Homework 12-solutions

3 a = 1 k = 1 . 5 × 10 7 s − 1 The concentration of A falls by a factor of 8, so the final concentration is 1 8 (1 . 06 × 10 − 6 M) = 1 . 325 × 10 − 7 M ln [A] 0 [A] = akt ln parenleftbigg 1 . 06 × 10 − 6 1 . 325 × 10 − 7 parenrightbigg = 1 (1 . 56 × 10 7 ) t 2 . 08 = 1 . 56 × 10 7 t t = 2 . 08 1 . 56 × 10 7 = 1 . 33 × 10 − 7 seconds 006 1.0points NOTE: There is no need to know the chemical equation for the process. The decomposition of cyclobutane is a first- order reaction. At a certain temperature, the half-life for this reaction is 137 seconds. What fraction of a sample of cyclobutane would be left after 685 seconds at this temperature? 1. 0.125 2. 0.0625 3. 0.0312 correct 4. 0.0156 5. 0.25 Explanation: t 1 / 2 = 137 s t = 685 s a = 1 k = ln 2 t 1 / 2 ln [cyclobutane] 0 [cyclobutane] t = akt = at ln 2 t 1 / 2 = (685 s) ln 2 137 s = 3 . 4657 [cyclobutane] 0 [cyclobutane] t = e 3 . 4657 = 32 [cyclobutane] t [cyclobutane] 0 = 1 32 = 0 . 03125 007 1.0points A reaction A → products is observed to obey first-order kinetics. Which of the following plots should give a straight line? 1. ln[A] vs 1 k 2. [A] vs 1 t 3. ln[A] vs k 4. [A] vs 1 k 5. [A] vs t 6. ln[A] vs t correct 7. [A] vs k 8. ln[A] vs 1 t Explanation: The first order integrated rate equation is ln parenleftbigg [A] 0 [A] parenrightbigg = akt ln[A] 0 − ln[A] = akt ln[A] = − akt + ln[A] 0 Since a , k , and ln[A] 0 are constants, this equa- tion is in the form y = mx + b , where y = ln [A] and x = t . A straight line is produced by y = mx + b . 008(part1of2)1.0points

6 H 2 O 2 (aq) + IO − (aq) → H 2 O( ℓ ) + O 2 (g) + I − (aq) with rate constant k 2 It is further proposed that k 1 ≫ k 2 . Which of the following statements is false about this mechanism? 1. The overall reaction is 2H 2 O 2 (aq) → 2H 2 O( ℓ ) + O 2 (g). 2. H 2 O 2 is a reactant. 3. I − and IO − are both intermediates in the reaction. correct 4. I − (aq) is a catalyst in this reaction. Explanation: The sum of the mechanisms gives the over- all reaction. Both I − and IO − are cancelled out when the two steps are added, leaving 2 H 2 O 2 (aq) → 2 H 2 O( ℓ ) + O 2 (g) as the overall reaction. H 2 O 2 is thus a reac- tant in this reaction, while I − and IO − are not. IO − is an intermediate in the reaction as it is generated as a product in the first step but consumed in the second. It is not ob- served in the overall reaction, nor is it added to the reaction mix to act as a catalyst. I − , on the other hand, is a catalyst (not an in- termediate) as it is consumed as a reactant in the first step but regenerated in the second step, so that it is not consumed in the overall reaction. However, it would be added to the reaction mixture in order to act as a catalyst. 017 1.0points The reaction A + 3 B → C + 2 D has a rate constant k = 1 . 0 × 10 − 5 s − 1 at 27 ◦ C. If the activation energy for the reaction is 20,000 cal/mol, what is the value of the rate constant at 0 ◦ C? 1. None of these 2. 3 . 6 × 10 − 7 correct 3. 3 . 3 × 10 − 5 4. 2 . 8 × 10 − 4 5. 3 . 0 × 10 − 6 Explanation: k = 1 . 0 × 10 − 5 s − 1 E a = 20 , 000 cal / mol T 1 = 27 ◦ C = 300 K T 2 = 0 ◦ C = 273 K Use the combined Arrenius equation, ln k 2 k 1 = parenleftbigg E a R parenrightbigg parenleftbigg 1 T 1 − 1 T 2 parenrightbigg k 2 k 1 = e ( E a /R )(1 /T 1 − 1 /T 2 ) k 2 = k 1 e ( E a /R )(1 /T 1 − 1 /T 2 ) k 2 = 10 − 5 exp bracketleftBig parenleftbigg 20 , 000 1 . 987 parenrightbigg × parenleftbigg 1 300 K − 1 273 K parenrightbigg bracketrightBig = 3 . 6 × 10 − 7 AlternateSolution: ln k 2 k 1 = E a R parenleftbigg 1 T 1 − 1 T 2 parenrightbigg ln k 2 − ln k 1 = E a R parenleftbigg 1 T 1 − 1 T 2 parenrightbigg ln k 2 = E a R parenleftbigg 1 T 1 − 1 T 2 parenrightbigg + ln k 1 = parenleftbigg 20000 cal / mol 1 . 987 cal / mol · K parenrightbigg × parenleftbigg 1 300 K − 1 273 K parenrightbigg + ln ( 1 . 0 × 10 − 5 ) ln k 2 = − 3 . 32 + ( − 11 . 5) = − 14 . 82 k 2 = 3 . 6 × 10 − 7 018 1.0points What is the activation energy for a reaction which proceeds 50 times as fast at 400 K as it does at 300 K? Correct answer: 39030 . 3 J / mol rxn.