§9.4 Determination of the reaction order

r = k [A][B] [C]  Whenever we determine the order of a reaction, we can write out the rate equation of the reaction and tell the detail of the kinetic characteristics of the reaction according to the rate equation. Otherwise, the rate equation can provide useful information about the mechanism of the reaction. Therefore, determination of the order of the reaction is a work of great importance. Integration method Differential method Partial order method Isolation method Methods for determination of reaction order

4.1 Integration methods The integration methods are to use the integrated rate equation to determine the order of the reaction. Integration methods includes: 1) attempt method (trial-and–error ) 2) graphic method 3) half-life method

r = k[C2H5ONa][C2H5(CH3)2SI] The attempt method: the values of k can be calculated from the selected integrated equation from a knowledge of initial concentration (c0) and the concentration at various time intervals (c). If the reaction is of the selected order of reaction, the k at different intervals thus obtained should be the same. C2H5ONa + C2H5(CH3)2SI  NaI + C2H5O C2H5 + S(CH3)2 r = k[C2H5ONa][C2H5(CH3)2SI] A + B  P r = k [A][B]

Table 1 kinetic data for C2H5ONa + C2H5(CH3)2SI reaction at 337.10 K t/s 102[A]/ moldm-3 102[B] / moldm-3 9.625 4.920 720 8.578 3.878 1200 8.046 3.342 1800 7.485 2.783 2520 6.985 2.283 3060 6.709 2.005 3780 6.386 1.682  4.704

r = k[C2H5ONa][C2H5(CH3)2SI] Table2 k of the reaction of different order ,  =0 =1 =2 =0 =1 =2 105 104 103 1.454 1.599 3.313 1.764 7.579 3.642 720 1.108 1.143 3.088 1.604 7.357 3.678 1200 0.935 1.205 3.051 1.550 10.02 3.760 1800 1.042 0.960 2.751 1.333 10.93 3.773 2520 0.511 0.747 2.405 1.093 11.11 3.731 3060 0.449 0.685 2.440 13.32 3.729 k t Therefore, the rate equation is: r = k[C2H5ONa][C2H5(CH3)2SI]

Comment: The attempt method is a laborious method For reaction without simple order, it is impossible to ascertain reaction order using this method. the experimental error may cause confusion sometimes.

2) The graphic method The linear relationship of reaction with different order is different. order Linear relationship zeroth c ~ t first lnc ~ t second 1/c ~ t third 1/c2 ~ t

r = k[A] The rate equation of A  P can be expressed as Table 3 kinetic data for A  P. t / s c / moldm-3 1.000 3000 0.050 500 0.606 3500 0.030 1000 0.368 4000 0.018 1500 0.223 4500 0.011 2000 0.135 5000 0.007 2500 0.082

3) half-life method S = 1 (1n) = 1, n = 2 the half-life of a reaction is proportional to the initial concentration of the reactant Graphic method S = 1 (1n) = 1, n = 2 Therefore, the reaction is of second order.

Calculation method NH4OCN  CO(NH2)2 n1 = 2.051, n2 = 2.019 c0/moldm-3 0.05 0.10 0.20 t1/2/h 37.03 19.15 9.45 n1 = 2.051, n2 = 2.019 n = 2.035  2

4.2 differential method Graphic method Use the differential form of the rate equation to determine the order of the reaction. Graphic method Table 4 decomposition of CH3CHOCH4+CO. Decomposition % 5 10 15 20 r / Pamin-1 1137 998.4 898.4 786.5 685.2 25 30 35 40 45 625.2 574.5 500.0 414.6 356.0

ln r = -1.593+1.865 lnc Linear fitting results: Linear correlation coefficient: 0.998 Therefore, the order of the reaction is 2.

c c1 c2 c3 c4 t1 t2 t3 t4 t r1 r2 r3 r4 c c0,1 t c0,2 c0,3 r0,1 r0,2 r0,3 Determination of reaction order through several parallel experiments. Determination of reaction order through one experiment. Reaction order with respect to time: nt Reaction order with respect to concentration: nC The method of initial rates is applicable of a wide variety of reactions and is particularly useful in reactions that are complicated by processes involving intermediate or products.

Calculation method nt= 2.534; 1.952; 2.327; 2.274  nt = 2.272  2 Decomposition % 5 10 15 20 r / Pa min-1 1137 998.4 898.4 786.5 685.2 25 30 35 40 45 625.2 574.5 500.0 414.6 356.0 nt= 2.534; 1.952; 2.327; 2.274  nt = 2.272  2

r = k[A][B][M] n = + +  Table 5 relationship between nC and nt. nc = nt Both intermediate and product do not affect the reaction > nt Intermediate or product catalyze the reaction < nt Intermediate or product inhibit the reaction r = k[A][B] n = +  r = k[A][B][M] n = + + 

4.3 Partial order method To plot lnr versus lncA, if a linear relation can obtained,  = 0,  = 0. If no linear relation can be observed, adjust the value of  and  until a line can be obtained. The slope of this line is , and the corresponding value of  and  can be obtained simultaneously.

4.4 Isolation method Three methods: When cB and cC were controlled Fixation of concentration method; Excess concentration method; Application of stoichiometric ratio

1) Fix the concentration of other reactants Rate equation of 2NO + 2H2  N2 + 2H2O is r = k[NO] [H2]. No. Initial pressure / Pa Initial rate NO H2 1 50662.5 20265 486.36 2 10132.5 243.18 3 25331.25 121.59

2) Excess concentration C12H22O11 + H2O  C6H12O6 + C6H12O6 In excess concentration method, the concentration of B and C is made very much larger than that of A。 This technique is particularly useful in determining rate constants for reactions involving water in aqueous solution. Pseudo order reaction.

3) Using stoichiometric ratio aA + bB  P Initial concentration 1 b/a Conversion concentration x bx/a Residual concentration 1-x (b/a)(1-x) r = k[A] [B] = k (b/a)(1-x)+ = k(b/a)(1-x)n Other methods: Unit of k Dependence of t1/2 on c0