9.4 Determination of the reaction order

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

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

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. methods Integration methods Differential methods Partial order methods Isolation methods

3 9.4.1 Integration methods trial and error The integration methods are to use the integrated rate equation to determine the order of the reation. (1) The attempt method: C 2 ONa + C 2 (CH 3 ) 2 SI NaI + C 2 O C 2 + S(CH 3 ) 2 r = k[c 2 ONa] [C 2 (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.

4 9.4.1 Integration methods trial and error Table 1 kineti data for C 2 ONa + C 2 (CH 3 ) 2 SI reation at K t/s 10 2 [A]/ mol dm [B] / mol dm r = k [A] [B]

5 9.4.1 Integration methods trial and error Table2 k of the reation of different order, k t =0 =1 =0 =2 =0 =1 =0 =0 =1 =0 =2 = Therefore, the rate equation is: r = k[c 2 ONa][C 2 (CH 3 ) 2 SI]

6 9.4.1 Integration methods trial and error Comment: 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.

7 9.4.1 Integration methods graphi method (2) The graphi method The linear relationship of reation with different order is different. The rate equation of A P an be expressed as r = k[a] Table 3 kineti data for A P. Reation order zeroth first seond third Linear relationship ~ t ln ~ t 1/ ~ t 1/ 2 ~ t t / s / mol dm -3 t / s / mol dm

8 9.4.1 Integration methods graphi method C / mol dm ln (C / mol dm -3 ) t / s t / s / C 2 80 For ertain onlusion, the reation should be studied in a wide time range. 1/ C(/ mol dm -3 ) t / s t / s

9 9.4.1 Integration methods half life method (3) half-life method the half-life of a reation is proportional to the initial onentration of the reatant t k n 1 1/ 2 0 Graphi method ln t ln k (1 n)ln 1/ 2 0 S = 1 (1 n) = 1, n = 2

10 9.4.1 Integration methods half life method Calulation method ln t ln k (1 n)ln 1/ 2 0 ln t ' ln k (1 n) ln ' n 1 1/ 2 0 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 =

11 9.4.2 differential method Use the differential form of the rate equation to determine the order of the reation. r d dt n k ln ln ln r k n (1) Graphi method Table 4 deomposition of CH 3 CHO CH 4 +CO. Deomposition % r / Pa min Deomposition % r / Pa min ln r = ln Linear orrelation oeffiient: 0.998

12 9.4.2 differential method (2) Calulation method ln r ln k nln ln r ' ln k nln ' Deomposition % r / Pa min Deomposition % r / Pa min n t ln ln r r ' ' n C ln ln r r ' ' n t = 2.534; 1.952; 2.327; n t =

13 9.4.2 differential method r 1 r 2 r 3 r 4 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 0,1 r 0,1 0,2 r 0,2 0,3 r 0,3 Determination of reation order through several parallel experiments. Reation order with respet to onentration: n C ln r t ln k nln 0 0 t 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.

14 9.4.2 differential method Table 5 relationship between n C and n t. r = k[a] [B] n = + r = k[a] [B] [M] n = + + Deomposition of N 2 O over Ag for treatment of exhaust of mobile: r k[n2o] 1 b [O ] 2 = n t n > n t < n t

15 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) 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. To plot lnr versus ln A, if a linear relation an obtained, = 0, = 0.

16 9.4.4 Isolation method ln r ln k ln ln ln A B C ln r ' ln k ln ln ln When B and C were ontrolled ln r r ' ln Three methods: ' A B C ' 1) Fixation of onentration method; 2) Exess onentration method; 3) Appliation of stoihiometri ratio A A (1) Fix the onentration of other reatants Rate equation of 2NO + 2H 2 N 2 + 2H 2 O is r = k[no] [H 2 ]. Initial pressure / Pa No. NO H 2 Initial rate

17 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'[c12 H22O 11] 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. (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 Other methods: 1) Unit of k 2) Dependene of t 1/2 on 0

18 1) Integration method (1) attempt method (trialand 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 (1) fix other onentration 4) Isolation method (2) Exess onentration (3) With speial ratio

9.4 Determination of the reaction order

9.4 Determination of the reaction order 0,1 0,2 0,3 r 0,1 r 0,2 r 0,3 t 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