9.4 Determination of the reaction order

Transcription

1 0,1 0,2 0,3 r 0,1 r 0,2 r 0,3 t

2 Signifiane r = k [A] [B] [C] One we determine the order of a reation, we an write out the rate equation of the reation and tell the details of the kineti harateristis of the reation aording to the rate equation. Otherwise, the rate equation an provide useful information about the mehanism of the reation. Therefore, determination of the order of the reation is a work of great importane.

3 1) Integration method (1) attempt method (trial-and error ) (2) graphi method Methods for determination of reation order 2) Differential method 3) Partial order method (3) half-life method (1) Graphi method (2) Calulation method 4) Isolation method

4 9.4.1 Integration methods The integration methods are to use the integrated rate equation to determine the order of the reation. (1) The attempt method: C 2 H 5 ONa + C 2 H 5 (CH 3 ) 2 SI NaI + C 2 H 5 O C 2 H 5 + S(CH 3 ) 2 r = k[c 2 H 5 ONa] [C 2 H 5 (CH 3 ) 2 SI] A + B P r = k [A] [B] The values of k an be alulated from the seleted integrated equation from a knowledge of initial onentration ( 0 ) and the onentration at various time intervals (). If the reation is of the seleted order of reation, the k at different intervals thus obtained should be the same.

5 Table 1 kineti data for C 2 H 5 ONa + C 2 H 5 (CH 3 ) 2 SI reation at K t/s 10 2 [A]/ mol dm [B] / mol dm

6 Table2 k of the reation of different order, =0 =1 =0 =2 =0 =1 t k =0 =0 =1 =0 =2 = Therefore, the rate equation is: r = k[c 2 H 5 ONa][C 2 H 5 (CH 3 ) 2 SI]

7 Comment: 9.4 Determination of the reation order 1) It is a rather laborious method 2) For reation without simple order, it is impossible to asertain reation order using this method. 3) the experimental error may ause onfusion sometimes.

8 9.4.1 Integration methods (2) The graphi method The linear relationship of reation with different order is different. order zeroth first seond third Linear relationship ~ t ln ~ t 1/ ~ t 1/ 2 ~ t

9 The rate equation of A P an be expressed as Table 3 kineti data for A P. r = k[a] t / s / mol dm -3 t / s / mol dm

10 C / mol dm ln (C / mol dm -3 ) t / s 100 t / s 1/ C(/ mol dm -3 ) / C t / s t / s For ertain onlusion, the reation should be studied in a wide time range.

11 (3) half-life method the half-life of a reation is proportional to the initial onentration of the reatant t k n ln t ln k (1 n)ln 1 1/ 2 0 1/ 2 0 ln t 1/ lnc 0 Graphi method S = 1 (1 n) = 1, n = 2 Therefore, the reation is of seond order.

12 Calulation method ln t ln k (1 n)ln 1/ 2 0 ln t ' ln k (1 n) ln ' 1/ 2 0 n 1 t ln t ' ln 1/ 2 1/ ' NH 4 OCN CO(NH 2 ) 2 0 /mol dm t 1/2 /h n 1 = 2.051, n 2 = n =

13 9.4.2 differential method Use the differential form of the rate equation to determine the order of the reation. r 9.4 Determination of the reation order d dt n ln ln ln k (1)Graphi method r k n Table 4 deomposition of CH 3 CHO CH 4 +CO. Deomposition % r / Pa min Deomposition % r / Pa min

14 lnr / Pa min Linear fitting results: ln r ln k nln lnc / mol dm -3 ln r = ln Therefore, the order of the reation is 2. Linear orrelation oeffiient: 0.998

15 9.4 Determination of the reation order 0, r 1 r 2 0,2 0,3 r 0,1 r 0,2 r 3 r 4 r 0,3 t 1 t 2 t 3 t 4 t Determination of reation order through one experiment. Reation order with respet to time: n t ln r ln k nln Determination of reation order through several parallel experiments. Reation order with respet to onentration: n C ln r t ln k nln 0 0 The method of initial rates is appliable of a wide variety of reations and is partiularly useful in reations that are ompliated by proesses involving intermediate or produts. t

16 (2) Calulation method ln r ln k nln ln r ' ln r ' ln k nln ' n t ln r ' Deomposition % r / Pa min Deomposition % r / Pa min n C ln ln r r ' ' n t = 2.534; 1.952; 2.327; n t =

17 Table 5 relationship between n C and n t. = n t Both intermediate and produt do not affet the reation n > n t Intermediate or produt atalyze the reation < n t Intermediate or produt inhibit the reation r = k[a] [B] r = k[a] [B] [M] n = + n = + +

18 9.4.3 Partial order method r k a A B C ln r ln k ln ln ln A B C ln r ln k (ln A ln B ln C) To plot lnr versus ln A, if a linear relation an obtained, = 0, = 0. If no linear relation an be observed, adjust the value of and until a line an be obtained. The slope of this line is, and the orresponding value of and an be obtained simultaneously.

19 9.4.4 Isolation method ln r ln k ln ln ln A B C ln r ' ln k ln ln ln ' A B C When B and C were ontrolled Three methods: ln 1) Fixation of onentration method; 2) Exess onentration method; 3) Appliation of stoihiometri ratio r r ' ln ' A A

20 9.4.4 Isolation method (1) Fix the onentration of other reatants Rate equation of 2NO + 2H 2 N 2 + 2H 2 O is r = k[no] [H 2 ]. No. Initial pressure / Pa NO H 2 Initial rate

21 9.4.4 Isolation method (2) Exess onentration C 12 H 22 O 11 + H 2 O C 6 H 12 O 6 + C 6 H 12 O 6 r k[c12h 22O 11][H2O] r k'[c H O ] In exess onentration method, the onentration of B and C is made very muh larger than that of A This tehnique is partiularly useful in determining rate onstants for reations involving water in aqueous solution. Pseudo order reation.

22 9.4.4 Isolation method (3) Using stoihiometri ratio aa + bb P Initial onentration 1 b/a Conversion onentration x bx/a Residual onentration 1-x (b/a)(1-x) r = k[a] [B] = k (b/a) (1-x) + = k(b/a) (1-x) n

23 9.4.5 Other methods: 1) Unit of k 2) Dependene of t 1/2 on 0

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