Chemistry 106, Chapter 11 Exercises

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Chemistry 106, Chapter 11 Exercises Reaction Rate 1. Consider the combustion of ethane: C 2 H 6 (g) + 7O 2 (g) 4CO 2 (g) + 6H 2 O(g) If the ethane is burning at the rate of 0.20 M/s, at what rates are CO 2 and H 2 O being formed? Ans. CO 2, 0.8 M/s; H 2 O, 1.2 M/s 2. For the reaction 5Br - (aq) + BrO 3 - (aq) + 6H + (aq) 3Br 2 (aq) + 3H 2 O it was found that at a particular instant bromine was being formed at the rate of 0.039 M/s. At that instant, at what rate is a. water being formed? Ans. 0.039 M/s b. bromide ion being oxidized? Ans. 0.065 M/s c. H + being consumed? Ans. 0.078 M/s 3. The order of a reaction with respect to some reagent is determined to be 0 order. Determine the effect on the rate if the concentration of that reactant is: a. doubled b. tripled. 4. The order of a reaction with respect to some reagent is determined to be 1st order. Determine the effect on the rate if the concentration of that reactant is: a. doubled b. tripled. 5. The order of a reaction with respect to some reagent is determined to be 2nd order. Determine the effect on the rate if the concentration of that reactant is: a. doubled b. tripled c. quadrupled. Answers for 3-5: 3 no affect for both, 4a. doubled, 4b. tripled, 5a. rate would be 4 times greater, 5b. 9 times, 5c. 16 times

Rate Expressions 6. Complete the following table for the reaction below. 2R(g) + 3S(g) products The reaction is first order with respect to R and second with respect to S. [R] [S] k L 2 /(mol 2. min) Rate a 0.200 0.200 1.49 b 0.633 0.42 0.833 c 0.100 0.298 0.162 d 0.0500 0.0911 0.00624 Ans. a. 0.0119 b. 4.9 L c. 2.33 M d. 15.0 L 2 /(mol 2. min) 7. Complete the following table for the following reaction. The reaction is 1 st order in both X and Y. 2X(g) + Y(g) products [X] [Y] k L/(mol.min) Rate M/hr a 0.100 0.400 1.89 b 0.600 0.884 0.159 c 0.025 13.4 0.0479 d 0.592 0.233 0.00112 Ans. a. 0.0756 M/hr b. 0.300 M c. 0.143 M d. 8.12 x 10-3 L/(mol. hr) 8. For the reaction A products The following data were obtained. Rate () 0.0167 0.0107 0.00601 0.00267 [A] 0.100 0.0800 0.0600 0.0400 a. Write the rate expression for the reaction. Ans. rate = k[a] 2 b. Calculate k for the experiment. Ans. k = 1.67 L/(mol. min)

9. For the reaction involving the decomposition of Y, the following data were obtained. Rate () 0.288 0.245 0.202 0.158 [Y] 0.200 0.170 0.140 0.110 a. Write the rate expression for the reaction. Ans. rate = k[y] b. Calculate k for the experiment. Ans. k = 1.44 min -1 10. For the reaction S 2 O 8 2- (aq) + 3I - (aq) 2SO 4 2- (aq) + 3I - (aq) the following data were obtained at a certain temperature. Expt. [S 2 O 2-8 ] [I - ] Initial Rate 1 0.0200 0.0155 1.15 x 10-4 2 0.0250 0.0200 1.85 x 10-4 3 0.0300 0.0200 2.22 x 10-4 4 0.0300 0.0275 3.06 x 10-4 a. Write the rate expression for the reaction. Ans. rate = k[s 2 O 8 2- ][I - ] b. Calculate k. Ans. 0.371 L/(mol. min) c. When [S 2 O 8 2- ] = 0.105 M and [I - ] = 0.0875 M, what is the rate of the reaction. Ans. 3.41 x 10-3 11. For the reaction BF 3 (g) + NH 3 (g) BF 3 NH 3 (g) the following data were obtained at a certain temperature. Expt. [BF 3 ] [NH 3 ] Initial Rate 1 0.100 0.100 0.0341 2 0.200 0.233 0.159 3 0.200 0.0750 0.0512 4 0.300 0.100 0.102 a. Write the rate expression for the reaction. Ans. rate = k[bf 3 ][NH 3 ] b. Calculate k. Ans. 3.41 L/(mol. min) c. When [BF 3 ] = 0.553 M and [NH 3 ] = 0.300 M, what is the rate of the reaction. Ans. 0.566

12. Hydrogen bromide is a highly reactive and corrosive gas used mainly as a catalyst for organic reactions. It is produced by reacting hydrogen and bromine gases together. H 2 (g) + Br 2 (g) 2HBr The rate is followed by measuring the intensity of the orange color of the bromine gas. The following data are obtained. Expt. [H 2 ] [Br 2 ] Initial Rate M/s 1 0.100 0.100 4.74 x 10-3 2 0.100 0.200 6.71 x 10-3 3 0.250 0.200 1.68 x 10-2 a. Write the rate expression for the reaction. Ans. rate = k[h 2 ][Br 2 ] 1/2 b. Calculate k. Ans. 0.150 L 1/2 /(mol 1/2. s) c. When [H 2 ] = 0.455 M and [Br 2 ] = 0.215 M, what is the rate of the reaction? Ans. 0.0316 M/s 13. For the reaction 6I - (aq) + BrO 3 - (aq) + 6H + (aq) 3I 2 (aq) + Br - (aq) + 3H 2 O the rate was followed by measuring the appearance of I 2. The following data were obtained. [I - ] [BrO - 3 ] [H + ] Initial Rate (M/s) 0.0020 0.0080 0.020 8.89 X 10-5 0.0040 0.0080 0.020 1.78 X 10-4 0.0020 0.0160 0.020 1.78 X 10-4 0.0020 0.0080 0.040 3.56 X 10-4 0.0015 0.0040 0.030 7.51 X 10-5 a. Write the rate expression. Ans. rate = k[i - ][BrO 3 - ][H + ] 2 b. Find k. Ans. 1.4 x 10 4 L 3 /(mol 3. s) c. What is [H + ] when the rate is 5.00 x 10-4 M/s and [I - ] = 0.0075 M and [BrO 3 - ] = 0.015 M? Ans. 1.8 x 10-2 M 14. In dilute acid, sucrose (C 12 H 22 O 11 ) decomposes to glucose and fructose. The following data were obtained for the decomposition of sucrose. Time (min) [C 12 H 22 O 11 ] 0 0.368 20 0.333 60 0.287 120 0.235 160 0.208 Write the rate expression for the reaction. Ans. rate = k[c 12 H 22 O 11 ] 2

15. Nitrosyl bromide (NOBr) decomposes to nitrogen monoxide and bromine. Use the following data to obtain a rate expression for this reaction. Time (s) 0 6 12 18 24 [NOBr] 0.0286 0.0253 0.0229 0.0208 0.0190 Ans. rate = k[nobr] 2 Reactant Concentration and Time Relationship for First Order Reactions 16. The first order rate constant for the decomposition of a certain hormone in water at 25 o C is 3.42 x 10-4 day -1. a. If a 0.0200 M solution of the hormone is stored at 25 o C for two months, what will its concentration be at the end of that period? Ans. 0.0196 M b. How long will it take for the concentration of the solution to drop from 0.0200 M to 0.00350 M? Ans. 5.09 x 10 3 days (~14 yrs) c. What is the half-life for this hormone? Ans. 2.03 x 10 3 days (5.5 yrs) 17. In the first order decomposition of acetone at 500 o C, CH 3 -CO-CH 3 (g) products it was found that the concentration was 0.0300 M after 200 min and 0.0200 M after 400 min. a. Find the rate constant. Ans. 2.03 x 10-3 min -1 b. Find the half life. Ans. 342 min c. Find the initial concentration. Ans. 0.0450 M 18. The decomposition of dimethyl ether (CH 3 OCH 3 ) to methane, carbon monoxide, and hydrogen gases it was found to be first order. At 500 o C, a 150.0 mg sample of dimethyl ether is reduced to 43.2 mg after three quarters of an hour. a. Find the rate constant. Ans. 1.65/hr b. Find the half life at 500 o C. Ans. 0.420 hr c. How long will it take to decompose 95 % of the dimethyl ether? Ans. 1.8 hr 19. The first order rate constant for the decomposition of a certain drug at 25 o C is 0.215 month -1. a. If 10.0 g of the drug is stored at 25 o C for one year, how many grams of the drug will remain at the end of the year? Ans. 0.758 g b. What is the half life of the drug? Ans. 3.22 months c. How long will it take to decompose 65 % of the drug? Ans. 4.9 months 20. The decomposition of phosphine, PH 3, to P 4 (g) and H 2 (g) is first order. Its rate constant at a certain temperature is 1.1 min -1. a. What is the half-life in seconds? Ans. 38 s b. What percentage of phosphine is decomposed after 1.25 min? Ans. 75 % c. How long will it take to decompose one fifth of the phosphine? Ans. 0.20 min

21. The decomposition of ethane, C 2 H 6, is a first order reaction. It is found that it takes 212 s to decompose 0.00839 M C 2 H 6 to 0.00768 M. a. What is the rate constant for the reaction? Ans. 4.17 x 10-4 s -1 b. What is the rate of decomposition (in M/hr) when [C 2 H 6 ] = 0.00422 M? Ans. 6.34 x 10-3 M/hr c. How long (in minutes) will it take to decompose C 2 H 6 so that 27 % remains? Ans. 52 min d. What percentage of C 2 H 6 is decomposed after 22 min? Ans. 42% 22. Copper-64 is one of the metals used to study brain activity. Its decay constant is 0.0546 hr -1. If a solution containing 5.00 mg of Cu-64 is used, how many milligrams of Cu-64 remain after eight hours? Ans. 3.23 mg 23. Iodine-131 is used to treat tumors in the thyroid. Its first order half-life is 8.1 days. If a patient is given a sample containing 5.00 mg of I-131, how long will it take for 25% of the isotope to remain in her system? Ans. 16 days Rate Expressions from Reaction Mechanisms 24. Reaction: H 2 + I 2 2HI Mechanism: I 2 2I (fast) H 2 + I + I 2HI (slow) Determine the rate expression. Ans. rate = k[h 2 ][I 2 ] 25. Reaction: 2H 2 + 2NO N 2 + 2H 2 O Mechanism: 2NO N 2 O 2 (fast) N 2 O 2 + H 2 H 2 O + N 2 O (slow) N 2 O + H 2 N 2 + H 2 O (fast) Determine the rate expression. Ans. rate = k[no] 2 [H 2 ] 26. Reaction: CO + NO 2 CO 2 + NO Mechanism: 2NO 2 2NO + O 2 (slow) O 2 + 2CO 2CO 2 (fast) Determine the rate expression. Ans. rate = k[no 2 ] 2

27. For the reaction below there are two possible mechanisms. 2NO + O 2 2NO 2 Mechanism a: NO + O 2 NO 3 (fast) NO 3 + NO 2NO 2 (slow) Mechanism b: NO + NO N 2 O 2 (fast) N 2 O 2 + O 2 2NO 2 (slow) Determine the rate expression for each. Ans. a. rate = k[no] 2 [O 2 ], b. rate = k[no] 2 [O 2 ]

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