Chapter 4 and 15 solutions

Chapter 4 and 15 solutions - 60 E 57 C CHAPTER 4 SOLUTION...

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Unformatted text preview: 60 E 57. C. CHAPTER 4 SOLUTION STOICHIOMETRY The oxidation state of copper increases by 2 (0 to +2) and the oxidation state of silver decreases by 1 (+1 to 0). We need 2 Ag-atoms for every Cu~atom. The balanced equation is: Cu(s) + 2Ag+(aq) -> Cu2+(aq) + 2Ag[s) The equation is balanced. Each hydrogen atom gains one electron (+1 -* 0) and each zinc atom loses two electrons (0 -> +2). We need 2 H-atoms for every Zn-atom. This is the ratio in the given equation: Zn(s) + HZSO4(aq) 4* ZnSOr(aq) + His) Review section 4.1 l of the text for rules on balancing by the half-reaction method. The first step is to separate the reaction into two half-reactions then balance each half-reaction separately. No; —» NO + 2 H20 (3e-+4H++No;—>No+2H20)x2 (Cu -> Cu2+ + 2 e‘) >< 3 Adding the two balanced half-reactions so electrons cancel: 3Cu->3Cu""+6e‘ 6e'+8H*+2N03‘—*2N0+4H20 3 Cu(s) + 3 H”’(aq) + 2 NO3'(aq) 4' 3 Cu1+(aq) + 2 NO(g) + 4 H200) (3503- + 2 Cr“ + 7 H20 6 e‘ +14 H+ + C1307” —+ 2 Cr3+ + 7 H20 (2C1-—>c12+2e-)x3 Add the two balanced half-reactions with six electrons transferred: 6Cl'->3C12+6e' 6 e'+]4H++Cr2012'e+ 2cfi*+ ero 14 irraq) + Cr1012‘(aq)+ 6 Cl'(aq) —> 3 C12(g) + 2 C13+(aq) + 7 H200) Pb —> PbSO‘ rho2 a Pbso,t Pb + st04 a Pbso.1 + 2 11* rho2 + st0.1 A PbSO4 + 2 H20 Pb + sto. a Pbso4 + 2 E + 2 e' 2 e" + 2 Ir + Pbo2 + H2804 a Pesoe + 2 H20 Add the two half-reactions with two electrons transferred: 2 e' + 2 H’" + rho2 + also, -> lasso,1 + 2 H20 Pb + stor » PbSO4 + 2 11* + 2 e' Pb(s) + 2 HZSOdaq) + Pb03[s) + 2 PbSO4(s) + 2 1-1200) This is the reaction that occurs in an automobile lead storage battery. CHAPTER 4 SOLUTION STOICHIOMETRY 61 d. Mn“ 4 MnO4' (4H20+Mn2+—+Mn04'+8H*+5 e‘) x 2 NaBiO; —> Bi“ + Na+ 5 H‘“ +NaBi03 —> Bi“ + Na* + 3 H20 (26'+6H*+NaBi03 —> Bi3*+Na*+3 H10) x 5 8H30+2Mn2*—>2Mno4'+16H*+10e' 10e-+30H++5Na3103+513i3++5Na++15H20 8H20+301-I“+2Mn¢‘+5NaBiO3—>2M1104'4-5Bi3++5Na++15H20+16H+ Simplifying: 14 H*(aq) + 2 Mn“(aq) + 5 NaBi03(s) -+ 2 Mn04'(aq) + 5 Bi3+(aq) + S Na+(aq) + 7 H200) e. HaAsO4 -> AsH3 (Zn —> Zn” + 2 e‘) x 4 H3A504 —> AsH, + 4 H20 8 e'+ 8H++H3As04+ AsH3+4 H20 8 6+ 8 H+ +H3A504 4» A5143 +4 H20 4Zn->4Zn2++8c' 8 HTaq) + H3A504(aq) + 4 Zn(s) -* 4 anTaq) + AsI-I3(g) + 4 H200) f. A3203 -+ H3A504 A5203 *> 2 H3A504 (S HZO+A5203+ 2H3ASQ4+4H*+4e') X 3 N03; -> NO + 2 H10 41-F+N0;->N0+2Hzo (3 e'+4H++N03‘—>N0+2H10) X 4 12e‘+16H‘+4N03‘->4NO+8H10 15 H20+3Aszop 6H3A504+ 12H"+ 12 e' 7 1420(1) + 4 H+(aq) + 3 1451045) + 4 NO3‘(aq) 4 4 N0(g) + 6 H3A504(aq) (5 6+ 8H++Mn04‘->Mn2+‘+4HZO) x 2 10 Br‘—PSBr2+103‘ g. (2 BrA Br; +2 6') X 5 - Mao; ~> Mn2+ + 4 H20 10 6+ 16H++2MnO4'—>2Mn2++8H20 I 16 H+(aq) + 2 Mn04‘(aq) + 10 Br'(aq) —> 5 Br2(1) + 2 Mn1"(aq) + 8 H200) 62 CHAPTER 4 SOLUTION STOICHIONLETRY h. CH3OH a CHQO C130,” a Cr“ (CH30H ~> CH20 + 2 11* + 2 3-) x 3 14 H* + Crzofi' er 2 Cr“ + 7 H20 6e‘+14H++ Cr2072'-> 2013+ +7 H10 3 CH3OI-I-+ 3 CH20+6 H++6 e‘ 6 e' + 14 H” + Orzo-,2“ a 2 013* + 7 H20 M 8 H"(aq) + 3 CH30H(aq) + Cr20,1‘(aq)—* 2 C15+(aq) + 3 CH20(aq) + 7 H20(l) 58. Use the same method as with acidic solutions. After the final balanced equation,_then convert H’ to OH' as described in section 4.11 of the text. The extra step involves converting I-F into H10 by adding equal moles ofOH' to each side of the reaction. This converts the reaction to a basic solution while keeping it balanced. a. A] or ARCH); . M110; 4 MnO, 41-120+Al—>A1(OIrI),{+4H+ 3 e'+-4I-I++Mn04'-+Mn01+2H20 4 H20 + A1 a A1(0H),; + 4 1r + 3 e“ 4H20+Al ->Al(OH)4'+4I-I++3 e' 3 e'+4H"+MnO4‘->Mn02+2H20 ____,___—__ 2 H100) + A1(s) + MnOflaq) -> Al(OH);(aq) + Mn02(s) Since I-I+ doesn’t appear in the final balanced reaction, we are done. b. Cl2 —> C1' C12 —> 010' 2e‘+C12->201' 2H20+C12—>2010+4H++2e“ 2e‘+C12-+2C1‘ 2H20+c1,+2c10-+4H*+2e- 21-120+2C12-+2C1'+2C10‘+4H+ Now convert to a basic solution. Add 4 OH‘ to both sides of the equation. The 4 011' will react with the 4 H" on the product side to give 4 H20. After this step, cancel identical species on both sides (2 H20). Applying these steps gives: 4 0H“ + 2 C12 —> 2 01' + 2 C10“ + 2 H20, which can be further simplified to: - 2 OH‘(aq) + Clz(g) -r Cl‘(aq) + ClO'(aq) + H200) N02'->NH3 Al-r A10; 6e'+7H*+N02'-*NH;+2H20 (2 H10+Al-+A101'+4H*+3 e')><2 Common factor is a transfer of 6 e'. 6e‘+7H"+N02'—>NH3+2H20 4H20+2A1+2Al02'+81-I*+6e‘ W OH‘+ 21-120 +N01‘+ 2 Al-PNH3+2A102‘+H++OH' Reducing gives: OH‘(aq) + H200) + N02'(aq) + 2 Al(s) » NH3(g) + 2 A102‘(aq) 61. 62. 63. 64. CHAPTER 4 SOLUTION STOICHIOMETRY HNO; *r N02 HNO3 a No1 + H20 (c'+H++HNC)3—>NOZ+HQO) x 2 Mn—PMn2*+2e' N1114Mn2++2€ 2e‘+2H*+2HNO3-*2N02+2H10 _. 2 H*(aq) + Mn(s) + 2 HNO3(aq) —> Mn2+(aq) + 2 N02(g) + 2 H200) or 4 mag) + Mn(s) + 2 NO3’(aq) + Mn2+(aq) + 2 1002(3) + 2 H200) (HINO3 is a stlfong acid.) (4H30+Mn2+-+Mn04'+8H*+5 (3') x2 [2e‘+2H"+104'—r103‘+H20) x5 8H20+2Mn2++2Mn04'+16H*+10e' 106+10W+510,{->5103'+5H20 M 3 H200) + 2 Mnl+(aq) + 5 104'CaCi) " 2 Mn04‘(a€D + 5 103139) + 5 H+(aq) HCl and HNO3 are strong acids which completely dissociate to I-l+ and the anions in solution. Au+4Cl'—>AuCl;+3e‘ 3e'+4H*+N03'—*NO+2H20 Adding the two balanced half—reactions: Au(s) + 4 Cl‘(aq) + 4 I-Y(aq) + N03‘(aq). -> AuClflaq) + N0(g) + 2 H300) (S‘e'+8H"+MnO4‘->Mnfl++4H20)>< 2 5H2C204+10002+10H*+10e' 10e‘+16H++2MnO4'—>2Mn2*+8H20 mzczo4+2coz+2w+2ejxs M 6 H*(aq) + 5 H2C204(aq) + 2 MnOJaq) —> 10 00103) + 2 Mn" aq) + 8 H200) 1 mol H3C204 2 mol MnOd: >< ——-— = 4.700 >< 10“ mo] Mn04' 90034 g 5 mol chzo4 0.1053 g ch104 x 4.700x10“1 ano ‘ ___m#:n0_2__i x M :15” x 10-2 Mmod- Molarity = 28.97 mL L 3. Fe?" —+ Fe?“ + c’ 5 e‘ + s H“ + Mno; a Mn2+ + 4 H20 The balanced equation is: 3 WW!) + Mn04'(aCI) + 5 FezTaCD —" 5 F83+(3ID + MBZTfiQ) + 4 H200) 0.0216 mol M1104. 5 11101129,2+ ________._.._. x .__._._.__ mol Mn04_ 20.62 x 10'3 L 50111 X = 2.23 X 10“3 mol Fe2+ L soln ,3 3+ M = 4.46 x 10-2 MFe” Molarity = 50.00 x 10-3 L 488 CHAPTER 15 CHEMICAL KINETICS b. For the first experiment: 12.5 x 1074 mol = k[ 0.080 mol] ( 0.040 1661] ’ k = 3.9 x 10., L “101.15.. L s L L The other values are: Initial Rate k (mol L“ s“) (L 11101“ 5") 12.5 >< 10“3 3.9 x 10-3 6.25 X 10"5 3.9 X 10'3 6.25 X 10'6 3.9 X 10‘3 5.00 X 10'6 ' 3.9 X 10'3 7.00 X 10'5 3.9 X 10'3 km,“ = 3.9 X 10'3 L meal'1 5'1 17. a. Rate = k[NOCl]“; Using experiments two and three: 2.66 x 104 z k(2.0 x 1016)" , 4.01 = 2.0“, n = 2; Rate = k[NOCl]2 6.64 >4103 141.0 ><10“5)r1 3 3 5.98 x 104 molecules = k 3.0 x 1016 molecules CHI 5 2 , k = 6.6 X 10'” reni3i'niolecules‘ls“l cm The other three experiments give (6.7, 6.6 and 6.6) x 10'29 cm3 molecules'15‘1, respectively. The mean value for k is 6.6 X 10'29 cm3 molecules'1s". 6.6 ><10'29 cm3 x 1L X 6.022 x 1013molecules 4.0 x 10-31. molecules 5 1000 cm 3 mol m0] 5 18. a. Rate = k[Hb]"[C0]" Comparing the first two experiments, [CO] is unchanged, [Hb] doubles, and the rate doubles. Therefore, x = I and the reaction is first order in Hb. Comparing the second and third experiments, [Hb] is unchanged, [(30) triples and the rate triples. Therefore, y = 1 and the reaction is first order in CO. b. Rate = k[Hb] [CO] c. From the first experiment: 0.619 ,umol L‘1 s‘1 = k (2.21 jm:noir'L)(1.00 nmoUL), k = 0.280 L tnnol‘l s'1 The second and third experiments give similar k values, so km“ = 0.280 L mnol‘1 s‘l. CHAPTER 15 CHEMICAL KINETICS 489 _________________..__..———-—-—-——-——-—-—--——~—-- 1 d. Rate = k[Hb][CO] = 0280 L x M X M = 2.26 mot L-1 5'1 ,umol 5 L L 19. a. Rate = k[ClOz]“[OI-I']Y; From the first two experiments: 2.30 x 10" = k(0.100)"(0.100)’ and 5.75 x 10'2 = k(0.0500)"(0.100)” Dividing the two rate laws: 4.00 = M = 2.00“, x = 2 (0.0500)* Comparing the second and third experiments: 2.30 x 10-1 = k(0.100)(0.100)" and 1.15 x 10-1 = k(0.100)(o.0500)v (0.100)y (0.050)y Dividing: 2.00 = = 2.0’, y = l The rate law is: Rate = k[C103]2[OH'] 2.30 X 104111011." 5'1 = k(0.100 molfL)2(0.100 moUL), k = 2.30 X 102 L2 n:Itol‘2 s" = kmall 2 2 2 b, Rate: =o,594m01L.1 mo! 2 s L L 20. Rate = k[NO]“[02]Y; Comparing the first two experiments, [01] is unchanged, [N0] is tripled, and the rate increases by a factor of nine. Therefore, the reaction is second order in NO (32 = 9). The order of 02 is more difficult to determine. Comparing the sécorid and third experiments; I? 18 2 18 M = W, 1,74 = 0.694 (2.50)); 2,51 = 2502, y =1 1.30 x 10” k (3.00 x 1018mm x 10””)3r Rate = k[NO]2[021; From experiment 1: 2.00 x 101‘5 molecules cm“3 s“ = k (1.00 >< 1013 moleculest'cm’)2 (1.00 x 10“ moleculesfcm’) k = 2.00 X 10'“ cm‘ moleeules‘2 5‘1 = kImam 2.00 x 10'33 ern‘5 x 6.21 x 1013 molecules 2 X 7.36 x 1018 molecules Rate = 3 molecules.2 s cm3 em = 5.68 x 10” molecules cm'3 s“ 21. Rate = k[N1051"; The rate laws for the first two experiments are: 2.26 X 10'3 = k(0.190)" and 3.90 X 10“ = M00750)x 490 CHAPTER 15 CHEMICAL KINETICS X Dividing: 2.54 = fl = (2.53)*, x = 1; Rate = k[N,O,] (00750)" —4 —1 —l . = Rate = X mol L S = x 5.1; km”: X104 S-l [N205] 0.0750 moUL Integrated Rate Laws 22. 3. Since the 1! [A] vs time plot was linear, then the reaction is second order in A. The slope of the If [A] vs. time plot equals the rate constant it. Therefore, the rate law, the integrated rate law and the rate constant value are: Rate = k[A]2; L = kt + _L; k = 3.60 x 10-2 L mol“ 5" [A] {A}, I b. The half-life expression for a second order reaction is: tm = k [A] O For this reaction: tIn = 1 = 9.92 x 103 s 3.60 ><10'2 L 11101 '1 s ‘1 x 2.80 ><10’3 mollL Note: We could have used the integrated rate law to solve for t1,2 where [A] = (2.80 x 10'3 f2) moUL. c. Since the half—life for a second order reaction depends on concentration, then we must use the integrated rate law to solve. 1 1 1 =3.60x10'2LXH 1 7.00 x 10-4114 mol 5 2.30 x 10‘3 M 1.43 x103 - 357 = 3.60 x102 t, t= 2.93 x 10‘s 23'. 3. Since the ln[A] vs time plot was linear, then the reaction is first order in A. The slope of the ln[A] vs time plot equals —k. Therefore, the rate law, the integrated rate law and the rate constant value are: Rate = k[A]; ln[A] = -kt + ln[A]o; k= 2.97 X 10‘2 min" b. The half-life expression for a first order rate law is: tm ___ E 2 0.6931 , tm = 0.6931 = 23.3 min k k 2.97 x 10'2 min-1 c. 2.50 X 10'3 M is US of the original amount of A present initially, so the reaction is 87.5% complete. When a first order reaction is 87.5% complete (or 12.5% remains), then the reaction has gone through 3 half-lives: 100% a 50.0% —> 25.0% ~> 12.5%; t=3 ><tm=3 x233 min=69.9 min to: tlr‘l tm T CHAPTER 15 CHEMICAL KINETICS 491 ____________,____._____—-—-—-—-— 24. 25. Or we can use the integrated rate law: In = _kt, In X ': M = _ x 10-2 mind) t, t: [A10 2.00x10 -M 111(0125) —2.91 x104 min’1 = 70.0 min 3.. Since the [Qmom vs time plot was linear, then the reaction is zero order in CZHSOH. The slope of the [Gil-LOB} vs time plot equals -k. Therefore, the rate law, the integrated rate law and the rate constant value are: Rate = k[C2HSOl-I]° = k; [CZHSOH] = ~kt + [QEOI—IL; k = 4.00 X 10'5 mol L'1 s’1 b. The half-life expression for a zero order reaction is: t”z = [AL/2k. = [CZHSOHJG : 1.25 x 10-2 mom. 2k 2x4.00x10'5molL‘ls" Note: we could have used the integrated rate law to solve for tm where [CZHSOH] = (1.25 x 104:?) molfL. =156s tin c. [CEHSOI-I} = -kt + [cansomw 0 1nth = {4.00 x 10-5 mol L" 5-1) t + 1.25 x 10-2 molfL -2 t: 1.25x10 molfL =313s 4.00x10'5 mol L"1 s ‘1 The first assumption to make is that the reaction is first order. For a first order reaction, a graph of In [H202] vs time will yield a straight line. If this plot is not linear, then the reaction is not first order and we make another assumption. Time [1-1101] 111 [H202] one (5) (moUL) 0 1.00 0.000 120. 0.91 41.094 "-°° 300. 0.78 41.25 '3' 600. 0.59 -053 i“ 1200. 0.37 -0.99 5 4m 1800. 0.22 -i.51 2400. 0.13 -2.04 3000. 0.082 -2.50 3600. 0.050 -3.00 4°“ Note: We carried extra significant figures in 0 50° “00 '500 2‘00 300° 3600 some of the ln values in order to reduce round "ms", off error. For the plots, we will do this most of the time when the In function is involved. CHAPTER 15 CHENflCAL KINETICS 495 ________________—___.__———-—-————~—-——— 29. 30. 31. From the data, the pressure of C2H50H decreases at a constant rate of 13 torr for every 100. s. Since the rate of disappearance of CZHSOH is not dependent on concentration, the reaction is zero order in CzHSOH. __ 13torr latm k - x 100. s 760torr The rate law and integrated rate law are: =13 X104atmfs Rate =k=1.7 x 10“ atmfs; PC HsOH =-lct+ 250. torr[ 76m 2 - orr 1 “I” ] = 4s + 0.329 atm At 900. s: PCZHSOH = -1.7 ><10“i annfs X 900. s + 0.329 atm = 0.176 mm = 0.18 am =130t0rr a. Since the 1! [A] vs. time plot is linear with a positive slope, the reaction is second order with respect to A. The y-intercept in the plot will equal 1l[A]o. Extending the plot, the y—intercept will be about 10, so 1110 = 0.1 M= [A]o. b. The slope of the 121A] vs time plot will equal k. (60 - 20) Limo] slope = k = = 10 Umol-s (5 - 1) S i=kt+ 1 = ‘0L x95+ 1 =100, [A]=0.01M [A] [A]o mol 5 0.1 M c. For a second-order reaction, the half-life does depend on concentration: tU2 = Mi] . a First half-life: tm=———1—fi =1 5 10L x 0.1 moi mol 5 L Second half-life ([A]° is now 0.05 M): tm = 13(10 x 0.05) = 2 5 Third half-life ([A]{) is now 0.025 M): t1}.2 = 1l(10 X 0.025) = 4 s a. We check for first order dependence by graphing 1n [concentration] vs. time for each set of data. The rate dependence on NO is determined from the first set of data since the ozone concentration is relatively large compared to the NO concentration, so it is effectively constant. time (ms) [NO] (molecules/cm3) in [NO] 0 6.0 X 103 20.21 100. 5.0 X 108 20.03 500. 2.4 X 103 19.30 700. 1.7 X 103 18.95 1000. 9.9 X 101r 18.41 495 CHAPTER 15 CHEMICAL KINETICS ___________.____,__._._—..m——-——-—— O 250 500 750 . 1000 time(ms) Since 111 [NO] vs. t is linear, the reaction is first order with respect to NC). We follow the same procedure for ozone using the second set of data. The data and plot are: time (ms) [03] (moleculesfcm3) In [03] 0- 1.0 X lCllo 23.03 50. 8.4 x 109 22.85 100. 7.0 X 109 22.67 200. 4.9 X 109 22.31 300. 3.4 x109 21.95 23 f—| to O ""’ 22 E 21 U 100 200 300 time (m s) The plot of In [03} vs. t is linear. Hence, the reaction is first order with respect to ozone. b. Rate = k[NO}[03] is the overall rate law. c. For NO experiment, Rate = 1:“ [NO] and k” = {slope from graph of 111 [N0] vs. t). [8.41 — 20.21 W =13 s" (1000. —O)><10"3 s k’ = -slope = - CHAPTER 15 CHEMICAL KINETICS 497 M 32. For ozone experiment, Rate = k" [03] and k" = {slope from in [03] vs. t). (21.95 43.03) (300. — 0))(10'3 s H... — -slope = - =16 s" d. From NO experiment, Rate = k[NO][03] = k’ [NO] where k’ = k[03]. k’ = 1.8 s'1 = k(1.0 X 10” moleculesfcms), k= 1.8 X 10'14 cm3 molecules“1 5" We can check this from the ozone data. Rate = k” [03] = k[NO][03] where k” = k[NO]. It” = 3.6 s“ = k(2.0 X 10“ moleculesfcn-E), k = 1.8 x 10"4 cm3 molecules" 5" Both values of k agree. This problem differs in two ways from the previous problems: 1. a product is measured instead of a reactant and 2. only the volume of a gas is given and not the concentration. We can find the initial concentration of CfiHsNzCl from the amount of N2 evolved afier infinite time when all the CfilrlsNfil has decomposed (assuming the reaction goes to completion). -3 n: E}: : 1.00 atm x (58.3 x10 13:220 X103 molNz RT 0.08206 L atrn X 323 K moi K Since each mole of CSHSNZCI that decomposes produces one mole of N2, then the initial concentration (t = 0) of CfiI-LNZCI was: —3 2.20x10 mol =OIOSSOM 40.0x 1031. We can similarly calculate the moles of N2 evolved at each point of the experiment, subtract that from 2.20 x 10'3 mo] to get the moles of CEHSNZCI remaining, and then calculate [CSHSNQCI] at each time. We would then use these results to make the appropriate graph to determine the order of the reaction. Since the rate constant is related to the slope of the straight line, we would favor this approach to get a value for the rate constant. There is a simpler way to check for the order of the reaction that saves doing a lot of math. The quantity (Vm - Vt) where Vm = 58.3 mL N2 evolved and VI = mL of N2 evolved at time t will be proportional to the moles of CGHSNZCI remaining; (Vm — V) will also be proportional to the concentration of C6H5NZCI. Thus, we can get the same information by using (V00 — V!) as our measure of [CsHsNzClL If the reaction is first order, a graph of in (Va, — V!) vs. t would be linear. The data for such a graph are: 493 CELAPTER 15 CHEMICAL KINETICS {(8) V. (mL) (V00 - VI) 1110!; — V!) 0 0 58.3 4.066 6 19.3 39.0 3.664 9 26.0 ' 32.3 3.475 14 36.0 22.3 3.105 22 45.0 13.3 2.588 30. 50.4 1.9 2.07 We can see from the graph that this plot is linear, so the reaction is first order. The differential rate law is: —d[CSHSN2Cl]fdt = rate = kICGHSNZCI] and the integrated rate law is: ln[05}15N2Cl] = -kt + h1[CSI-15N2Cl]a. From separate data, It was determined to be 6.9 X 10‘2 s". 33. For a first order reaction, the integrated rate law is: ‘ In([A]f[A]D) = -kt. Solving for k: In [ 0.250 01001. = -k X 120. s, k=0.0116 s'1 1.00 moUL In M =-0.0116s‘1xt, t=150.s 2.00molfL 34. In [A] =~kt; k= 113 = 06931 =4.5 x 10-2 (1-1 [A10 rm 14.30 If [A]o = 100.0, then after 95.0% completion, [A] = 5.0. In “549— =—4.ss x102 d" x t, t=62 days 1000 __ l or k — 1 “AL: tIJ’IIAlo k = ————~—~—— = 0.12 L r1101" 5'1 143 5(0060 mOUL) 35. For a second order reaction: 1],; = T CHAPTER 15 CHEMICAL KINETICS 499 ____________,___.__.—.—————-~——--—-—-————-—-—-- 36. 3?. 38. 39. a. The integrated rate law for a second order reaction is: 111A] = kt + 1/ [161]” and the half-life expression is: t1]2 = 1fk[A]o. We could use either to solve for tm. Using the integrated rate law: _._—-1———= “2.005 + m—1———, k= M = 0.555Lmol" s-1 (090012) molfL 0.900 molfL 2.00 s b. _Fl——=0.555an:.1‘15.-l x t+ 1 ,t= 8'9L’m01 =165 0.100 molfL 0.900 molfL 0.555 L 11101 '1 s '1 a. Ifthe reaction is 3 8.5% complete, then 38.5% of the original concentration is consumed, leaving 61.5%. [A] = 61.5% of [AL or [A] = 0.515 [A]; in 0615 [A10 [A] J =-kt, in ] =-k(480.s) EAL, ln(0.615) = —k(480. 3), -0.486 = -k(480. s), k = 1.01 X 10‘3 s'1 0 b. tm = (In 2)/k 2 0.15931fl.01><10'3 s“ = 686 s c. 25% complete: [A] = 0.?5 [Ale ln(0.75) = —1.01 x 10'3 (t), t= 280 s 75% complete: [A] = 0.25 [A]; ln(0.25)= -1.01 x 10'3 (t), t= 1.4 x 103 5 Or, we know it takes 2 X In for reaction to be 75% complete. t = 2 X 686 s = 1370 s 95% complete: [A] = 0.05 [1010; 111(005) = ~1.01 x 10'3 (t), t = 3 x 103 s Successive half-lives increase in time for a second order reaction. Therefore, assume reaction is second order in A. t1”: _!_.—.- k: ._.l_ ..-_.._._.......__l_._.—— = 1.0141110141126114 10A]; tm[A]D loommroM) L=kt+ 1 1'011 xao.0min+ l [A] [A]o molmin 0.10M =90.M", [A]=1.1><10'2M b. 30.0 min = 2 half-lives, so 25% of original A is remaining. [A] = 0.250110 M) = 0.025 M a. [A] = -kt + [A]o; Ifk = 5.0 x 10-2 moi L-1 s" and [A], = 1.00 x 10-3 M, then: [A =-(5.0 X 10':a mol L’1 s“)t + 1.00 x 10-3 mom, A b. [21° =—(s.0 >< 10-2)t,.1+ [A], since att=tm, [A] = [A],,12. ..3 A -0.50[A]., = -(5.0 x 102) 1m, rm = w = 1.0 x 10-2 5; Or we can use t1.2 = L19. 5.0 x 10" 2 500 CHAPTER 15 CHEMICAL KINETICS ________________.__._._.——_———--———--———-——-— c. [A] = -ict + [A]o=-(5.0 X 10~2 mol L" s")(5.0 x 10'3 s) + 1.00 X 10'3 moUL = 15 X 10“ mol/L [A}Md=1.00 X103 moUL - 7.5 X 10“ moHL = 2.5 X 10" moUL [B1pmducecl =[A1maeted = 2-5 X 104 M 40. 100% —> 50% —* 25% *i' 12.5%; This process is 3 half-lives = 304 h) = 42 hours. 41. 3. Since [A]o < < [B]o or [C]o, then the B and C concentrations remain constant at 1.00 M for this experiment. So: rate = k[A]2[B][C] = k’[A]2 where k' = k[B] [C] For this pseudo second order reaction: J-= 't+ 1 , _'.—L—=k'(3.00min)+ ._1__ [A] [A]o 3.26 X 10-5 M 1.00 x 10-4 M k’ = 6890 Lrnol‘l min" = 115 L mol'I s‘1 r - -1 -1 .k' =k[B][C},k- 1‘ — “3 “‘01 5 = 115 L3 mol“3 5-1 [BHC] (1.00 M) (1.00M) b. For this pseudo second order reaction: rate = k’[A]2, tm = k: 1 = __fi——1———T = 8?.0 s We 115 Lmol '15 “(1.00 x 10‘4 % c. J" =k't+ 1 = 115 Lmol" s-1 x 600. s + 1 = 7.90 x 10* Umol, [A] [A30 1.00x 10-4 1‘59 [A] = #1—— =12? x 10-5 1’19 7.90 x 104 Limo] L From the stoichiometry in the balanced reaction, 1 mol of B reacts with every 3 mol of A. amountA reacted = 1.00 x 104M— 1.27 x 10-5 M: 8.? x105}; lmolB 3molA amount B reacted = 8.? X 10‘5 molfL x = 2.9 x 10‘5 M [B] = 1.00M— 2.9 X104 M= 1.00M As we mentioned in part a, the concentration of B (and C) remain constant since the A concentration is so small. ...
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Chapter 4 and 15 solutions - 60 E 57 C CHAPTER 4 SOLUTION...

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