/s? 14. The rate laws for certain enzyme-activated reactions in your body have a specific rate constant k, with units of M/s. What is the overall order of these reactions? (a) 0 (b) 1 (c) 2 (d) 3 (e) Cannot be determined. The next two questions are about this reaction: 2NO + Cl 2 2NOCl 15. The rate law for the above reaction has been determined to be rate = k[no[cl 2. What is the overall order of the reaction? (a) 0 (b) 1 (c) 2 (d) 3 (e) Cannot be determined. 16. A mechanism involving the following steps has been proposed for the above reaction: (I) NO + Cl 2 NOCl 2 (II) NOCl 2 + NO 2NOCl Based on the rate law given in the preceding problem, which step is the rate-limiting step? (a) Step I (b) Step II (c) Both Steps I & II (d) Either Steps I or II 17. Consider the following reaction in aqueous solution, I (aq) + OCl (aq) IO (aq) + Cl (aq) and the following initial concentration and initial rate data for this reaction: [I, M [OCl, M initial rate, M s x x x x 10 4 Which of the following is the correct rate law for this reaction? (a) Rate = k[i (b) Rate = k[ocl (c) Rate = k[i 2 (d) Rate = k[i [OCl (e) Rate = k[i 2 [OCl 18. Which of the following statements best describes how the "Method of Initial Rates" is used to measure the initial rate of an equilibrium reaction? (a) The rate of the reaction is measured when the reaction is very close to equilibrium. (b) The rate of the reaction is measured immediately after the reaction is started. (c) The rate of the reaction is measured when the reaction is about one-half complete. Page No.: 4

5 (d) The rate of the reaction is measured after five half-lives. (e) The rate of an equilibrium reaction cannot be measured using this method. 19. Which of the following are the correct units for the rate constant, k, for a zero-order reaction? (a) M s 1 (b) M 1 s 1 (c) M 2 s 1 (d) M 3 s 1 (e) M 20. Which of the following statements is TRUE? (a) The existence of certain intermediates in a reaction mechanism can sometimes be proven because intermediates can sometimes be trapped and identified. (b) Intermediates in a reaction mechanism cannot be isolated because they do not have finite lifetimes. (c) Reaction mechanisms cannot have any more than one intermediate. (d) Intermediates in a reaction mechanism appear in the overall, balanced equation for the reaction (e) None of the above statements is TRUE. 21. Which of the following statements best describes how a catalyst works? (a) A catalyst changes the potential energies of the reactants and products. (b) A catalyst decreases the temperature of the reaction which leads to a faster rate. (c) A catalyst lowers the activation energy for the reaction by providing a different reaction mechanism. (d) A catalyst destroys some of the reactants, which lowers the concentration of the reactants. (e) A catalyst raises the activation energy for the reaction which produces a faster rate. 22. In terms of the "Collision Theory of Chemical Kinetics", the rate of a chemical reaction is proportional to: (a) the change in free energy per second. (b) the change in temperature per second. (c) the number of collisions per second. (d) the number of product molecules. (e) none of the above 23. Nitrogen monoxide, NO, reacts with hydrogen, H 2, according to the following equation: 2 NO + 2 H 2 N H 2 O If the mechanism for this reaction were, 2NO + H 2 N 2 + H 2 slow H 2 + H 2 2H 2 O fast which of the following rate laws would we expect to obtain experimentally? (a) Rate = k[h 2 [H 2 (b) Rate = k[no 2 [H 2 (c) Rate = k[no 2 [H 2 2 (d) Rate = k[no[h 2 (e) Rate = k[n 2 [H 2 Page No.: 5

6 24. Consider the following reaction in aqueous solution, 5 Br (aq) + BrO 3 (aq) + 6 H + (aq) 3 Br 2 (aq) + 3 H 2 O (l) If the rate of disappearance of Br (aq) at a particular moment during the reaction is 3.5 x 10 4 M s 1, what is the rate of appearance of Br 2 (aq) at that moment? 25. Consider the following gas-phase reaction, 2 HI H2 + I2 and the following experimental data obtained at 555 K, [HI, M rate, M s x x x 10 9 What is the order of the reaction with respect to HI? 26. Radioactive phosphorus is used in the study of biochemical reaction mechanisms. The isotope phosphorus-33 decays by first-order kinetics with a half-life of 14.3 days. If a chemist initially has a 7.5 M solution of pure phosphorus-33, calculate the concentration (in M) of phosphorus-33 in the solution after 2.4 days. 27. Hydrogen iodide, HI, decomposes in the gas phase to produce hydrogen, H 2, and iodine, I 2 : 2 HI H2 + I2 The value of the rate constant, k, for this reaction was measured at several different temperatures and the data are shown below: temperature, K K, M 1 s x x x x 10 3 Calculate the value of the activation energy (in kj/mol) for this reaction. 28. Listed below are some statements that pertain to chemical kinetics. For each statement, first decide whether the statement is TRUE or FALSE. If the statement is FALSE, briefly explain why the statement is FALSE. If the statement is TRUE, you do not need to provide any additional explanation. (a) Rate laws for chemical reactions can be determined from the stoichiometry of the overall balanced equation. (b) The rate of a chemical reaction that occurs in solution depends on the concentration, the temperature and the viscosity of the solvent. (c) The "Method of Initial Rates" cannot be used for equilibrium reactions. (d) Experimentally, transition states can sometimes be trapped or isolated whereas intermediates cannot be either trapped or isolated. Page No.: 6

7 1.50 M 1.50 M mol/l hr 29. Consider the following reaction, 2Cl (aq) + 2OH (aq) ClO 3 (aq) + Cl (aq) + H 2 O(l) Write an expression that describes the relationship between the rates of disappearance of Cl and OH and the rates of appearance of ClO 3, Cl and H 2 O. 30. A student was charged with the task of determining the activation energy, Ea, for a particular first-order reaction. The student measured the value of the rate constant for this reaction at several temperatures and obtained the following data: K, s 1 T, K 3.94 x x x x Nitrogen monoxide, NO, reacts with ozone, O 3, to produce nitrogen dioxide, N, and oxygen, : NO + O 3 N + The experimentally determined rate law for this reaction is: Rate = k[o 3. Consider the following proposed mechanism for this reaction: Step 1: O 3 + O fast Step 2:NO + O N slow This proposed mechanism is NOT an acceptable possibility for this reaction. Briefly explain why this mechanism is not acceptable. ALSO, identify the rate-determining step and any intermediates in this proposed mechanism. 32. Using the information in the previous question, and your knowledge about reaction mechanisms, write an acceptable mechanism for the reaction described in the previous question 33. In many kinetics studies, the rate of the reaction is determined almost immediately after the reactants are mixed. The BEST reason for doing this is: (a) The reaction proceeds faster as time increases. (b) Intermediates are easier to detect. (c) The reaction proceeds slower as time increases. (d) Reverse reactions are avoided. (e) The concentrations of the reactions hasn't changed much. USE THE FOLLOWING DATA FOR THE NEXT THREE QUESTIONS. Nitric oxide gas reacts with chlorine gas according to the equation, 2 NO + Cl 2 2 NOCl The following data were obtained for this reaction: initial [NO initial [Cl 2 initial rate 0.50 M 0.50 M 1.19 mol/l hr 1.00 M 0.50 M 4.79 mol/l hr 1.00 M 1.00 M 9.59 mol/l hr Page No.: 7

8 34. Which of the following rate laws is consistent with these data? (a) Rate = k[no (b) Rate = k[no[cl 2 1/2 (c) Rate = k[no[cl 2 (d) Rate = k[no 2 [Cl 2 (e) Rate = k[no 2 [Cl What is the OVERALL order of the reaction of NO with Cl2? (a) 1 (b) 1.5 (c) 2 (d) 3 (e) What is the value of the rate constant for the reaction of NO with Cl2? (a) 2.38 (b) 3.35 (c) 4.76 (d) 9.52 (e) For the chemical reaction 2N 2NO +, a plot of [N vs. time gives a curved line, a plot of 1/[N gives a straight line with a positive slope, and a plot of ln[n vs. time gives a curved line. What is the order of reaction? (a) Zero order. (b) First order. (c) Second order. (d) A fractional order. (e) Impossible to determine from this data 38. Consider the following reaction: 2 NOBr 2NO + Br 2 The reaction is known to be second order with k = 0.80 L/mol s. If you start with a concentration of mol/l of NOBr, what will be its concentration after 22 seconds? (a) 2.0 x 10 9 mol/l (b) 5.4 x 10 2 mol/l (c) 3.4 x 10 2 mol/l (d) 8.7 x 10 1 mol/l (e) 1.8 x 10 1 mol/l 39. Carbon-14 decays by a first order process and has a half life of 5,730 years. Assuming some charcoal from a campfire 29,000 years old was found, what fraction of the original carbon-14 would remain today? (a) (b) (c) (d) 3.51 (e) In terms of the collision model of kinetics, which of the following factors BEST accounts for the fact that not all collisions result in a reaction? (a) The temperature of the system. (b) The orientation of the molecules at the moment of collision. (c) The energy with which the collisions occur. (d) The activation energy of the complex. (e) All of these factors are important. Page No.: 8

9 41. The reaction 2N + O 3 N 2 + obeys the rate law, Rate = K observed [N [O 3 Which of the following mechanisms is consistent with this experimental rate law? (a) N + N N 2 O 4 (fast equilibrium) N 2 O 4 + O 3 N 2 + (slow) (b) N + O 3 N (fast) N + N N 2 + 5/2 (slow) (c) N + O 3 NO 3 + (slow) NO 3 + N N 2 (fast) (d) N + N N 2 + (slow) N 2 + O 3 N 2 (fast) (e) None of these mechanisms are possible. 42. According to the collision model of kinetics, certain activation energy must be overcome before a reaction can proceed. Based on the data given below, what is a reasonable estimate of the activation energy for the decomposition of NOCl? 2NOCl 2NO + Cl 2 temperature (K) rate constant, k (L/mol s) x x x 10 1 (a) 1.00 x 10 2 J/K mol (b) 1.23 x 10 3 J/K mol (c) 1.05 x 10 5 J/K mol (d) 1.34 x 10 6 J/K mol (e) 1.22 x 10 8 J/K mol 43. The reaction rates for many spontaneous reactions are actually very slow. Which of the following is the best explanation for this observation? (a) Kp for the reaction = 0. (b) The activation energy is high. (c) The standard free energy change for the reaction is > 0. (d) These reactions are endothermic (e) The standard entropy change is < We observed a demonstration of the reaction: H2O2 -> H2O + 1/2 O2 to which I- was added. A large foaming mass of bubbles was formed. The following mechanism has been proposed for this reaction: H 2 + I H 2 O + IO (slow) H 2 O + IO H 2 O + 1/2 + I (fast) The function of the I in this reaction is to: (a) Raise the H of the products (b) Lower the G between reactants and products. (c) Increase the concentration of products (d) Lower the activation energy. (e) Raise the S of the reactants. Page No.: 9

10 45. In the lab, a chemist measured the rate constant, k, at 25 C for four different second-order reactions which were all performed in the same solvent. Which of the four reactions was the fastest reaction? (a) Reaction 1: k = 2.9 x 10 7 M 1 s 1 (b) Reaction 2: k = 4.2 x 10 5 M 1 s 1 (c) Reaction 3: k = 7.8 x 10 2 M 1 s 1 (d) Reaction 4: k = 3.6 x 10 6 M 1 s 1 (e) There is insufficient information to answer this question. 46. In lecture, we studied the decomposition of hydrogen peroxide, H 2, in aqueous solution to produce water, H 2 O, and oxygen gas, : 2H 2 (aq) 2 H 2 O (l) + If the average rate of disappearance of H 2 over a certain time interval is 6.80 x 10 5 M s 1, what is the average rate of appearance of during this same time interval? (a) 4.62 x 10 9 M s 1 (b) 3.40 x 10 5 M s 1 (c) 6.80 x 10 5 M s 1 (d) 1.36 x 10 4 M s 1 (e) There is insufficient information to answer this question. 47. In 1918, Fritz Haber, a German chemist, received the Nobel prize in chemistry for his work on developing a direct synthesis of ammonia on a commercial scale. Ammonia, which is used heavily by farmers as a fertilizer, is produced commercially by the Haber process: N 2 + 3H 2 2NH 3 Commercially, this reaction is performed at high temperature and in the presence of a heterogeneous catalyst (iron oxide) to increase the rate of the reaction. Which of the following "forms" of iron oxide would be the most effective for increasing the rate of the reaction? (a) 1 g of iron oxide pellets (10 small spherical pellets) (b) 1 g of iron oxide pellets (1 large spherical pellet) (c) 1 g of iron oxide powder (e) 1 g of iron oxide wire (f) 1 g of iron oxide sitting on a table outside of the reaction vessel 48. Aspirin, C 9 H 8 O 4, slowly decomposes at room temperature by reacting with water in the atmosphere to produce acetic acid, C 2 H 4, and 2-hydroxybenzoic acid, C 7 H 6 O 3 (this is why old bottles of aspirin often smell like vinegar): C 9 H 8 O 4 (aspirin) + H 2 O C 2 H 4 (acetic acid) + C 7 H 6 O 3 Consider the following initial concentration and initial rate data for this reaction: [Aspirin, M [H 2 O, M initial rate, M s x x x x Which of the following is the correct rate law for this reaction? (a) Rate = k[aspirin (b) Rate = k[aspirin[h 2 O (c) Rate = k[h 2 O (d) Rate = k[aspirin 2 [H 2 O (e) Rate = k[aspirin 2 [H 2 O 2 Page No.: 10

11 49. Using the "Method of Initial Rates" in kinetic studies is advantageous because it allows us to measure the initial rates for which of the following types of reactions? (a) spontaneous reactions (b) reactions with large activation energies (c) equilibrium reactions (d) reactions carried out at low temperature (e) all of the above 50. The radioactive element, thallium-201, is used medicinally as a radiotracer to study damage in heart tissue. If a patient is injected with a g dose of pure thallium-201, calculate the amount of time that would be required for the amount of thallium-201 in the patient's body to reach g. Thallium-201 decays by a first-order process with a half-life, t1/2 = 73.0 hours. (a) hours (b) 5.70 hours (c) 113 hours (d) 226 hours (e) 310 hours 51. Consider the gas-phase decomposition of hydrogen iodide, HI, to produce hydrogen, H 2, and iodine, I 2, 2 HI H 2 + I 2 and the following data which were obtained at a temperature of 282oC: time, h [HI 1/[HI ln [HI Which of the following statements is TRUE? (a) The decomposition of HI is a first-order process. (b) The decomposition of HI is a zero-order process. (c) A plot of ln [HI versus time is linear with a slope of -k. (d) A plot of 1/[HI versus time is linear with a slope of +k. (e) The half-life for this reaction is 180 hours. 52. For a certain reaction that follows second-order kinetics, A + B C + D + E the value of the rate constant, k, was measured at several different temperatures and the data are shown below: temperature, C K, M 1 s Calculate the value of the activation energy, Ea, for this reaction. (a) 13.9 kj (b) 27.4 kj (c) 52.0 kj (d) 97.8 kj Page No.: 11

12 53. Chlorine, Cl 2, reacts with hydrogen sulfide, H 2 S, in aqueous solution to produce solid sulfur and hydrogen chloride, HCl: Cl 2 (aq) + H 2 S (aq) S (s) + 2 HCl (aq) The rate law for this reaction is found to be: Rate = k[cl 2 [H 2 S. Which of the following is an acceptable possibility for the mechanism of this reaction? (a) Cl 2 Cl + + Cl slow Cl + H 2 S HCl + HS fast Cl + + HS HCl + S fast (b) Cl 2 + H 2 S HCl + Cl + + HS slow Cl + + HS HCl + S fast (c) Cl 2 Cl + Cl fast Cl + H 2 S HCl + HS fast HS + Cl HCl + S slow (d) All of these mechanisms are acceptable possibilities. (e) None of these mechanisms are acceptable possibilities. 54. A "diffusion-controlled" reaction is a reaction in which all collisions between the reacting species lead to products (these reactions are called "diffusion-controlled" because the rate is controlled only by how fast the reactant molecules can "diffuse" together). In aqueous solution at 25 C, the reaction of a strong acid, H 3 O +, with a strong base, OH, is an example of this type of reaction. The rate constant, k, for this reaction is 1.4 x M 1 s 1, H 3 O + (aq) + OH (aq) 2 H 2 O (l) Which of the following statements is most likely TRUE? (a) Increasing the temperature would have no effect on the rate of this reaction. (b) The activation energy for this reaction must be very large. (c) The rate of this reaction would be independent of the concentrations of H 3 O + and OH. (d) The rate constant for this reaction would be different if the reaction were carried out in a more viscous solvent than water. (e) None of the above. 55. Consider the following gas-phase reaction, Cl F 2 2 ClF 3 Write an expression that describes the relationship between the rate of disappearance of Cl 2, the rate of disappearance of F 2 and the rate of appearance of ClF In lecture, we used the reaction of permanganate ion, MnO 4, with oxalic acid, H 2 C 2 O 4, to study the effects of several factors upon the rate of this reaction (this was the solution that went from purple to colorless): 2 MnO 4 (aq) + 5H 2 C 2 O 4 (aq)+ 6H + (aq) 2 Mn 2+ (aq) + 10C + 8H 2 O(l) Write the general form of the differential rate law for this reaction. Page No.: 12

13 57. Consider the following reaction: 2 Cl (aq) + 2OH (aq) ClO 3 (aq) + Cl (aq) + H 2 O (l) and the following initial rate data: [Cl, mol/l [OH, mol/l initial rate, mol/l s x x x 10 1 (a) Determine the order of each reactant and write the differential rate law for this reaction. (b) Calculate the value of the rate constant,k, for this reaction. Be sure to include the appropriate units for the rate constant! (c) What is the overall order for this reaction? (d) Describe what would happen to the rate of this reaction if we tripled the concentration of Cl and doubled the concentration of OH. 58. Homes in certain parts of the country contain high levels of the radioactive isotope, radon-222. Radon-222 decays by first-order kinetics with a half-life of 3.82 days. Calculate how long it would take for 95% of a sample of radon-222 to decay. 59. Using the Collision Model of Chemical Kinetics, describe what requirements must be met for a reaction to occur between two colliding reactant molecules. 60. Consider the hydrogenation of ethylene, C 2 H 4, using the catalyst platinum oxide, Pt, to produce ethane, C 2 H 6 : C 2 H 4 + H 2 C 2 H 6 This is an example of heterogeneous catalysis which often involves gaseous reactants being adsorbed on the surface of a solid catalyst (i.e., Pt ). The rate of hydrogenation of ethylene on the surface of the Pt catalyst follows first-order kinetics for low concentrations of ethylene. However, as the concentration of ethylene is increased, the hydrogenation reaction becomes zero-order. Explain why the hydrogenation reaction in the presence of the heterogeneous catalyst Pt should be zero-order at high concentrations of ethylene. 61. Consider the following gas-phase reaction between hydrogen, H 2, and iodine, I 2, to produce hydrogen iodide, HI: H 2 + I 2 2 HI The values for the rate constant, K, for this reaction are 2.45 x 10 4 L/mol s at 302 C and L/mol s at 508 C. (a) Calculate the value of the activation energy for this reaction. (b) Calculate the value of the rate constant at 434 C. 62. Nitrogen dioxide, N reacts with carbon monoxide, CO, to form nitric oxide, NO, and carbon dioxide, C : N + CO NO + C The experimentally determined rate law for this reaction is: Rate = k[n 2. A proposed mechanism for this reaction is shown below. Step 1: N + N NO 3 + NO slow Step 2:NO 3 + CO N + C fast Page No.: 13

14 Determine whether this is a reasonable mechanism for this reaction and identify the ratedetermining step and any intermediates in this proposed mechanism. Be sure to explain your reasoning. 63. The following data were collected for the reaction between hydrogen (H 2 ) and nitric oxide (NO) at 700 C, 2H 2 + 2NO 2H 2 O + N 2 experiment [H 2, M [NO, M initial rate, M s x x x 10 7 What is the overall order of this reaction? (a) 0 (b) 1 (c) 2 (d) 3 (e) The reaction in which N forms a dimer, 2N N 2 O 4 has the following experimentally determined rate law: Rate = k[n 2 where k = 400 L mol 1 s 1 How long (in seconds) would it take for a sample of N with an initial concentration of 0.50 M to decrease to a concentration of M? USE THE FOLLOWING INFORMATION TO ANSWER THE NEXT TWO (2) QUESTIONS. 2H 2 (aq) 2H 2 O(l) + The experimentally determined rate law is: Rate = (0.056 s 1 )[H If the initial concentration of H 2 is 3.0 M, calculate the half-life (in seconds) for this reaction. 66. If the initial concentration of H 2 is 3.0 M, calculate the concentration of H 2 (in M) after 3.0 minutes. 67. Collision theory is used to explain how chemical species undergo a reaction. Using this theory and the kinetic molecular model, which of the following does NOT influence the rate of a chemical reaction? (a) The temperature of the system. (b) The geometry or orientation of the collision. (c) The velocity of the reactants at the point of collision. (d) The concentrations of the reactants. (e) All of the above influence the rate. 68. According to collision theory, which of the following is NOT a true statement concerning a catalyst? Page No.: 14

15 (a) A catalyst changes the temperature of a reaction. (b) The mechanism of a reaction will change when a catalyst is added. (c) A catalyst provides a different activation energy for a reaction. (e) A catalyst changes the speed of a reaction, but not the equilibrium constant. USE THE FOLLOWING INFORMATION TO ANSWER THE NEXT THREE (3) QUESTIONS. Mn n+ Tl + + 2Ce 4+ > Tl Ce 3+ The experimentally determined rate law is: Rate = k[ce 4+ [Mn 2+ with the following proposed mechanism involving ions of manganese: Step 1: Ce 4+ + Mn 2+ Ce 3+ + Mn 3+ Step 2: Ce 4+ + Mn 3+ Ce 3+ + Mn 4+ Step 3: Tl + + Mn 4+ Tl 3+ + Mn Which ion of manganese is the catalyst according to the information provided above? (a) Mn 4+ (b) Mn 3+ (c) Mn 2+ (d) All of the above. (e) There is not enough information provided to answer the question. 70. Which step in the proposed mechanism is the rate-limiting step? (a) Step 1 (b) Step 2 (c) Step 3 (d) All of the above. (e) There is not enough information provided to answer the question. 71. What is the overall order of the reaction? (a) 0 (b) 1 (c) 2 (d) 3 (e) Consider the following reaction in aqueous solution, I (aq) + OCl (aq) IO (aq) + Cl (aq) and the following initial concentration and initial rate data for this reaction, [I-, M [OCl-, M initial rate, M s x x x x 10 4 Which of the following is the correct rate law for this reaction? (a) Rate = k[i (b) Rate = k[ocl (c) Rate = k[i 2 (d) Rate = k[i 2 [OCl (e) Rate = k[i [OCl Page No.: 15

16 73. Which of the following CANNOT be affected/changed by a catalyst? (a) the mechanism of the reaction (b) the spontaneity of the reaction (c) the rate of the reaction (d) the activation energy of the reaction (e) all of the above can be affected/changed by a catalyst 74. Which of the following statements is TRUE? (a) Rate constants can have negative values. (b) The order of a reactant appearing in the rate law must always be a positive integer. (c) The order of each reactant appearing in the rate law is equal to the stoichiometric coefficient for that reactant in the overall balanced equation. (d) Reaction rates can have negative values. (e) The rate of disappearance of a reactant is generally not constant over time. 75. Consider the bromination of acetone, CH 3 COCH 3, in the presence of acid, CH 3 COCH 3 (aq) + Br 2 (aq) + H + (aq) CH 3 COCH 2 Br(aq) and the following initial rate data: [CH 3 COCH 3, M [Br 2, M [H +, M initial rate, M s x x x x x 10 4 Which of the following is the correct rate law for this reaction? (a) Rate = k[ch 3 COCH 3 [Br 2 [H + (b) Rate = k[ch 3 COCH 3 2 [Br 2 2 [H + (c) Rate = k[ch 3 COCH 3 [Br 2 (d) Rate = k[ch 3 COCH 3 [H + (e) Rate = k[ch 3 COCH The following data were obtained for the gas-phase decomposition of hydrogen iodide, HI, at 400 C, 2HI H 2 + I 2 time, sec [HI, M Calculate the concentration (in M) of HI after 1100 seconds. 77. The study of chemical kinetics can provide information about which of the following? (i) rates of chemical reactions (ii) reaction mechanisms (iii) factors that influence rates of chemical reactions Page No.: 16

17 (a) i only (b) i and ii (c) i and iii (d) ii and iii (e) i, ii and iii 78. The reaction in which N forms N 2 O 4 is second order in N, 2N N 2 O 4 Calculate the value of the rate constant for this reaction if it takes seconds for the initial concentration of N to decrease from 0.50 M to 0.25 M. 79. Consider the following reaction and experimental data, 2N N k, M 1 s 1 temperature, K Calculate the value (in kj/mol) of the activation energy for this reaction. 80. An INCREASE in which of the following will not produce an increase in the rate of a chemical reaction? (a) activation energy (b) temperature (c) reactant concentration (d) An increase in any of these will increase the rate. (e) Rate will not be affected by any of these 81. Which of the following would DECREASE the rate of a chemical reaction? (a) decreasing the activation energy (b) increasing the concentrations of the reactants (c) increasing the temperature (d) adding a catalyst (e) None of these will decrease the rate. 82. The rate of the reaction, S 2 + 4Cl 2 + 8OH 8Cl 2 + SO 4 + 4H 2 O is measured at a particular moment in time and it is found that - [S 2 / t=2.0 x 10 2 mol L 1 s 1. At this same moment in time, what is the rate (in mol L 1 s 1 ) at which Cl is being formed? 83. For the reaction, BH 4 (aq) + 4H 2 O(l) B(OH) 4 (aq) + 4H 2 the following data were obtained: Page No.: 17

18 time, h [BH 4, M Calculate the value of the rate constant for this reaction if the rate law is: Rate = k[bh Consider the following reaction at 25 C, 2A B + C where the initial concentration of A is 0.48 M. Assuming that this reaction is second-order in A, calculate how long (in seconds) it would take for the concentration of A to reach 0.24 M if A is initially decomposing (i.e., at t = 0) at a rate of 4.0 x 10 3 mol L 1 s Which of the following statements is TRUE? For a fast reaction, (a) the values of the rate constant and the half-life are both large. (b) the values of the rate constant and the half-life are both small. (c) the value of the rate constant is small and the value of the half-life is large. (d) the value of the rate constant is large and the value of the half-life is small. (e) it is not possible to determine the values of the rate constant or the half-life. 86. What is an appropriate rate law for the following reaction? 2NO + 2N (a) Rate = k(no) 2 (b) Rate = k(no) 2 ( ) (c) Rate = k(n ) 2 (d) Rate = K( ) (e) Cannot be determined from the information given. 87. The rate of a zero order reaction: (a) increases as reactant is consumed. (b) is independent of temperature. (c) depends on the concentration of the products. (d) decreases as reactant is consumed. (e) is independent of concentration of reactants or products. USE THE REACTION AND DATA BELOW TO ANSWER THE NEXT FOUR QUESTIONS. NO + O 3 N + initial [NO, M initial [O 3, M initial rate of reaction, M s 1 trial x x x 10 5 trial x x x 10 5 trial x x x 10 5 trial x x x 10 5 trial x x x 10 5 Page No.: 18

19 88. The experimental rate law for the reaction is: (a) Zero order in NO and first order in O 3 (b) First order in NO and first order in O 3. (c) Second order in NO and zero order in O 3 (d) Second order in NO and second order in O 3. (e) Independent of the concentration of O An acceptable value for the rate constant of this reaction is: (a) 6.7 x 10 5 (b) 7.6 (c) 3.6 x 10 6 (d) 1.8 x (e) 8.2 x You prepare another trial in which the initial (NO) is 3.15 x 10 6 mol/l and the initial (O 3 ) is 3.15 x 10 6 mol/l. You predict that the initial rate of reaction will be: (a) 3.11 x mol/l s (b) 7.54 x mol/l s (c) 1.98 x 10 1 mol/l s (d) 9.95 mol/l s (e) 3.6 x 10 5 mol/l s 91. A plot of (NO) vs. time would most closely resemble a: (a) straight line with a positive shape. (b) curve in which the (NO) decreases rapidly at first and then slows down until a minimum concentration is achieved. (c) straight line with a negative slope. (d) straight line with a slope of zero. (e) curve in which the (NO) increases rapidly at first and then slows down until a maximum concentration is achieved. 92. Which of the following expressions correctly describes the relationship between the rates at which N and Cl 2 are consumed in the reaction below? 2 N + Cl 2 2 N Cl (a) - (N ) t = (Cl 2 ) t (b) - (N ) t = 2 (Cl 2 ) t (c) - (N ) t = (Cl 2 ) t (d) - (N ) t = - (Cl 2 ) t (e) - (N ) t = 2 (Cl 2 ) t 93. The following reaction is first-order in N 2 O 3 and has a half-life of minutes: N 2 2N + 1/2 How long will it take for the concentration of N 2 to decrease from mol/l to mol/l? (a) 2.41 minutes (b) 3.60 minutes (c) 9.63 minutes (d) 14.3 minutes (e) 19.3 minutes Page No.: 19

20 USE THE REACTION AND DATA BELOW TO ANSWER THE NEXT THREE QUESTIONS. 2N 2 4N + [N 2, M time, s The rate law for this reaction is: (a) zero-order in N 2. (b) half-order in N 2. (c) first-order in N 2. (d) second-order in N 2. (e) third-order in N The half-life for this reaction is: (a) between 0 and 12 seconds. (b) between 12 and 20 seconds. (c) between 120 and 1,200 seconds. (d) between 1,200 and 12,000 seconds. (e) between 12,000 and 120,000 seconds. 96. The concentration of N 2 after 5,000 seconds is: (a) between and mol/l (b) between and 0.10 mol/l (c) between 0.10 and 0.4 mol/l (d) between 0.4 and 0.8 mol/l (e) between 0.8 and 1.2 mol/l 97. Results of a 1985 analysis of a piece of parchment indicated that 97.6% of the carbon-14 that was present initially still remained in the sample. With which of the following battles is this sample likely to be associated? The rate constant (k) for the first-order decay of carbon-14 is 1.21 x 10 4 /year. (a) Battle of Actium in 31 BC, Octavian defeating Mark Anthony. (b) Battle of Lugdunum (Lyon), 197 AD, Septimius Severus defeating Clodius Albinus. (c) Battle of Hastings, 1066 AD, William of Normandy defeating Harold II of England. (d) Battle of Yorktown, 1781 AD, the Marquis de Lafayette defeating Lord Cornwallis. (e) Battle of Waterloo, 1815 AD, the Duke of Wellington defeating Napoleon Bonaparte. 98. The following reaction and rate law have been experimentally determined: 2N + F 2 2N F, rate = k(n )(F 2 ) Which of the following mechanisms provides the best explanation of the experimental rate law? (a) 2N + F 2 2N F (one step) (b) N + F 2 N F + F (fast) N + F N F (slow) (c) F 2 2F (slow) (d) N + F 2 N F + F (slow) 2N + 2F 2N F (fast) N + F N F (fast) (e) None of these mechanisms are consistent with the experimental data. Page No.: 20

21 99. Nitrogen monoxide, NO, reacts with ozone, O 3, to produce nitrogen dioxide, N, and oxygen,, NO + O 3 N + Consider the following mechanism for this reaction: (1) O 3 + O slow (2) NO + O N fast Which one of the following rate laws would be consistent with the mechanism proposed above? (a) Rate = k[no[o[o 3 (b) Rate = k[no (c) Rate = k[no[o 3 (d) Rate = k[no[o (e) Rate = k[o For the mechanism described in the previous question, which species are intermediates? (a) O and NO (b) NO and O 3 (c) NO only (d) O only (e) N only 101. Nitrogen monoxide, NO, reacts with hydrogen, H 2, to produce nitrogen, N 2, and water, H 2 O, 2NO + 2H 2 N 2 + 2H 2 O Consider the following mechanism for this reaction: (1) 2NO N 2 fast (2) N 2 + H 2 N 2 O + H 2 O slow (3) N 2 O + H 2 N 2 + H 2 O fast Which one of the following rate laws would be consistent with the mechanism proposed above? (a) Rate = k[no 2 [H 2 2 (b) Rate = k[no[h 2 (c) Rate = k[h 2 2 [N 2 (d) Rate = k[no 2 [H 2 (e) Rate = k[no A particular chemical reaction involves a single reactant. What is the order of the reaction if the rate increases by a factor of eight when the concentration of the reactant is doubled? (a) zero order (b) first order (c) second order (d) third order (e) fourth order 103. Consider the reaction, 2N 2 4N + and the following experimental data: [N 2, M rate, M s x x x 10 4 What is the value of the rate constant, k, for this reaction? Page No.: 21

22 104. Hydrogen sulfide (H 2 S) reacts with oxygen gas according to the following equation: 2H 2 S + 2S(s) + 2H 2 O(l) Which of the following statements is TRUE? (a) The reaction is 3rd order overall. (b) The rate law is given by rate = k[h 2 S 2 [. (c) The reaction is 2nd order overall. (d) The rate law is given by rate = k[h 2 S[. (e) The rate law cannot be determined from the information given The following data were collected for the decay of H radicals: time, s [H, molecules cm 3 ln [H 1/[H x x x x x x x x x x These data indicate that the decay of H occurs by a second order process BECAUSE: (a) A plot of 1/[H versus time is linear with a slope of positive k. (b) The half-life of the reaction is 2 seconds. (c) A plot of ln[h versus time is linear with a slope of positive k. (d) The rate of the reaction increases with time. (e) The plots of 1/[H and ln[h versus time are both linear Gaseous N 2 decomposes according to the following equation: N 2 2N + 1/2 The experimental rate law is - [N 2 / t = k[n 2. At a certain temperature the rate constant is k = 5.0 x 10 4 /second. In how many seconds will the concentration of N 2 decrease to one-tenth of its initial value? (a) 2.0 x 10 3 seconds (b) 4.6 x 10 3 seconds (c) 2.1 x 10 2 seconds (d) 1.4 x 10 3 seconds (e) 5.0 x 10 3 seconds 107. The gas phase reaction of nitrogen dioxide and carbon monoxide given below was found by experiment to be second-order with respect to N and zero-order with respect to CO below 25 C. N + CO NO + C Which of the following mechanisms is consistent with these data? (a) N + 2CO N + 2C, (fast) (b) N + 2CO N + 2CO, (slow) N + N 2NO, (slow) N + N 2NO, (fast) (c) N + N NO 3 + NO, (fast) (d) N + N NO 3 + NO, (slow) NO 3 + CO N + C, (slow) NO 3 + CO N + C, (fast) Page No.: 22

23 108. With respect to the figure below, which choice correctly identifies all of the numbered positions? #1 #2 #3 #4 (a) catalyst catalyst activated complex product (b) reactants activated complex intermediate product (c) reactants activated complex catalyst product (d) reactants intermediate activated complex product (e) reactants intermediate activated complex catalyst 109. According to collision theory, not all collisions between molecules lead to reaction. Which of the following statements provide reasons why this is so? (i) The total energy of the two colliding molecules is less than some minimum amount of energy. (ii) Molecules cannot react with each other unless a catalyst is present. (iii) Molecules that are improperly oriented during collision will not react. (iv) Molecules in different states of matter cannot react with each other. (a) 1 and 2 (b) 1 and 3 (c) 2 and 3 (d) 1 and 4 (e) 3 and What potential problem, discussed in lecture, can be avoided by using the "Method of Initial Rates" for kinetic studies? (a) Endothermic reactions. (b) Reactions performed at low temperature. (c) Equilibrium reactions. (d) Non-spontaneous reactions. (e) Reactions with large activation energies 111. For the reaction of ethyl bromide, CH 3 CH 2 Br, with hydroxide ion, OH, to produce ethyl alcohol, CH 3 CH 2 OH, and bromide ion, Br, CH 3 CH 2 Br + OH CH 3 CH 2 OH + Br the form of the rate law is: Rate = k[ch 3 CH 2 Br[OH Which of the following are the correct units for the rate constant, k? (a) s 1 (b) mol L 1 s 1 (c) L mol 1 s 1 (d) L2 mol 2 s 1 (e) L 3 mol 3 s 1 Page No.: 23

24 112. Consider a third-order reaction which involves a single reactant. If the concentration of the reactant is doubled, the rate of the reaction will: (a) increase by a factor of two. (b) increase by a factor of four. (c) increase by a factor of eight. (d) increase by a factor of nine. (e) remain the same In aqueous solution, the permanganate ion, MnO 4, reacts with nitrous acid, HN, as follows: 2MnO 4 (aq) + 5HN (aq) + H + (aq) 2Mn 2+ (aq) + 5NO 3 (aq) + 3H 2 O (l) Calculate the rate (in M s 1 ) at which the HN concentration is decreasing if the MnO 4 is decreasing at a rate of M s In lecture, we used the reaction of permanganate ion, MnO 4, with oxalic acid, H 2 C 2 O 4, to study the effects of various changes upon the rate of this reaction (these were the solutions that went from purple to colorless): 2MnO 4 (aq) + 5H 2 C 2 O 4 (aq) + 6 H + (aq) 2Mn 2+ (aq) + 10C + 8H 2 O (l) Consider the following initial concentration and initial rate data for this reaction: [MnO 4, M [H 2 C 2 O 4, M [H +, M initial rate, M s x x x x 10 3 Calculate the value of the rate constant, k, for this reaction Laughing gas, N 2 O, can be prepared from H 2 and NO: H 2 + 2NO N 2 O + H 2 O A study of initial concentration versus initial rate at a certain temperature yields the following data for this reaction: [H 2, M [NO, M initial rate, M s x x x x 10 6 Calculate the value of the rate constant for this reaction The rate constant of a first-order reaction is 4.60 x 10 4 /s at 350 C. If the activation energy is 104 kj/mol, at what temperature will the rate constant be 8.80 x 10 4 /s? (a) 669 C (b) 402 C (c) 371 C (d) 350 C (e) 183 C Page No.: 24

25 117. Consider the following reaction at 500 K, 2C 4 H 6 C 8 H 12 and the experimental data shown below, [C 4 H 6, M rate, M s x x x x x x x x 10 8 The order of the reaction with respect to C 4 H 6 is: (a) half order. (b) first order. (c) second order. (d) third order. (e) fourth order At 350 K, a particular second-order reaction, consisting of a single reactant, A, has a rate constant equal to 4.5 x 10 3 M 1 s 1. If the initial concentration of A is 0.80 M, how many half-lives are required for the concentration of A to become equal to 0.10 M? (a) 1 half-life (b) 2 half-lives (c) 3 half-lives (d) 4 half-lives (e) 5 half-lives 119. The rate of the reaction N + CO NO + C depends only on the concentration of N below 225 C. At a temperature below 225 C, the following data were obtained. time, s [N, M x x x x x Calculate the value of the rate constant for this reaction. Page No.: 25

26 A n s w e r s a x e 5. a 6. a x e 9. b 10. c 11. d 12. d a 15. c 16. a 17. d 18. b 19. a 20. a 21. c 22. c 23. b x (a) FALSE (b) TRUE (c) FALSE (d) FALSE 29. -d[cl -d[oh -d[clo = = 3 d[clo = 2 d[h = 2 O 2dt 2dt dt dt dt kj/mol 31. This mechanism is not acceptable because the predicted rate law for the rate-determining step (Step 2) does not agree with that determined experimentally: Rate (exp) = k[o 3 Rate (Step 2) = k[no[o This mechanism does, however, satisfy the first test. The steps do sum to give the overall balanced reaction. There is only one intermediate here, O. 32. If we use the same mechanism as in question 9, but make Step 1 slow and Step 2 fast, both tests are satisfied: Step 1: O 3 + O slow Step 2: NO + O N fast 33. d 34. d 35. d 36. d 37. c 38. c 39. b 40. e 41. c 42. c 43. b 44. d 45. e 46. b 47. c 48. b 49. e 50. e 51. d 52. c 53. b 54. d 55. -d[cl 2 /dt = -1/3 d[f 2 /dt = +1/2 d[clf 3 /dt 56. Rate = k[mno 4 m [H 2 C 2 O 4 n [H + p Page No.: 26

27 57. (a) Rate = k[cl 2 [OH (b) k(avg) = 2.31 x 10 2 L 2 /mol 2 s (c) 3 (d) The rate would increase by a factor of days. 59. (a) The reactants must have the proper orientation when they collide. (b) The reactants must have sufficient kinetic energy when they collide. 60. At low concentrations of ethylene, the rate of the reaction depends on the concentration (first order). At higher concentrations of ethylene, the rate no longer depends on the concentration (zero order). Since this reaction occurs on the SURFACE of the catalyst, once we have added enough ethylene to completely "cover" the surface of the catalyst, additional ethylene will have no effect (no available surface for the added ethylene). It thus becomes a zero order reaction at this "saturation" point. 61. (a) 150 kj/mol. (b) 8.58 x 10 2 L/mol s. 62. Test #1: Do steps sum to give overall balanced reaction? Here, they do. Test #2: Does rate law proposed for this mechanism agree, in form, with the experimentally determined rate law? The rate law based on the rate-determining step (the first step) is: Rate = k[n [N which is the same as: Rate = k[n 2. This is the same form as the experimental rate law: Rate = k[n 2. The mechanism is, therefore, an acceptable possibility. Finally, NO 3 is the only intermediate in this mechanism. 63. d x e 68. a 69. c 70. a 71. c 72. e 73. b 74. e 75. d e a 81. e x 10 3 hr x d 86. e 87. e 88. b 89. c 90. e 91. b 92. e 93. d 94. c 95. c 96. c 97. d 98. d 99. e 100. d 101. d 102. d x e 105. a 106. b 107. d 108. d 109. b 110. c 111. c 112. c x x x c 117. c 118. c x 10 4 Page No.: 27