Chemistry 132 NT. Rates of Reaction. More can be accomplished with the phrase I must do something than with the phrase something should be done.

Transcription

1 Chemisry 13 NT More can be accomplished wih he phrase I mus do somehing han wih he phrase somehing should be done. Anon 1 Raes of Reacion Module Changes of Concenraion wih Time Concenraion-Time Equaions Half-Life Graphing Kineic Daa The burning of seel wool

2 Review The effec of concenraion on reacion rae. Deerminaion of he Rae Law for a given reacion by he mehod of iniial raes. 4 Change of Concenraion wih Time A rae law simply ells you how he rae of reacion changes as reacan concenraions change. A more useful mahemaical relaionship would show how a reacan concenraion changes over a period of ime. 5 Change of Concenraion wih Time A rae law simply ells you how he rae of reacion changes as reacan concenraions change. Using calculus we can ransform a rae law ino a mahemaical relaionship beween concenraion and ime. This provides a graphical mehodfor deermining rae laws. 6

3 Concenraion-Time Equaions Zero-Order Rae Law Suppose we look a a simple generic zero order reacion of he reacan A o form producs. A fi producs Remember ha he rae of his reacion is unaffeced by he concenraion of A. I s Rae Law would be: Rae = k[a] o = k 7 Concenraion-Time Equaions Zero-Order Rae Law You could wrie he rae law in he form; Rae D[A] = - = k[a] D o = Using calculus, we can derive he following relaionship beween [A] and ime,. [ A] = -k+[a ] o k 8 Concenraion-Time Equaions Zero-Order Rae Law You could wrie he rae law in he form; Rae D[A] = - = k[a] D o = Here [A] is he concenraion of reacan A a ime, and [A] o is he iniial concenraion. [ A] = -k+[a ] o k 9

4 A Problem To Consider Suppose ha he decomposiion of a hypoheical compound A is zero order wih a rae consan of 1.8 x 10-4 (mol/l. s). If he iniial concenraion of A is 1.00 mol/l, wha is he concenraion of A afer 600 seconds? The zero-order concenraion-ime equaion for his reacion would be: [ A] = -k+[a ] o 10 A Problem To Consider Suppose ha he decomposiion of a hypoheical compound A is zero order wih a rae consan of 1.8 x 10-4 (mol/l. s). If he iniial concenraion of A is 1.00 mol/l, wha is he concenraion of A afer 600 seconds? Subsiuing he given informaion we obain: -4 [A] = [-( )(600) + (1.00)]mol / L [ A] = [-(0.108) + (1.00)]mol / L [ A] = 0.89 mol / L 11 Concenraion-Time Equaions Firs-Order Rae Law Suppose we look a a simple generic firs order reacion of he reacan A o form producs. A fi producs In a firs -order reacion, he rae is direcly proporional o he concenraion of A. Is Rae Law would be: Rae = k[a] 1

5 Concenraion-Time Equaions Firs-Order Rae Law You could wrie he rae law in he form; D[A] Rae = - = k[a] D 13 Concenraion-Time Equaions Firs-Order Rae Law Using calculus, you ge he following equaion. [A] ln [A] = o -k Here [A] is he concenraion of reacan A a ime, and [A] o is he iniial concenraion. The raio [A] /[A] o is he fracion of A remaining a ime. 14 A Problem To Consider The decomposiion of N o NO and O is firs order wih a rae consan of 4.8 x 10-4 s -1. If he iniial concenraion of N is 1.65 x 10 - mol/l, wha is he concenraion of N afer 85 seconds? The firs -order ime-concenraion equaion for his reacion would be:? [N O5 ] ln [N O ] = 5 o - k 15

6 A Problem To Consider The decomposiion of N o NO and O is firs order wih a rae consan of 4.8 x 10-4 s -1. If he iniial concenraion of N is 1.65 x 10 - mol/l, wha is he concenraion of N afer 85 seconds? Subsiuing he given informaion we obain: [N O5 ] ln mol / L -4 = - ( s ) (85 s) A Problem To Consider The decomposiion of N o NO and O is firs order wih a rae consan of 4.8 x 10-4 s -1. If he iniial concenraion of N is 1.65 x 10 - mol/l, wha is he concenraion of N afer 85 seconds? Subsiuing he given informaion we obain: [N ] ln = mol / L 17 A Problem To Consider The decomposiion of N o NO and O is firs order wih a rae consan of 4.8 x 10-4 s -1. If he iniial concenraion of N is 1.65 x 10 - mol/l, wha is he concenraion of N afer 85 seconds? Taking he inverse naural log of boh sides we obain: [ NO5] = e = mol / L 18

7 A Problem To Consider The decomposiion of N o NO and O is firs order wih a rae consan of 4.8 x 10-4 s -1. If he iniial concenraion of N is 1.65 x 10 - mol/l, wha is he concenraion of N afer 85 seconds? Solving for [N ] a 85 s we obain: - [N O5] = ( mol/ L) (0.673) = mol/L 19 A Problem To Consider In he presence of excess hiocyanae ion, SCN -, he following reacion is firs order in iron(iii) ion, Fe 3+ ; he rae consan, k, is 1.7 h Fe (aq) + SCN (aq) fi Fe(SCN) (aq) How many hours are required for his reacion o reach 90% compleion? Firs, we mus noe ha a 90% compleion implies ha only 10% of he reacans are lef. This implies 3+ [Fe ] = [Fe ] o 0 A Problem To Consider In he presence of excess hiocyanae ion, SCN -, he following reacion is firs order in iron(iii) ion, Fe 3+ ; he rae consan, k, is 1.7 h Fe (aq) + SCN (aq) fi Fe(SCN) (aq) How many hours are required for his reacion o reach 90% compleion? Going o our firs -order concenraion-ime equaion, we obain: [Fe ln [Fe 3+ ] = -k ] 3+ o 1

8 A Problem To Consider In he presence of excess hiocyanae ion, SCN -, he following reacion is firs order in iron(iii) ion, Fe 3+ ; he rae consan, k, is 1.7 h Fe (aq) + SCN (aq) fi Fe(SCN) (aq) How many hours are required for his reacion o reach 90% compleion? Subsiuing values for k and he raio [Fe 3+ ] /Fe 3+ ] o ln( 0.10) = -(1.7 h -1 ) A Problem To Consider In he presence of excess hiocyanae ion, SCN -, he following reacion is firs order in iron(iii) ion, Fe 3+ ; he rae consan, k, is 1.7 h Fe (aq) + SCN (aq) fi Fe(SCN) (aq) How many hours are required for his reacion o reach 90% compleion? Solving for we ge: ln(0.10) = -1.7 h = hours 3 Concenraion-Time Equaions Second-Order Rae Law You could wrie he rae law in he form D[A] Rae = - = D k[a] 4

9 Concenraion-Time Equaions Second-Order Rae Law Using calculus, you ge he following equaion. 1 1 = k + [A] [A] o Here [A] is he concenraion of reacan A a ime, and [A] o is he iniial concenraion. 5 Concenraion-Time Equaions Rae Law Summary The following able summarizes he Rae Laws and concenraion-ime equaions we have jus oulined. Rae Law Concenraion-ime equaion Zero-order Firs-order Second-order Rae=k[A] 0 Rae = k[a] 1 Rae = k[a] [ A] = -k + [A ln ] o [ A] [A] o = - k = k + [ A] 1 [A] 1 o 6 Half-life The half-life of a reacion is he ime required for he reacan concenraion o decrease o one-half of is iniial value. For a firs -order reacion, he half-life is independen of he iniial concenraion of reacan. In one half-life he amoun of reacan decreases by one-half. Subsiuing ino he firs -order concenraion-ime equaion, we ge: 1 ln( ) = -k1 7

10 Half-life The half-life of a reacion is he ime required for he reacan concenraion o decrease o one-half of is iniial value. Solving for 1/ we obain: 1 = k The nex slide illusraes he half-life of a firs -order reacion. 8 Half-life Sulfuryl chloride, SO Cl, decomposes in a firsorder reacion o SO and Cl. SO Cl(g) fi SO(g) + Cl(g) A 30 o C, he rae consan is. x 10-5 s -1. Wha is he half-life of SO Cl vapor a his emperaure? Subsiue he value of k ino he relaionship beween k and 1/ = 1 k 30

11 Half-life Sulfuryl chloride, SO Cl, decomposes in a firsorder reacion o SO and Cl. SO Cl(g) fi SO(g) + Cl(g) A 30 o C, he rae consan is. x 10-5 s -1. Wha is he half-life of SO Cl vapor a his emperaure? Subsiue he value of k ino he relaionship beween k and 1/ = s Half-life Sulfuryl chloride, SO Cl, decomposes in a firsorder reacion o SO and Cl. SO Cl(g) fi SO(g) + Cl(g) A 30 o C, he rae consan is. x 10-5 s -1. Wha is he half-life of SO Cl vapor a his emperaure? Subsiue he value of k ino he relaionship beween k and 1/. 4 1 = s 3 Half-life For a second-order reacion half-life depends on he iniial concenraion and becomes larger as ime goes on. Again, assuming ha [A] = ½[A] o afer one halflife, i can be shown: 1 = 1 k[a] o Each succeeding half-life is wice he lengh of is predecessor. 33

12 Graphing Kineic Daa In addiion o he mehod of iniial raes, discussed earlier, rae laws can be deduced by graphical mehods. Noe ha he zero-order concenraion-ime equaion can be idenified as he equaion of a sraigh line. [ A] = -k+[a y ] o = mx + b 34 Graphing Kineic Daa In addiion o he mehod of iniial raes, discussed earlier, rae laws can be deduced by graphical mehods. Noe ha he zero-order concenraion-ime equaion can be idenified as he equaion of a sraigh line. This means if you plo [A] vs. ime you will ge a sraigh line for a zero-order reacion. 35 Graphing Kineic Daa In addiion o he mehod of iniial raes, discussed earlier, rae laws can be deduced by graphical mehods. If we rewrie he firs-order concenraion-ime equaion in a slighly differen form, i can be idenified as he equaion of a sraigh line. [A] ln = [A] - o k 36

13 Graphing Kineic Daa In addiion o he mehod of iniial raes, discussed earlier, rae laws can be deduced by graphical mehods. If we rewrie he firs-order concenraion-ime equaion in a slighly differen form, i can be idenified as he equaion of a sraigh line. ln[ A] - ln[a] o = -k 37 Graphing Kineic Daa In addiion o he mehod of iniial raes, discussed earlier, rae laws can be deduced by graphical mehods. If we rewrie he firs-order concenraion-ime equaion in a slighly differen form, i can be idenified as he equaion of a sraigh line. ln[ A] = -k+ ln[a y ] o = mx + b 38 Graphing Kineic Daa In addiion o he mehod of iniial raes, discussed earlier, rae laws can be deduced by graphical mehods. If we rewrie he firs-order concenraion-ime equaion in a slighly differen form, i can be idenified as he equaion of a sraigh line. This means if you plo ln[a] vs. ime you will ge a sraigh line for a firs-order reacion. 39

14 Plo of log [N ] versus ime. Time (s) [N ] log[n ] N O5(g) fi 4NO(g) + O(g) The figure displayed shows a plo of log [N ] a various imes during he decomposiion reacion. The fac ha he poins lie on a sraigh line is confirmaion ha he rae law is firs order. Graphing Kineic Daa In addiion o he mehod of iniial raes, discussed earlier, rae laws can be deduced by graphical mehods. If we rewrie he second-order concenraion-ime equaion in a slighly differen form, i can be idenified as he equaion of a sraigh line. 1 [A] = k+ 1 [A ] o y = mx + b 4

15 Graphing Kineic Daa In addiion o he mehod of iniial raes, discussed earlier, rae laws can be deduced by graphical mehods. If we rewrie he second-order concenraion-ime equaion in a slighly differen form, i can be idenified as he equaion of a sraigh line. This means if you plo 1/[A] vs. ime you will ge a sraigh line for a second-order reacion. The nex slide illusraes he graphical mehod of deducing he order of a reacion. 43 Ploing he daa for he decomposiion of nirogen dioxide a 330 C. Time (s) (A) log[no ] (B) 1/[NO ] NO(g) fi NO(g)+ O(g) Plo of log [NO ] agains ime. Noe ha a sraigh line does no fi he poins well.

16 Plo of 1/[NO ] agains ime. Noe how closely he poins follow he sraigh line, indicaing ha he decomposiion is second order. Operaional Skills Using he concenraion-ime equaion for firs-order reacions Relaing he half-life of a reacion o he rae consan Time for a few review quesions