山东大学：《物理化学》课程教学资源（讲义资料）9.4 Determination of reaction order-for students

89.4 Determination of the reaction order

§9.4 Determination of the reaction order c c0,1 t c0,2 c0,3 r0,1 r0,2 r0,3

89.4 Determination of the reaction order Significance r=k[AjaB]ICY Integration methods Once we determine the order of a reaction we can write out the rate Differential methods equation of the reaction and tell the details of the kinetic characteristics of the methods reaction according to the rate equation Partial order methods Otherwise, the rate equation can provide useful information about the mechanism of the reaction Isolation methods Therefore. determination of the order of the reaction is a work of great importance

r = k [A][B]  [C]  Once we determine the order of a reaction, we can write out the rate equation of the reaction and tell the details 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. Significance §9.4 Determination of the reaction order methods Integration methods Differential methods Partial order methods Isolation methods

89.4 Determination of the reaction order 9.4.1 Integration methods--trial and error The integration methods are to use the integrated rate equation to determine the order of the reaction (1)The attempt method C2 ONa+ C2HS(CH3)2SI>Nal+ C2HSOCHs + S(CH3)2 r=k[C2H, ONa]aC2 Hs(CH)2SI] A+B→>Pr=k[A][B] The values of k can be calculated from the selected integrated equation from a knowledge of initial concentration(co)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

(1) 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. A + B → P C2H5ONa + C2H5 (CH3 ) 2 SI → NaI + C2H5O C2H5 + S(CH3 ) 2 r = k[C2H5ONa][C2H5 (CH3 ) 2 SI] r = k [A][B] 9.4.1 Integration methods—trial and error The integration methods are to use the integrated rate equation to determine the order of the reaction. §9.4 Determination of the reaction order

89.4 Determination of the reaction order 9.4.1 Integration methods--trial and error Table I kinetic data for C2HS ONa+ CHs(CH3)2SI reaction at 337.10 K ts 10[A/ moldm-3 102B]/mol-dm-3 0 9.625 4.920 720 8.578 3.878 1200 8.046 3.342 1800 7485 2.783 2520 6985 2.283 3060 6.709 2.005 3780 6.386 1682 4.704 r=kA]B1B

t/s 102 [A]/ moldm-3 102 [B] / moldm-3 0 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 Table 1 kinetic data for C2H5ONa + C2H5 (CH3 ) 2 SI reaction at 337.10 K r = k [A][B] 9.4.1 Integration methods—trial and error §9.4 Determination of the reaction order

89.4 Determination of the reaction order 9.4.1 Integration methods--trial and error Table2 k of the reaction of different order CF1 0 =2 0 a=1 B B=1 0 2 B=1 104 104 103 103 0 1.454 1.599 3.313 1764 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 1.042 13.32 3.729 Therefore, the rate equation is: r=KICH ONallC2Hs(CH3)2sI

=0 =1 =0 =2 =0 =1 =0 =0 =1 =0 =2 =1 105 104 104 103 103 103 0 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 1.042 13.32 3.729 Table2 k of the reaction of different order r = k[C2H5ONa][C2H5 (CH3 ) 2 Therefore, the rate equation is: SI] k t ,  9.4.1 Integration methods—trial and error §9.4 Determination of the reaction order =1 =1 103 3.642 3.678 3.760 3.773 3.731 3.729

89.4 Determination of the reaction order 9.4.1 Integration methods--trial and error Comment: 1) It is a rather laborious method 2) For reaction without simple order, it is impossible to ascertain reaction order using this method 3)the experimental error may cause confusion sometimes

1) It is a rather laborious method 2) For reaction without simple order, it is impossible to ascertain reaction order using this method. 3) the experimental error may cause confusion sometimes. Comment: 9.4.1 Integration methods—trial and error §9.4 Determination of the reaction order

89.4 Determination of the reaction order 9.4.1 Integration methods--graphic method (2)The graphic method The rate equation ofa-> Pcan be expressed as r=kaja The linear relationship of reactions with different orders are different Table 3 kinetic data for A-P t/s c/moldm t/s c/ moldm Reaction order Linear relationship 0 1.000 3000 0.050 zeroth 500 0.606 3500 0.030 first Inc t 1000 0.368 4000 0.018 1500 0.223 4500 0.0 second 1/ct 2000 0.135 5000 0.007 third 1/c2~t 2500 0.082

(2) The graphic method The linear relationship of reactions with different orders are different. Reaction order Linear relationship zeroth c ~ t first lnc ~ t second 1/c ~ t third 1/c 2 ~ t 9.4.1 Integration methods—graphic method §9.4 Determination of the reaction order Table 3 kinetic data for A → P. The rate equation of A → P can be expressed as r = k[A] t / s c / moldm-3 t / s c / moldm-3 0 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

89.4 Determination of the reaction order 9.4.1 Integration methods--graphic method 010002000300040005000 10002000300040005000 t/s t/s For certain conclusion the reaction should be 040 studied in a wide time range 01000200030004000 010002000300040005000

0 1000 2000 3000 4000 5000 0.0 0.2 0.4 0.6 0.8 1.0 C / mol dm-3 t / s 0 1000 2000 3000 4000 5000 -5 -4 -3 -2 -1 0 ln (C / mol dm-3) t / s 0 1000 2000 3000 4000 5000 0 40 80 120 160 1/ C(/ mol dm-3) t / s 0 1000 2000 3000 4000 5000 0 20 40 60 80 100 1 / C2 t / s For certain conclusion, the reaction should be studied in a wide time range. 9.4.1 Integration methods—graphic method §9.4 Determination of the reaction order

89.4 Determination of the reaction order 9.4.1 Integration methods--half-life method Graphic method (3)half-life method 10 the half-life of a reaction is proportional to the initial concentration of the reactant n 1/2 Int=In k+(l-n)Inc In C S=-1

(3) half-life method the half-life of a reaction is proportional to the initial concentration of the reactant 1 1/ 2 0 n t kc − = 1/ 2 0 ln ln (1 )ln t k n c = + − S = −1 Graphic method (1−n) = −1, n = 2 9.4.1 Integration methods—half–life method §9.4 Determination of the reaction order

89.4 Determination of the reaction order 9. 4.1 Integration methods-half-life method Calculation method NH4OCN→>CO(NH2)2 Intu2=In k+(1-n)Inc Co/mold 0.05 0100.20 Intv2 =Ink+(l-n)Inco tun/h 370319.159.45 41/2 n=1 n1=2051,m2=2.019 n=2.035≈2 The half-life of the reaction reduces with Increasing the initial concentration

1/ 2 0 ln ln (1 )ln t k n c = + − Calculation method 1/ 2 0 ln ' ln (1 )ln ' t k n c = + − 1/ 2 1/ 2 0 0 ln ' 1 ln ' t t n c c = − c0 /moldm-3 0.05 0.10 0.20 t1/2/h 37.03 19.15 9.45 NH4OCN → CO(NH2 )2 n1 = 2.051, n2 = 2.019 n = 2.035  2 9.4.1 Integration methods—half –life method §9.4 Determination of the reaction order The half-life of the reaction reduces with increasing the initial concentration