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 differential method The differential methods use the differential rate equation to determine the order of the reaction (1) The attempt method: (Trial and error) 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] (Trial and error) The differential methods use the differential rate equation to determine the order of the reaction. §9.4 Determination of the reaction order 9.4.1 differential method
89.4 Determination of the reaction order 9.4.1 differential method Table I kinetic data for C2 HSONa+ 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]/ moldm-3 102 [B] / moldm-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 Determination of the reaction order 9.4.1 differential method
89.4 Determination of the reaction order 9.4.1 differential method 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 , =1 =1 103 3.642 3.678 3.760 3.773 3.731 3.729 §9.4 Determination of the reaction order 9.4.1 differential method
89.4 Determination of the reaction order 9.4.1 differential method Partial order method r=kc If no linear relation can be observed adjust the value of B and y until a line can Inr=In k+aNca +BIncB+rInc be obtained The slope of this line is a and the corresponding value of B and y can be obtained simultaneousl Inr=In k+a(nCA+IncB+=Incc) To plot Inr versus Inc. if a linear relation can obtained, B=0,y=0 Is it a trial and el
Partial order method A B C a r kc c c = A B C ln ln ln ln ln r k c c c = + + + A B C ln ln (ln ln ln ) r k c c c = + + + 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. Is it a trial and error? §9.4 Determination of the reaction order 9.4.1 differential method
89.4 Determination of the reaction order 9.4.1 differential method Comment: Trial and error 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: Trial and error §9.4 Determination of the reaction order 9.4.1 differential method
89.4 Determination of the reaction order 9.4.1 differential method Graphic method Use the differential form of the rate 7.0 equation to determine the order of the reaction 三四 kc" Inr=Ink+nInc Table 4 decomposition of CH, CHO-CH+CO. 5.5 3.8 4.0 4.6 4.8 Decomposition 0 5 10 15 20 InC/ mol dm-3 r/ Pa- min 1137994898478656852nr=-1.593+1865lnc Decomposition 25 30 45 Linear correlation coefficient: 0.998 r/Pa- min 62525745500041463560
Use the differential form of the rate equation to determine the order of the reaction. dc n r kc dt = − = ln ln ln r k n c = + Graphic method Decomposition % 0 5 10 15 20 r / Pamin-1 1137 998.4 898.4 786.5 685.2 Decomposition % 25 30 35 40 45 r / Pamin-1 625.2 574.5 500.0 414.6 356.0 Table 4 decomposition of CH3CHO→CH4+CO. ln r = -1.593 + 1.865 lnc Linear correlation coefficient: 0.998 §9.4 Determination of the reaction order 9.4.1 differential method
89.4 Determination of the reaction order 9.4.1 differential method (2) Calculation method Inr=Inktnlnc Decomposition %o 0 5 10 15 20 r/ Pa minl l137998489847865685.2 Inr=InktnInc Decomposition %o 25 30 35 40 45 In r/ Pa minI 62525745500.04146356.0 H=2534;1.952;2.327;2274 ∴nt=2.272≈2 Ino What kind of rate do we use?
(2) Calculation method ln ' ln ln ' r k n c = + ln ln ln r k n c = + ln ' ln ' t r r n c c = 0 0 0 0 ln ' ln ' C r r n c c = Decomposition % 0 5 10 15 20 r / Pa min-1 1137 998.4 898.4 786.5 685.2 Decomposition % 25 30 35 40 45 r / Pa min-1 625.2 574.5 500.0 414.6 356.0 nt= 2.534; 1.952; 2.327; 2.274 nt = 2.272 2 §9.4 Determination of the reaction order 9.4.1 differential method What kind of rate do we use?
89.4 Determination of the reaction order 9.4.1 differential method C 0,1 C 03 C 3 Determination of reaction order through one Determination of reaction order through several experimen parallel experiments Reaction order with respect to time: n, Reaction order with respect to concentration: nc Inr=Ink+nInc Inr_o=In k+nIn co 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
0 0 ln ln ln t r k n c = = + Determination of reaction order through several parallel experiments. Reaction order with respect to concentration: nC c c0,1 t c0,2 c0,3 r0,1 r0,2 r0,3 Determination of reaction order through one experiment. Reaction order with respect to time: nt c c1 c2 c3 c4 t1 t2 t3 t4 t r1 r2 r3 r4 ln ln ln r k n c = + 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. §9.4 Determination of the reaction order 9.4.1 differential method