9.2 Reaction rate and rate equation

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2 9.2.1 Expession of eaction ate The ate () of a chemical eaction is defined as the concentation change of a eactant o a poduct pe unit time. mean ate [A] c c = t t t c c 1 instantaneous ate: Physical meaning: d[a] c 2 c t 1 t 2 t the slope of the [A] ~ t cuve at time t. Initial instantaneous ate? t 1 t

3 9.2.1 expession of eaction ate N 2 N 2 + 3H 2 == 2NH 3 dcn dch dc 2 2 NH3 H 2 NH 3 It is appaent that N H NH When expessed using diffeent species, the ate of the eaction may attain diffeent values, which is not convenient and sometimes may even cause confusion.

4 9.2.1 expession of eaction ate Definition: extent of eaction o advancement () n i i,0 i n whee i is the stoichiometic coefficient of the eaction. Definition: aa + bb gg + hh The tue ate of the eaction o ate of convesion (J): J d Unit?

5 Fo geneal eaction: aa + bb gg + hh When the extent of eaction is d dn dn dn dn d a b g h J 9.2 Reaction ate and ate equation expession of eaction ate A B G H d 1 dn 1 dn 1 dn 1 dn a b g h A B G H When the eaction takes place in a containe with constant volume Define ate J V

6 9.2.1 expession of eaction ate J d 1 a dn 1 b dn 1 g dn A B G 1 h dn H 1 a d[a] 1 b d[a] 1 g d[g] 1 h d[h] 1 d[ c i Unit: mol m -3 s -1 i ]

7 9.2.2 measuement of eaction ate 1 i d[ c i ] Physical meaning: slope of the c ~ t cuve kinetic cuve c Initial ate dc t0 Rate at any time dc tt t = 0 t = t t The key subject of kinetic study is to measue the concentation of some species afte abitay time intevals.

8 9.2.2 measuement of eaction ate The concentation of the species can be measued using eithe chemical o physical methods. Fo example: CH 3 COOC 2 H 5 + NaOH CH 3 COONa + C 2 H 5 OH The eaction can be stopped by emoving of CH 3 COOC 2 H 5, and the consumption of NaOH can be detemined by chemical titation.

9 9.2.2 measuement of eaction ate The change in physical popeties of the eaction system which elates to the concentation of eactants o poducts can be usually chosen as indicato of the pogess of the eaction. The fist successful example fo measuing concentation of eactant physically was made by Wilhelmy in He detemined the esidual concentation of sucose by measuing the change of the otation angle of a beam of plane-polaized light passing though the hydolysis solution (optical activity).

10 9.2.2 measuement of eaction ate Ludwig Fedinand Wilhelmy (Dec. 25, 1812, Feb. 18, 1864) was a Geman scientist who is usually cedited with publishing the fist quantitative study in chemical kinetics 1850, Wilhelmy's wok in chemical kinetics concened the acid-catalyzed convesion of a sucose solution into a 1:1 mixtue of fuctose and glucose, a eaction that he followed with a polaimete. He wote a diffeential equation to descibe the eaction, integated it, and used it to intepet his expeimental esults. [3] Wilhelmy found that the eaction's ate was popotional to the concentations of sucose and of acid pesent.

11 9.2.2 measuement of eaction ate C 12 H 22 O 11 + H 2 O C 6 H 12 O 6 + C 6 H 12 O 6 sucose glucose fuctose Substance sucose glucose fuctose [] 25 D o +52 o - 92 o [] 66.5 The otation angle of the 1:1 mixtue of glucose and fuctose [] 1 is 20 o [] 2 We still use in it in ou physical 20 t 1 t 2 t chemisty laboatoy

12 9.2.2 measuement of eaction ate CH 3 COOC 2 H 5 + NaOH CH 3 COONa + C 2 H 5 OH the ate of which can be monitoed using ph mete o conductomete. N 2 O 5 = N 2 O O 2 When this eaction takes place in a containe with constant volume, the ate of the eaction can be monitoed by measuing the pessue change. And when this eaction takes place unde constant pessue, the advance of the eaction can be monitoed by measuing the volume incease. dilatomete.

13 9.2.2 measuement of eaction ate FTIR spectoscopy Stetch of epoxy goup

14 9.2.2 measuement of eaction ate The physical paametes usually used fo monitoing eaction pocess includes volume, pessue, electic conductance, ph, efactive index, themal conductivity, polaimety, spectomety, chomatogaphy, etc. Analyzing methods: 1) Static method 2) Flow method 1) Real time analysis 2) Quenching All the above methods ae valid only fo eactions with half-lives of at least a few seconds, i.e., slow eaction. Fo fast eaction of halflives anging between 10 0 ~ s, special methods ae equied.

15 9.2.2 measuement of eaction ate Flow method Mixe detecto Moving diection Stable flow: l t Difficulties in study on kinetics

16 Bainstom: List the factos that affect eaction ate. Concentation Tempeatue Catalyst Othe molecules Solvent: viscosity, density, polaity, pemeativity, Pessue Solvent Radiation: Field:

17 9.2.3 Rate equation and the law of mass action The concentation-dependence of ate: = (c i ) = (c A, c B, c C ) Whee c i epesents concentation of individual specie pesent in ate equation. In many instances, the ate of a eaction is popotional to the concentations of the eactants aised to some powe. dc A kc A c B c C ate equation Rate law

18 9.2.3 Rate equation and the law of mass action Fo example: k[h ] [I ] H 2 + I 2 = 2 HI H 2 + Cl 2 = 2 HCl k[h 2] [Cl 2] dc A kc c c A B C Whee ate coefficient/constant (k) is a popotionality constant /coefficient independent of concentation. The exponent shows the effect of concentation on the eaction ate. In 1895, Noyes defined them as patial ode of the eactant.

19 9.2.3 Rate equation and the law of mass action, is the patial ode of the eaction with espect to A o B, espectively k[h 2] [Cl 2] This implies that the eaction obeying ate law is fist-ode in H 2 and 0.5-ode in Cl 2. the sum of the patial ode n = is the oveall ode of the eaction, o moe simply, the eaction ode k[h 2] [Cl 2] The oveall ode is 1.5.

20 9.2.3 Rate equation and the law of mass action 2SO 2 + O 2 2SO 3 d[so ] k[so 2][SO 3] is fist-ode in SO 2, -0.5-ode in SO 3 and 0.5 ode oveall. n,,,, etc., diffeent fom the stoichiometic coefficient, may be integes, decimals, of plus o minus values. Rate law must be detemined fom measuements of eaction ate and cannot be deduced fom the eaction stoichiomety.

21 9.2.3 Rate equation and the law of mass action Fo elementay eaction, = a, = b, etc. dc A A kcacb cc dc kc c c a b c A B C Patial ode = stoichiometic coefficient Reaction ode = numbe of molecules involved in the eaction Fo example: 2I + H 2 = 2HI 1 d[i] k 2 2 [I] [H 2] Law of mass action valid only fo elementay eaction

22 An execise 2A k 1 k 3 k 2 B + C D k 4 E d [A] d [B] d [C] d [D] d [E]

23 Goup wok-1: Wite the diffeential fom of ate equation and deduce the integation ate equations of eactions with simple odes. A membe of a chosen goup will be asked to deduce the equation on blackboad this Thusday.