AP Chemistry: Kinetics Practice Problems

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Esmond Valentine Lawson
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1 AP Chemitr: Kinetic Practice Problem Direction: Write our anwer to the following quetion in the pace provided. For problem olving, how all of our work. Make ure that our anwer how proper unit, notation, and ignificant digit. Do not ue a calculator on the multiple choice quetion.. Three major method ued to increae the rate of a reaction are adding a catalt, increaing the temperature, and increaing the concentration of a reactant. From the perpective of colliion theor, eplain how each of thee method increae the reaction rate. a. adding a catalt Adding a uitable catalt lower the energ demand of the reaction (the activation energ) b providing a le demanding pathwa. It doe thi b forming a different activated comple with a lower activation energ. b. increaing the temperature Increaing the temperature increae the average kinetic energ of the molecule. However, what i mot important here i that the fraction of molecule that have the energ necear to react (the activation energ) i increaed. c. increaing the concentration of the reactant Increaing the concentration of a reactant increae the probabilit of colliion, and therefore increae the poibilit of reaction, for the particle mut collide to react. Note that not all colliion reult in ucceful reaction.. Wh do large crtal of ugar burn more lowl than finel ground ugar? The rate of combution i proportional to the urface area of ugar epoed to ogen. Smaller crtal have more urface area and burn fater.. How do homogeneou catalt and heterogeneou catalt differ? A homogeneou catalt i a catalt that eit in the ame phae (liquid or ga) a the reactant. A heterogeneou catalt, on the other hand, i a catalt that eit in a different phae form the reactant. 4. Epre the rate of reaction in term of the rate of change of each reactant and each product in the following. a. ClO - (aq) ClO - (aq) + Cl - (aq) [ClO [ClO [Cl rate of reaction = - = = t t t b. SO (g) + O (g) SO (g) [SO [O [SO rate of reaction = - = = t t t c. C H 4 (g) + Br (g) C H 4 Br (g) [CH 4 [Br [CH 4Br rate of reaction = - = = t t t 5. In the Haber proce for the production of ammonia, N (g) + H (g) NH (g) What i the relationhip between the rate of production of ammonia and the rate of conumption of hdrogen? [H [NH rate of reaction = = t t 6. The rate contant A. alwa how an eponential increae with the Kelvin or abolute temperature. B. increae with increaing concentration. C. uuall increae with increaed preure for gae. D. never change (it i a contant). E. i the ame for a given reaction at the ame Kelvin or abolute temperature. Anwer: (E) In thi quetion be ure to note that it i the rate contant that i involved. Refer to the Arrheniu equation for the pecific relationhip.

2 7. What are the unit for each of the following if the concentration are epreed in mole per liter and the time in econd? a. rate of a chemical reaction The unit for rate are alwa mol/l. b. rate contant for a zero-order rate law Rate=k; k mut have unit of mol/l c. rate contant for a firt-order rate law Rate=k[A, k mut have unit of - d. rate contant for a econd-order rate law Rate=k[A, k mut have unit of L/mol 8. The reaction I - (aq) + S O 8 - (aq) I (aq) + SO 4 - (aq) wa tudied at 5 C. The following reult were obtained where [S O Rate = - t 8 [I - 0 (mol/l) [S O (mol/l) Initial Rate (mol/l ) a. Determine the rate law. Rate = k[i - [S O - 8 Compare eperiment and. rate rate rate rate k[ I [S O8 = - k[ I [S O k( ) ( ) =, 0.5 = 0.5, = k( ) ( ) - 8 k[ I [S O8 = - k[ I [S O Rate = k[i - [S O 8 - k( ) ( 0. 00) =, 0.5 = 0.5, = k( ) ( ) b. Calculate a value for the rate contant for each eperiment and an average value for the rate contant..5 0 mol F mol mol - L Eperiment = = k =.9 0 L H G 0 I L K J F H G I k L K J, mol mol F mol mol - L Eperiment = = k =.9 0 L H G 0 I L K J F H G I k L K J, mol mol F mol mol - L Eperiment = = k =.9 0 L H G 0 I L K J F H G I k L K J, mol mol F mol mol - L Eperiment 4 = = k =.9 0 L H G 0 I L K J F H G I k L K J, mol mol F mol mol - L Eperiment 5 = = k =.9 0 L H G 0 I L K J F H G I k L K J, mol K mean = L/mol

3 9. The following rate data were obtained at 5 C for the following reaction. What i the rate law epreion? What i the overall order of the reaction? A + B C Eperiment [A 0 (mol/l) [B 0 (mol/l) Initial Rate (mol/l ) Rate = k[a [B Eperiment and : [A i contant = 0.0 M [B increae b a factor of but the rate of reaction doe NOT change Therefore [B doe not affect the rate Therefore the order of reaction with repect to B = = 0 Eperiment and : [B i contant = 0.0 M [A decreae b a factor of and the rate of the reaction decreae b a factor of Therefore the reaction i firt order with repect to A = = Rate law epreion: Rate = k[a [B 0 = k[a The overall order of reaction i (+0) = 0. What i the rate law epreion for the following reaction, given the data below? What i the overall order of the reaction? A + B + C D + E Eperiment [A 0 (mol/l) [B 0 (mol/l) [C 0 (mol/l) Initial Rate (mol/l min) Rate = k[a [B [C z Eperiment and : Eperiment and : [A, [B are contant, [C increae b a factor of but the rate of the reaction doe NOT change. Therefore the reaction [C doe not affect the rate Therefore the order of reaction with repect to C = z = 0 and we can ignore thi data. [A i contant = 0.0 M [B increae b a factor of The rate increae b a factor of 9 Therefore the reaction i econd order with repect to B = = There are no eperiment where [A varie and [B remain contant, o we will have to evaluate the order of the reaction with repect to A mathematicall. rate rate A B = k [ [ k[ A [ B - - = ( 0. 5) ( ) = k ( 0. ) ( 0. 6) k( 0. ) ( 0. ) 4 =, therefore the reaction i firt order with repect to A. The rate law epreion i Rate = k[a[b The overall order i + = = F H G I K J

4 . Ue the rate law determined in quetion 9 to anwer the following quetion. What would happen to the rate of the reaction if the concentration of A wa halved and the concentration of B wa tripled during a reaction? Aume the initial concentration of A and B were both M. Therefore Rate = k[a[b = k()() =k After the change in the reaction, Rate = k(/)() = 9/ k Therefore the rate of the reaction would increae b a factor of 9/.. Rate data were collected for the following reaction at a particular temperature. ClO (aq) + OH - (aq) ClO - (aq) + ClO - (aq) + H O(l) Eperiment [ClO 0 (mol/l) [OH - 0 (mol/l) Initial Rate (M/) a. What i the rate-law epreion for thi reaction? Rate = k[clo [OH - Eperiment and : [ClO i contant. [OH - double The rate double. Therefore the reaction i firt order with repect to B = = Eperiment and 4: [ClO double [OH - i contant. The rate quadruple. Therefore the reaction i econd order with repect to A= = Rate = k[clo [OH - b. Calculate a value for k. Uing the data from Eperiment to calculate k, we have M/ = k(0.0 M)(0.0 M) k =. 0 M - - c. Decribe the order of the reaction with repect to each reactant and to the overall order. The reaction i econd order with repect to ClO, firt order with repect to OH - and third order overall.. Conider a chemical reaction between compound A and B that i firt order in A and firt order in B. From the information hown here, fill in the blank. Eperiment [A [B Rate (M - ) 0.0 M M M M 0.80 Rate=k[A[B Ue eperiment to find the value of k: - Rate 0. 4 M - k = = = M 4 [A[B ( 0. 0 M )(0.050 M) Then in eperiment, we olve for [A and in eperiment, we olve for [B. [ A = Rate 0 0 M = = 0. 8 M - k[ B ( 4 M )( M). [ B = Rate 0 80 M = = M - k[ A ( 4 M )( M ) 4

5 4. The rate of a chemical reaction A. i alwa dependent of the concentration of all reactant. B. i alwa increaed with increaing temperature. C. i directl proportional to the value of E. D. i greater with higher activation energie. E. i independent of urface area. Anwer: (B) The colliion model indicate that molecular colliion i necear for reaction. Becaue an increae in temperature raie molecular velocitie and the percentage of effective colliion, the reaction rate increae. 5. For the firt-order reaction of different ubtance A and X A B t / = 0.0 min X Y t / = 60.0 min Thi mean that A. doubling the concentration of A will have ½ the effect on half-life that doubling the concentration of B will have on it half-life. B. a certain number of gram of A will react twice a fat a the ame number of gram of X. C. a certain number of gram of X will react twice a fat a the ame number of gram of A. D. the rate contant for A B i lower than the rate contant of X Y. E. mole of A will react more rapidl than mole of X. Anwer: (E) It take half a much time for A to form B a for X to form Y, a een b the maller half-life. Note that option B would be incorrect a the gram of A and the gram of X are not the ame number of mole. 6. A reaction i firt order with repect to [X and econd order with repect to [Y. When [X i 0.0 M and [Y = 0.0 M the rate i M/min. The value of the rate contant, including correct unit, i A..00 M min - B..00 M - min - C..00 M - min - D..00 M - min - E min - Anwer: (B) From thee data, it follow that the rate law i Rate = k[xy. Solving for the rate contant and ubtituting data for thi reaction: K = Rate/[X[Y = M/min/(0.00 M)(0.00 M) = M/min/0.008 M =.00 M- min - 7. The rate contant for the decompoition of nitrogen dioide NO NO + O with a laer beam i.70 M - min -. Find the time, in econd, needed to decreae.00 mol/l of NO to.5 mol/l. Since the unit of the rate contant are M - min -, we know that the reaction i econd order overall. Since the reaction ha onl one reactant, NO, the reaction i econd order with repect to NO. The integrated rate equation for a reaction that i econd order with repect to NO a the onl reactant i = akt where a = toichiometric coefficient of NO [ NO t [ NO 0 - Subtituting, = ( 70. L mol min ) t 5. M. 00 M M M t = = min or ( )( 70. L mol min ) 8. What i meant b the half-life of a reactant? The half-life of a reactant i the time required for half of that reactant to be converted into product. For a firt order reaction, the half-life i independent of concentration o that the ame time i required to conume half of an tarting amount or concentration of the reactant. On the other hand, the half-life of a econd-order reaction doe depend on the tarting amount of the reactant. 5

6 9. The decompoition of hdrogen peroide wa tudied, and the following data were obtained at a particular temperature: Time () [H O (mol/l) auming that Rate = H O determine t a. the rate law Ue our graphing calculator to determine the rate law. The plot of ln [H O v. time i linear. Thu, the reaction i firt order. The rate law i Rate=k[H O b. the integrated rate law ln[h O t = -kt + - ln[h O 0 c. the value of the rate contant We determine the rate contant k b determining the lope of the ln[h O v time plot (lope = - k). Thi can be done uing our graphing calculator or b uing the old fahioned method of uing two point on the curve. B calculator: Uing two point on the curve give: 0 lope= k = = ( 00. ) = d. Calculate the [H O at after the tart of the reaction. To determine [H O at 4000., ue the integrated rate law where at t=0, [H O 0 =.00 M. ln[ H O ln[ H O = kt t 0 ln[ H O = ln[ H O kt t 0 4 ln[ H O t = ln[ ( 8. 0 ) = -.. [ H O = e = M - 0. It took 4 for 50.0% of a particular ubtance to decompoe. If the initial concentration wa M and the decompoition reaction follow econd-order kinetic, what i the value of the rate contant? For a econd order reaction: t/ = or k = k[ A t [ A k = 4 (0.060 mol / L) = 0. L / mol 0 / 0 6

7 . The dimerization of butadiene C 4 H 6 (g) C 8 H (g) wa tudied at 500. K, and the following data were obtained: Time () [C 4 H 6 (mol/l) [C4H 6 Auming that Rate = - t determine the a. form of the rate law Ue our graphing calculator to graph the data. L =time, L =[C 4 H 6, L =ln[c 4 H 6, L 4 =/[C 4 H 6 Make linear regreion for L, L ; L, L ; and L, L 4 and identif the equation with the bet r. Since the econd order plot of /[C 4 H 6 v. t i linear, then we can conclude that the reaction i econd order in butadiene. The rate law i: Rate = k[c 4 H 6 b. the integrated rate law = kt [ C4H6 t [ C4H 6 0 which can be written a = kt+ [ C4H6 t [ C4H 6 0 c. the rate contant The lope of the traight line equal the value of the rate contant. You can either ue two point on the line and determine the / or obtain the value from our graphing calculator. The lope equal 0.04 L/mol.. A certain firt-order reaction i 45.0% complete in 65. What are the rate contant and the half-life for thi proce? If [A 0 = 00.0, then after 65, 45.0: of A ha reacted or [A = For firt order reaction: ln[a t - ln[a 0 = -kt ln[ ln[00.0 = -k(65 ) k = t/ = = = 75 k The rate law for the decompoition of phophine (PH ) i [PH Rate = - t = k[ PH It take 0. for.00 M PH to decreae to 0.50 M. How much time i required for.00 M PH to decreae to a concentration of 0.50 M? ln[ PH ln[ PH = kt t 0 ln[ 0.50 t ln[.00 0 = k( 0 ) k = ln[ 0.50 t ln[.00 0 = ( t) t =

8 4. The rate of the reaction NO (g) + CO(g) NO(g) + CO (g) depend onl on the concentration of nitrogen dioide below 5 C. At a temperature below 5 C, the following data were collected: Time () [NO (mol/l) Determine the a. rate law Ue our graphing calculator to graph the data. L =time, L =[NO, L =ln[no, L 4 =/[NO Make linear regreion for L, L ; L, L ; and L, L 4 and identif the equation with the bet r. Since the econd order plot of /[NO v. t i linear, then we can conclude that the reaction i econd order in NO. The rate law i: Rate = k[no b. integrated rate law = kt [ NO t [ NO 0 which can be written a = kt+ [ NO t [ NO 0 c. value of the rate contant. The lope of the plot /[NO v. t give the value of k. Slope = L/mol d. Calculate the [NO at after the tart of the reaction L 4 = [ NO mol [ t [ NO t = 7. 6, [NO = 0. M t 0 5. A reaction mechanim A. i the um of all tep in a reaction ecept the rate determining tep. B. ha a H equal to the H for the mot demanding tep. C. alwa ha a rate determining tep. D. ma be abolutel proven from the rate law. E. i determined from the balanced epreion onl. Anwer: (C) In all erie of tep (the mechanim for the overall reaction), there mut alwa be a lowet tep. The rate determining tep i the lowet tep. 6. Write the rate law for the following elementar reaction. a. CH NC(g) CH CN(g) Rate = k[ch NC b. O (g) + NO(g) O (g) + NO (g) Rate = k[o [NO 8

9 7. Mot reaction occur b a erie of tep. The energ profile for a certain reaction that proceed b a twotop mechanim i On the energ profile, indicate a. The poition of reactant (R) and product (P). b. The activation energ for the overall reaction (E a ). c. E for the reaction. d. Which point on the plot repreent the energ of the intermediate in the two-tep reaction? e. Which tep in the mechanim for thi reaction i rate determining, the firt or the econd tep? Eplain. In a mechanim, the rate of the lowet tep determine the rate of the reaction. The activation energ for the lowet tep will be the larget energ barrier that the reaction mut overcome. Since the econd hump in the diagram i at the highet energ, then the econd tep ha the larget activation energ and will be the rate determining tep (the low tep). 8. A propoed mechanim for a reaction i C 4 H 9 Br C 4 H Br - Slow + C 4 H 9 + H O C 4 H 9 OH Fat C 4 H 9 OH + + H O C 4 H 9 OH + H O + Fat a. What i the overall balanced equation for the reaction? C 4 H 9 Br + H O C 4 H 9 OH + Br - + H O + b. What are the intermediate in the propoed mechanim? C 4 H 9 + and C 4 H 9 OH + c. Write the rate law epected for thi mechanim. Since tep i the rate determining tep, the rate law for thi mechanim i: Rate = k[c 4 H 9 Br 9. The mechanim for the reaction of nitrogen dioide with carbon monoide to form nitric oide and carbon dioide i though to be NO + NO NO + NO NO + CO NO + CO Slow Fat a. What i the overall balanced equation for the reaction? NO + CO NO + CO b. What i the intermediate in the propoed mechanim? NO c. Write the rate law epected for thi mechanim. Since tep i the rate determining tep, the rate law for thi mechanim i: Rate = k[no 9

10 0. The ozone, O, of the tratophere can be decompoed b reaction with nitrogen oide (commonl called nitric oide), NO from high-fling jet aircraft. O (g) + NO(g) NO (g) + O (g) The rate epreion i rate = k[o [NO. Which of the following mechanim are conitent with the oberved rate epreion? a. NO + O NO + O low Conitent, Slow firt tep determine the order. NO + O NO + O fat O + NO NO + O overall b. NO + O NO + O low, one tep Conitent, One tep reaction mechanim c. O O + O low Not conitent, low firt tep, no dependence on O + NO NO fat [NO i predicted b thi mechanim. O + NO NO + O overall d. NO N + O low Not conitent, low firt tep, no dependence on O + O O fat [O i predicted b thi mechanim. O + N NO fat O + NO NO + O overall e. NO N + O fat, equilibrium Conitent, low econd tep predict the firt order O + O O low dependence on O, But O i produced in a previou O + N NO fat fat tep, which predict the firt order dependence on O + NO NO + O overall NO.. A propoed mechanim for the following reaction, H + I HI i I I I + H H I H I + I HI fat, equilibrium fat, equilibrium low a. Identif an reaction intermediate in thi propoed mechanim. The intermediate are I, H I b. Show that thi mechanim predict the correct rate law, rate = k[h [I. From tep (the low, rate-determining tep): Rate = k [H I[I From tep, Rate f = Rate r or k r [I = k r [I kf [ I rearranging, [I = k r From tep, Rate f = Rate r or k r [I[H = k r [IH f [ I[H rearranging, [IH = k k r Subtituting the epreion for [I from tep into thi latter epreion, k f I k [ f [ H kr [IH = kr Subtituting thi epreion for [I and [IH into the rate law deduced from tep, and the combining term, Rate = k k f [ I kf [ H kr k f [ I k k f k = k k k k r f Rate = k[h [I The mechanim i conitent with the oberved rate law. r r r [ H [ I 0

11 . The rearrangement of cclopropane to propene ha been tudied at variou temperature. The following value for the pecific rate contant have been determined eperimentall. T(K) k ( - ) a. From the appropriate plot of thee data, determine the value of the activation energ for thi reaction. Slope = -E a /R = K E a = ( K)(8. J/mol K) = J/mol or 7 kj/mol b. Ue the graph to etimate the value of k at 500. K. ln k = -7 (/500 K) ln k = k = c. Ue the graph to etimate the temperature at which the value of k would be equal to ln ( ) = -7 (/) =-7 (/) = -7 (/) = 79 K. The activation energ for the reaction NO (g) + CO(g) NO(g) + CO (g) I 5 kj/mol, and E for the reaction i kj/mol. What i the activation energ for the revere reaction [NO(g) + CO (g) NO (g) + CO(g)? The activation energ for the revere reaction i E a, revere = 6 kj/mol + 5 kj/mol = 4 kj/mol 4. The reaction (CH ) CBr + OH - (CH ) COH + Br - in a certain olvent i firt order with repect to (CH ) CBr and zero order with repect to OH -. In everal eperiment the rate contant k wa determined at different temperature. A plot of ln k veru /T wa contructed reulting in a traight line with a lope value of K and -intercept of.5. Aume k ha unit of -. a. Determine the activation energ for thi reaction J 4 lope = - Ea / R, Ea = 0. 0 K = J / mol = 9.4 kj / mol K mol b. Determine the value of the frequenc factor A. intercept = ln A, A = e.5 = c. Calculate the value of k at 5 C. ln k = -Ea/RT + ln A Ea k = Aep( ) = 54. RT

12 5. One mechanim for the detruction of ozone in the upper atmophere i O (g) + NO(g) NO (g) + O (g) Slow NO (g) + O(g) NO(g) + O (g) Fat a. What i the overall reaction? O (g) + O O (g) b. Which pecie i a catalt? NO c. Which pecie i an intermediate? NO d. E a for the uncatalzed reaction i 4.0 kj. E a for the ame reaction when catalzed i.9 kj. What i the ratio of the rate contant for the catalzed reaction to that for the uncatalzed reaction at 5 C? Aume that the frequenc factor A i the ame for each reaction. k cat A ep [-E a (cat) / RT F E a (un) - E a (cat) k = Ea RT = = H G I A ep ( / ); ep K J k A ep [-E (un) / RT RT F un k cat 00 J / mol I 0.85 = ep e k un HG J / mol K 98 K K J = =. 8. The catalzed reaction i. time fater than the uncatalzed reaction at 5 C. a 6. The activation energ for thi reaction, X + Y Z, hown in the potential energ diagram, could be A. increaed b increaing [X. B. increaed b increaing [X and [Y. C. increaed b increaing the temperature. D. decreaed b removing Z from the tem a it form. E. decreaed b adding a uitable catalt. Adding a catalt uitable for thi reaction will lower the energ barrier (activation energ) b forming a different activated comple which ha a lower potential energ. 7. For all zero-order reaction A. a plot of time v. concentration quared i linear. B. E a i ver low. C. the rate i independent of time. D. the rate contant i zero. Anwer: (D) For zero-order reaction, Rate = k[x. Becaue anthing raied to the zero power i equal to one, Rate = k. Thi i another wa of aing that the rate of zero-order reaction do not change; the do not peed up and the do not low down, the either take place or the do not. 8. If both H and E a for the forward reaction are known, the revere reaction would have an E a A. of (- H ) + E a B. of H + E a C. equal E a for the forward reaction D. equal (-E a ) for the forward reaction. E. but none of the above decribe the value of E a. Anwer: (A) Thi activation energ for the revere reaction i the difference between the potential energ of the product and the energ of the activated comple, hence the um of the revere of the enthalp change of the forward reaction plu the activation energ of the forward reaction. 9. The value for the change in enthalp, H, and the activation energ, E a, for a given reaction are known. The value of E a for the revere reaction equal A. E a for the forward reaction B. -(E a ) for the forward reaction. C. the um of H and E a. D. the um of H and E a E. the difference of H and E a Anwer: (C) Look at a reaction progre diagram.

13 40. Write balanced net ionic equation for each of the following. a. Solid calcium carbonate i trongl heated. CaCO CaO + CO b. Solid barium oide i added to ditilled water. BaO + H O Ba + + OH - c. Solution of manganee(ii) ulfate and ammonium ulfide are mied. Mn + + S - MnS d. Carbon diulfide vapor i burned in ece ogen. CS + O CO + SO e. A olution of potaium dichromate i added to an acidified olution of iron(ii) chloride Thi i a redo reaction. Fe + Fe + - Cr O 7 Cr + Fe + Fe + 4H Cr O 7 Cr + + 7H O Fe + Fe + + e - 6e - + 4H Cr O 7 Cr + + 7H O 6Fe + 6Fe + + 6e - 6e - + 4H Cr O 7 Cr + + 7H O 6Fe + + 4H Cr O 7 6Fe + + Cr + + 7H O

b. The rate law can only be determined from experiment, not from the overall balanced reaction.

b. The rate law can only be determined from experiment, not from the overall balanced reaction. CHAPTER CHEMICAL KINETICS Quetion. a. Activation energ and ΔE are independent of each other. Activation energ depend on the path reactant to tae to convert to product. The overall energ change ΔE onl depend