4. CHEMICAL KINETICS

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1 4. CHEMICAL KINETICS Synopsis: The study of rtes of chemicl rections mechnisms nd fctors ffecting rtes of rections is clled chemicl kinetics. Spontneous chemicl rection mens, the rection which occurs on it s own without ny externl regent. A spontneous chemicl rection my be slow or fst (instntneous). For spontneous rection ΔG = ve. Spontneity dels with fesibility. Bsed on the speed of rections, the chemicl rections re of 3 types. i) Very slow rections: Ex. Rusting of iron, Formtion of H O from H nd O t room temperture] ii) Very fst rections ( instntneous rections) : ) Dischrge of pink color of KMnO 4 by oxlic cid in cid medium. b) H + F sun light HF c) H + Cl sun light HCl Al ionic rections nd neutrlistion rections re fst. iii) Slow rections: These rections occur with optimum speeds. Rtes of very slow nd very fst rections cn not be determined. Rte of these slow rections cn be mesured Ex: ) H O H O + O b) N O 5 N O 4 + O c) CH 3 COOC H 5 + NOH CH 3 COON + C H 5 OH Rection rte or rte of rection: The chnge in concentrtion per unit time is clled rte of rection. Unit of rte of rection : mol. lit.sec. Rte of rection cn be expressed with respect to rectnts or products. dc Rte = (-sign indictes decrese in the concentrtion of rectnts) dc Rte = + (+sign indictes increse in the concentrtion of products) The rte of rection will not remin constnt nd it chnges with time. Averge rte of rection is the rte of rection mesured in long time intervl. Instntneous rte of rection is the rte of rection mesured in infinitesimlly smll time intervl. For rection A B grphicl representtion of rte is s follows. The rte rection chnges with time exponentilly. Concentrtion O Time [B] [A] No rection tkes plce uniformly through out the course of the rection. Expressing the rte of rection: Generl eqution : ma + nb pc + qd d A d B d C Rte of rection = = = + m n p [ ] [ ] [ ] d[ D] = + q

2 Exmple : ) N O 5 4NO + O d N O5 d NO rte = = + 4 = [ ] [ ] d[ O ] + = [ N O ] d[ NO ] d[ O ] d 5 = ) SO + O SO 3 d SO d O rte = = = = [ ] [ ] d[ SO ] + 3 = [ SO ] d[ O ] d[ SO ] d 3 = = + The decrese in the concentrtion of the rectnt per unit time or increse in the concentrtion of the product per unit time is clled rte of the rection. The rtes of chemicl rections differ form one nother, since the number nd the nture of the bonds re different in the different substnces (rectnts products or both) A B d [ A ] d [ B ] rte = = + The unit for the rte of the rection is moles lit sec. N + O NO rte = rte= [ N ] d[ O ] d[ NO] d = = (or) [ ] d[ O ] d[ NO] = = + d N pp + qq rr + ss d P the rte = = p q d[] s = + s [ ] d[ Q] d[ R] = + r The rte of the rection mesured with respect to the decrese in the concentrtion of the rectnts decreses. The rte of the rection mesured with respect to the increse in the concentrtion of the products increses. The rte of rection t ny prticulr instnt of time during the course of rection is the rte of chnge of concentrtion of rectnt or product t tht instnt of time. The rte of the rection vries with time of the rection. The concentrtion of the rectnts in rection vries exponentilly with time. No rection tkes plce with uniform rte throughout the course of the rection. Fctors influencing rte of rection: ) Nture of the rectnts : The rte of rection depends on the nture of rectnts.

3 Rectnts which require less ctivtion energy rect fster thn the rectnts which require higher ctivtion energy. Ionic rections nd neutrlistion rections re very fst in solution s they involve simple exchnge of ions. Rections between covlent molecules re generlly slow s they involve shuffling of bonds. The rections which involve greter bond rerrngements re slow nd the rections involving lesser bond rerrngements re fst. Fst rections Slow rections i) H + + OH H O H O + O H O ii) NO + O NO CH 4 + O CO +H O ) Effect of concentrtion of rectnts : According to lw of mss ction, the rte of chemicl rection is directly proportionl to the product of concentrtion of rectnts. In cse of gseous rections, rte is directly proportionl to the product of prtil pressures of rectnts. If concentrtion is higher, the number of molecules per unit volume is, more nd the number of ctive collisions increses. According to collision theory, rte of rection increses with increse in the number of collisions. The dependence of rte of rection on the concentrtion of rectnts cn be mthemticlly expressed s dc = n k.c (n cn tke ny simple vlue including zero) 3) Effect of temperture : With increse in temperture rte of rection increses becuse the number of ctive collisions or ctivted molecules increses. According to Arhenious for most of the rections rte of rection doubles or triples for every 0 rise in temperture. Temperture coefficient (μ) = K T + 0 = (or) 3 K T Arhenious suggested simple empiricl reltion between specific rte nd temperture. E / RT K = A.e n K = n A E/RT.303 og K =.303 og A E /RT E og K = og A.303R T Plot of log k Vs T gives liner grph with ve slope. Log k slope = tnθ= E T 3

4 Slope gives the ctivtion energy nd intercept gives frequency fctor. 4) Effect of ctlyst : Ctlyst lters the speed of rection by chnging the ctivtion energy. Ctlyst lters the ctivtion energy by chnging the pth of the rection or mechnism of rection. A positive ctlyst increses the rte of rection by decresing the ctivting energy. In cse of some rections, rte is proportionl to the concentrtion of ctlyst. Ex : Acid ctlysed hydrolysis of ester. Absence of ctlyst P.E Presence of ctlyst O Rection co-ordinte A negtive ctlyst decreses the rte of rection by incresing the ctivtion energy. Enzymes re bioctlysts for biochemicl rections. P.E O Rection co-ordinte Presence of ve ctlyst Absence of ve ctlyst 4

5 5) Effect of rdition : Some chemicl rections tke plce very fst by bsorbing sunlight. Such chemicl rections re clled photoctlysed or photoccelerted or photosensitized rections. 6) Physicl stte of rectnts : In heterogeneous system, collisions re not much effective s tht of in homogeneous system. There fore rections re much fster in gseous nd liquid sttes. Rte of rection : Gseous stte > Liquid stte >Solid stte 7) Physicl size of rectnts; In cse of solids, rte increses with decrese in the size of prticle. Rte is fster in powdered stte thn tht of undivided stte becuse surfce re increses nd the possibility of contct between rectnt molecules increses. Rte lw nd rte constnt : The eqution which reltes the rte of the rection nd the concentrtion of the rectnts is known s rte eqution or rte lw. Rte eqution is written fter the experiment only. It is not relted to coefficients of rectnts in blnced eqution. Rte of rection does not depend on the rectnt if it s concentrtion is lrge excess. Isoltion methods re usully followed to study rte of the rection. na + mb products rte r α [A] n [B] m ; rte = K[A] n [B] m K is clled rte constnt or specific rte or rte per unit concentrtion of the rectnts. i) CH 3 COOC H 5(q) + NOH (q) CH 3 COON (q) + C H 5 OH (q)_ The rte eqution : K[CH 3 COOC H 5 ] [NOH] ii) H O H O + O rte α [H O ] iii) N O 5 N O 4 + O rte α [N O 5 ] iv) CH 3 COOC H 5 +H O CH 3 COOH + C H 5 OH rte α [ester] [H O] 0 v) CH 3 COOC H 5 +NOH CH 3 COON + C H 5 OH rte α [ester] [NOH] Order of the rection: The sum of the powers of the concentrtion terms of rectnts in the rte eqution is clled order of the rection. Order of rection my be zero or frction or negtive or whole number (n). Order of the rection cn be determined experimentlly. Moleculrity of the rection: 5

6 6 Chemicl Kinetics Moleculrity of rection is the number of rectnt molecules tking prt in rte determining step. A chemicl rection my tke plce in one or more steps. Different steps my proceed with different speeds. The slowest step is rte determining step. Moleculrity of simple rections is equl to the stoichiometric coefficients in blnced eqution. Moleculrity is theoreticl concept. Moleculrity is relted to mechnism of rection. Moleculrity is lwys whole number. Moleculrity cnnot be zero, ve, frctionl, infinite nd imginry. Generlly, moleclrity of rection cn not be greter thn three becuse more thn 3 molecules my not mutully collide with ech other. Exmples : i) H O H O + O uni moleculr ii) N O 5 N O 4 + O uni moleculr iii) PCl 5 PCl 3 + Cl uni moleculr iv) HI H + I Bimoleculr v) CH 3 COOH + C H 5 OH CH 3 COOC H 5 + H O Bimoleculr vi) C H O + H O C 6 H O 6 + C 6 H O 6 Bimoleculr vii) SO + O SO 3 Termoleculr viii) CO + O CO Termoleculr ix) FeCl 3 + SnCl SnCl 4 + FeCl Termoleculr Order of rection : zero, A products The concentrtion of rectnt decreses linerly with time. The rte of rection is uniform. The time required for the completion of rection is zero. Eqution for rte constnt : K o = t x. Units for rte constnt : moles lit sec. Hlf life : t / α. = initil conc. of the rectnts Exmples : H + Cl sun light HCl NH w ( or) 3 N + 3H M 0 HI Au H + I Order of rection : First A products r = k [A] eqution for rte constnt :

7 .303 k = log t x Units for rte constnt: sec The exponentil form of the bove eqution is, ( x) =.e kt x = ( e kt ) Hlf life : It is the time tken for 50% completion of rection or the time tken for concentrtion of rectnt to become hlf of it s initil vlue. For st order rections, t / is independent of initil concentrtion of rectnt. The concentrtion of the rectnt left fter n hlf lifes, ( x) = Rte constnt, k depends on the i) Nture of rectnt ii) Temperture of rection iii) Ctlyst Rte constnt, k is independent of i) Initil concentrtion of rectnt ii) Time Hlf life time : t / α t / = k Exmples :. N O5 NO4 + ( g) ( g) ( g) O. SO Cl (g) SO (g + Cl (g) 3. H O (q) H O (l) + O(g) 4. Acid hydrolysis of ester. CH 3 COOC H 5 + H O H + CH 3 COOH+C H 5 OH 5. NH 4 NO (q) N O + H O (l) 6. Disintegrtion of rdio ctive elements. 7. NH 4 NO 3 N O + H O 8. Inversion of cnesugr. H HO + HO C6HO6 C6HO6 C + + n. Order of rection - second order : A products (or) A + B products r = k [A] (or) r = k [A] [B] 7

8 x Eqution for rte constnt k =. t x Units for rte constnt : lit. mole.sec. Hlf life time : t / α t / = k Exmples: ) O 3 3O ) N O N + O 3) Cl O Cl + O 4) CH 3 COOH + NOH CH 3 COON + C H 5 OH 5) NO NO + O 6) C H 4 + H Ni C H 6 7) HI H + I Order of rection : Third order : 3A products (or) A + B products (or) A + B +C products. r = K 3 [A] 3 (or) r = K 3 [A] [B] (or) r=k 3 [A] [B] [C] eqution for rte constnt : ( ) k 3 = t x Units for rte constnt : lit.mole.sec. Hlf life time : t / α Exmples : NO + O NO NO + Cl NOCl FeCl 3 + SnCl FeCl + SnCl 4 (q) (q) (q) (q) Order of rection : n th order Units for rte constnt : lit n.mole n.sec. (or) (tm) n. sec Hlf life : t / α n Order of rection : Frctionl order Exmples : Decomposition of cetldehyde is 3/ order CH 3 CHO CH 4 + CO 8

9 r = k [CH 3 CHO] 3/ Rection between Hydrogen nd Bromine H + Br HBr r = k[h ] [Br ] / 3 order = + = Order of rection : negtive order : When the concentrtion of the rectnts increses, rte decreses. Decomposition of zone. O 3 3O. r = d( O3 ) k[ O3] = = k[ O ][ ] [ O ] 3 O The order of rection w.r.t oxygen is. Pseudo unimoelcur rections : The rections with moleculrity greter thn or equl to but order is one re clled Pseudo unimoleculr or Pseudo first order rections. Eg : i) Hydrolysis of ethyl cette in cid medium. ii) Inversion of cne sugr. Difference between moleculrity nd order of rection: Moleculrity The number of toms or ions or molecules prticipting in the rte determining step of the rection or ctivted complex of the rection is clled moleculrity. Order of rection The sum of the powers of the concentrtion terms of the rectnts in the rte eqution is clled order of the rection. Moleculrity is lwys whole number or integer. It cnnot become zero or frction or negtive. Order cn becomes negtive or frction or whole number. This is theoreticlly elucidted from the mechnism This is determined experimentlly. of the rection. All rections involve elementry steps, it my be one step or more steps. Moleculrity of complex rection hs no mening. It is expressed only for elementry steps. All rections need not hve order. Only those m n rections for which is in the form r = K.C. cn A C B. hve order. Order is the sme for the whole rection whether it involves single step or more steps. Moleculrity does not exceed 3. Order usully does not exceed 3. 9

10 METHODS OF DETERMINATION OF ORDER OF REACTION. TRAIL AND ERROR METHOD OR INTEGRATED FORM OF RATE EQUATION METHOD. Zero order R P 0 ( ) x x x= kt ( or) K = = t t First order R P.303 K = log t x ( ) log ( x ) t Second order R P x K = t x ( ) x ( x ) t Second order R+ R P.303 b( x) K = log t b b x ( ) ( ) log b b ( x ) ( x ) o t HALF-TIME( t / ) METHOD α / n t 0

11 ' '' n t / = '' ' t / where n = order of rection Vn t Hoff Differentil Method dc n = KC o For two initil concentrtions we C, C hve dc n dc n = KC; = KC dc dc log log n = log c log c ( ) Ostwld s Isoltion Method This method is useful to determine the order w.r.t ech rectnt of rection seprtely by tking other rectnts in excess quntity. A + B + C products Then order with respect to A is n A Order with respect to B is n B Order with respect to C is n C overll order of the rection = na + nb + nc Collision theory of rection rtes : Collision theory ws proposed by Arrhenius. The min postultes of collision theory re Collisions must occur between the molecules of recting gses for rection to occur. All collisions do not led to the formtion of products. (only fruitful collisions leds to formtion of products) The minimum mount of energy possessed by the colliding molecules to the formtion of products or rection to occur is known s threshold energy. The energy possessed by the molecules t STP is known s norml energy or internl energy. Norml energy possessed by norml molecules is lwys less thn threshold energy. The minimum excess energy required by the norml molecules during the collision to convert into products is known s ctivtion energy or energy of ctivtion. Activtion energy = Threshold energy energy of norml colliding molecules. Higher the ctivtion energy, lower is the rte of rection. Lower the ctivtion energy, higher is the rte of rection. ΔH = H p H R ΔH= difference in the ctivtion energies between rectnts nd products.

12 The ctivtion energy for nucler rection is zero. Arrhenius rte eqution : K = A. E /RT e Chemicl Kinetics K = Specific rte A = Frequency fctor (constnt) E = Activtion energy R = Gs constnt; T = Absolute temperture The frction of ctivted collisions is lwys smller thn the totl number of collisions. Actul rte of rection is much smller thn the rte of the rection clculted on the bsis of the norml collisions. Recting molecules must be properly oriented to mke effective collisions. First order rection: Rte eqution for first order A Product is dx = K[ A] dx or = K ( x ) The specific rte constnt.303 K = log t ( x) = initil concentrtion of the rectnt. (-x) = remining concentrtion of the rectnt. x = the concentrtion of the product t time t kt kt x = e or c = c e ( ) t 0 The unit for first order rte constnt is sec. The time required for the initil concentrtion of of the rectnt to become hlf of its vlue nmely (/) is known s hlf life (t / ) or hlf time of the rection t / = k The hlf life of first order rection is independent of the initil concentrtion. The eqution for hlf life period for rection of n th order cn be written s t / α ( n ). For the decomposition of N O 5 N O 4 + O..303 V The volume of O is mesured. Then the rte constnt K = log t V Here V =, V V t = ( x). Not only the time tken for the initil concentrtion is to rech hlf its vlue but the time tken for it to rech ny frction (/4 or 3/4) of the initil concentrtion is independent of initil concentrtion. This is one of the min chrcteristics of first order rection. For first order rection it cn be shown tht ) t / : t 3/4 : t 7/8 = : : 3 V t

13 b) t 90% : t 99% = : c) t 50% : t 90% = 3 : 0 d) t 50% : t 99.9% = : 0 In first order rection the grph between log(-x) nd t is stright line with negtive slope. Log(-x) slope = k.303 Time log ( x) Time slope = k.303 3

CHEMICAL KINETICS

CHEMICAL KINETICS Long Answer Questions: 1. Explin the following terms with suitble exmples ) Averge rte of Rection b) Slow nd Fst Rections c) Order of Rection d) Moleculrity of Rection e) Activtion Energy