Dr JADU SAMUEL CHEMICAL KINETICS Inroducion Chemicl ineics is brnch of physicl chemisry, which dels wih he sudy of he re of chemicl recions nd he vrious fcors ffecing i Such sudies lso enble us o elucide he mechnism by which recion occurs Depending on he speed, he recions re minly of hree ypes Fs recions: These recions occur insnneously nd in some cses i is no esy o mesure heir res Specil echniques hve been devised o sudy heir ineics Eg, mny ionic nd eplosive recions Slow recions: These re recions re so slow h i is difficul o observe he pprecible chnges in concenrions room emperure even fer monhs or yers 3 Modere recions: For hese recions, i is esy o deermine heir res Eg, The gseous recions lie decomposiion of HI or NO5, he recions in liquid phse lie he hydrolysis of eser, sugr ec come under his cegory Re of recion The re of recion is defined s he chnge in he concenrion of ny one of he recns or producs per uni ime I is usully denoed by The molr concenrion (mol L - of subsnce is represened by puing he symbol of he subsnce in squre brce, [ ] For he recion, R P, he is given by, decresein concenrion of ny recn d ime en incresein concenrion of ny produc dp ime en Uni for he re of recion: Since concenrion is epressed in mol L - nd ime seconds, he uni of re will be mol L - s - or mol dm -3 s - Re epressions Consider he recion, A B P Q The differen re epressions for his recion re: d A db dp dq R dc dc A dcb dcp Q or where [A] or CA represens he molr concenrion (mol L - of subsnce A Consider noher recion, A B 3P Q In his recion, he soichiomeric coefficiens of recns nd producs re differen I is o be remembered h he re of priculr recion mus remin consn irrespecive
of he recn or produc en for is deerminion So, in order o ge he sme vlue for re consn, we should wrie he re epressions per uni mole of ny recn or produc Thus he differen re epressions for his recion re: da db dp dq 3 Problems bsed on re epressions: Refer Te Boo Averge re nd Insnneous re The re mesured during ime inervl is clled verge re This becuse he re of recion goes on decresing wih progress of ime due o decrese in concenrion of he recns wih ime Thus during given ime inervl, he recion goes hrough differen res nd he re mesured is only n verge re I is denoed by The re of recion ny insn or momen is clled he insnneous re I is obined from he verge re, when he ime inervl ends o pproch zero I is denoed by 0 The insnneous re is deermined from he concenrion versus ime grph For his, ngen drwn o he curve priculr insn nd he slope of his ngen will give he insnneous re Fcors ffecing he re of recions Concenrion of recns Temperure 3 Clys 4 Rdiion I Re nd concenrion of recns Re lw gives he dependence of he re of recion wih concenrion of he recns This lw ses h consn emperure, he re of recion is direcly proporionl o he recn concenrion, ech concenrion being rised o some power
3 Consider he recion, A α B P A B y Q A B y where is re consn This epression is clled re equion or re lw Thus re equion gives he relionship beween he re of recion nd he concenrion of recns in chemicl recion The powers of concenrion erms, ie m nd n in he re equion re deermined by eperimen The vlues of m nd n my or my no be equl o he soichiomeric coefficiens of he given chemicl equion Definiion of re consn In he bove equion, suppose [A] = [B] = mol L -, hen Hence he re consn or specific recion re is defined s he re of he recion when he concenrion of ech recn is en s uniy Order of recion The order of recion is defined s he sum of eponens o which he concenrion erms of recns in he re lw re rised o epress he observed re of recion Re A B y The overll order of recion, n = + y The order of recion wih respec o A = The order of recion wih respec o B = y The order of recion is n eperimenlly mesured vlue nd my be whole number or frcionl number Recions of differen orders If n = 0, i is he zero order recion If n =, i is he firs order recion If n =, i is he second order recion If n = 3, i is he hird order recion If n = ½, 3/, 5/4, ec, i is he frcionl order recion If n > 3, i is he higher order recion And Pseudo-order recions Uni of specific recion re, Consider n n h recion, A Producs Iniil conc (mol L - 0 Concfer ime, (- Then he re of n h order recion ime is given by α A n = (- n
4 = /(- n = mol L - s - / (mol L - n = ( mol L - (-n s - or mol (-n L (n- s - Order of recion Uni of, mol (-n L (n- s - zero mol L - s - Firs s - Second L mol - s - Third L mol - s - Frcion (Sy 3/ L / mol -/ s - Zero order recions A recion is sid o be of zero order if he re of he recion is independen of he concenrion of ll recns For such recions, he re remins consn hroughou irrespecive of he chnge in concenrion Emples h Phoochemicl recions eg, H Cl HCl The decomposiion of HI on he surfce of gold HI H + I 3 The decomposiion of NH3 on he surfce of ungsen NH3 N + H Derivion of inegred re equion for zero order recions Consider zero-order recion of he ype, A Producs Iniil conc (mol L - 0 Concfer ime, (- A he beginning of he recion ( = 0, he concenrion of he recn A is mol L - If fer ime, moles of A hs chnged, he concenrion of A is (- mol L - Then he re of recion ime is given by, A 0 =
5 0 0 = ( where is clled re consn of he recion Slope = On rerrnging Eq, = On inegrion, = + I ( where I is inegrion consn nd is he number of moles he subsnce reced When = 0, = 0, herefore I = 0 Subsiuing for I in Eq, = (3 This is he inegred re epression for zero order recion Hlf-life period: The hlf-life period of recion is defined s he ime en for hlf of he recion o be compleed When = /, = / Subsiuing hese vlues in eqn (3, / / Therefore he hlf life period of zero-order recion is direcly proporionl o he iniil concenrion of he recns Firs order recions A recion is sid o be of firs order if he re of he recion depends upon he firs power of one recn concenrion only Emples i Decomposiion of nirogen penoide in crbon erchloride soluion NO5 NO + ½ NO ii Decomposiion of hydrogen peroide in queous soluion HO HO + O iii Rdiociviy Derivion of inegred re equion for firs order recions Consider firs order recion of he ype, A Producs (4
6 Iniil conc (mol L - 0 Concfer ime, (- A he beginning of he recion (=0, he concenrion of he recn A is mol L - If fer ime, moles of A hve chnged, he concenrion of A is (- mol L - Then he re of recion ime is given by, A α (- = (- ( Where is clled re consn of he recion On rerrnging Eq, On inegrion, - -ln(- = + I ( When = 0, = 0 Therefore I = -ln Subsiuing for I in Eq, -ln(- = ln = ln - ln(- ln ln ln(- ln(- = ln - Slope = - 303 log (3 This is he inegred re epression for he firs order recion Someimes he inegred re lw in he following form is lso used: Hlf-life period When = /, = / Subsiuing hese vlues in eqn (3,
7 303 log / / 303 log / 303 0300 / 0693 / 0693 / Therefore he hlf-life period of firs order recion is independen of he iniil concenrion of he recns Second order recions A recion is sid o be of second order if he re of he recion depends upon he produc of wo recn concenrions or he squre of one recn concenrion Emples i Hydrolysis of eser by NOH (Sponificion CH3-COOCH5 + NOH CH3-COOH + CH5OH Ehyl cee ceic cid ehyl lcohol ii Therml decomposiion of celdehyde CH3-CHO CH4 + CO OR CH3-CHO CH4 + CO Derivion of inegred re equion for second order recions involving one recn only or wo recns wih sme iniil concenrion Consider second order recion of he ypes, (i A Producs Iniil conc(mol L - 0 Conc fer ime, (- OR (ii A + B Producs Iniil conc ( =0 0 Conc fer ime, (- (- A he beginning of he recion ( = 0, he concenrion of he recn is mol L - If fer ime, moles of he recn hs chnged, he concenrion of he recn is (- mol L - Then he re of recion ime is given by, A α (- = (- ( (4
8 On rerrnging, ( On inegrion, (- I I ( Slope = When = 0, = 0 Therefore I = / Subsiuing for I in Eq ( (3 ( (4 ( ( Time, ( (5 OR from eqn (3 [ ] (6 This is he inegred re epression for he second order recion Hlf-life period When = /, = / Subsiuing hese vlues in eqn (5, / / ( / / ' (7 Therefore he hlf-life period of second order recion is inversely proporionl o he iniil concenrion of he recns
9 Derivion of inegred re equion for second order recions involving wo differen recns wih differen iniil concenrion Consider second order recion of he ype, A + B Producs Iniil conc (mol L - b 0 Conc fer ime, (- (b- A he beginning of he recion (=0, he concenrion of he recn A is mol L - nd concenrion of recn B is b mol L - If fer ime, moles of A hs chnged, hen he moun of B h would rec in he sme ime would lso be mol L - So he concenrion of A nd B ime would become (- mol L - nd (b- mol L - respecively Then he re of recion ime is given by, A B α (- (b- = (- (b- ( On rerrnging, ( ( b Resolving he lef hnd side ino pril frcions, ( b ( b ( On inegrion, b b ( ( ( ln( b ln( I ( b ln( ln( b I ( b b ln ( b when = 0, = 0 I Subsiuing for I in Eq ( Therefore ( I ln ( b b ln ( b b ln ( b b
0 ln b b ln ( b b ln ln b b b b ln ( b b b( ln ( b ( b 303 b( log ( b ( b (3 This is he inegred re epression for he second order recion Third order recions A recion is sid o be of hird order if he re of he recion depends upon he produc of hree concenrion erms or he hird power of one recn concenrion The hird order recions re rre compred o firs order nd second order recions These recions re of he following hree ypes: 3A producs A + B producs A + B + C producs Emples i Reducion of ferric chloride by snnous chloride FeCl3 + SnCl FeCl + SnCl4 ii Combinion of niric oide nd chlorine o form nirosyl chloride NO + Cl NOCl Derivion of inegred re equion for hird order recions involving one recn only Consider simples hird order recion of he ype, 3A Producs Iniil conc (mol L - 0 Conc fer ime, (- A he beginning of he recion (=0, he concenrion of he recn A is mol L - If fer ime, moles of A hve reced, he concenrion of A is (- mol l - Then he re of recion ime is given by, A 3 α (- 3 = (- 3 (
On rerrnging, 3 ( On inegrion, (- 3 I ( ( When = 0, = 0 Therefore I Subsiuing for I in Eq ( ( ( ( ( ( ( (3 OR from eqn (, ] [ ( The eqn (3 is he inegred re epression for he hird order recion Hlf-life period When = /, = / Subsiuing hese vlues in eqn (3, ( ( / ( ( / 4 3
/ 3 / 3 Then, / α / / (4 Therefore he hlf-life period of hird order recion is inversely proporionl o he squre of he iniil concenrion of he recns Higher order recions (n h order recions A recion is sid o be of higher order if he re of he recion depends upon he produc of more hn hree concenrion erms A + B + C + Producs The recions of higher order re very rre The reson for his my be eplined by he collision heory According o his heory, recion es plce only when he recn molecules come ogeher simulneously o collide wih ech oher The possibiliy of hree molecules colliding simulneously o ech oher is less hn for wo molecules nd hence he recions of hird order re fewer hn hose of second order Similrly, he chnces of four molecules o come ogeher simulneously nd collide re sill less Hence recions of fourh order or higher order re very rre Emples The cion of HCl on HClO3 in queous soluion is of eighh order 4H + + ClO3 - +Cl - ClO3 + Cl + + HO Derivion of inegred re equion for n h hird order recions Recions of fourh or higher order seem o be improbble In generl, consider recion of he n h order, where ll he iniil concenrions re he sme: na Producs Iniil conc(mol L - 0 Conc fer ime, (- A he beginning of he recion (=0, he concenrion of he recn A is mol L - If fer ime, moles of A hve reced, he concenrion of A is (- mol L - Then he re of recion ime is given by, α (- n = (- n ( n ( On inegrion, n ( -
3 I ( ( n ( n ( When = 0, = 0 Therefore I ( n ( n Subsiuing for I in Eq (, ( n ( n ( n ( ( n ( n ( n ( n ( ( n [ ] ( n ( n ( n ( [ ] (3 ( n ( n ( n ( This is he inegred re epression for he n h order recion [*NOTE This equion is pplicble for ll orders ecep when n = ] Hlf-life period When = /, = / Subsiuing hese vlues in eqn (3, ( n ( n / ( n ( / / ( n / ( n ( n ( n ( n ( n Thus he hlf-life period of n h order recion is inversely proporionl o he (n- h power of he iniil concenrion Frcionl order recions A recion is sid o be of frcionl order if he re of he recion depends upon he frcionl power of he recn concenrion Emples Conversion of pr-hydrogen o orho-hydrogen is of he order 5 H + pr-h orho-h + H The inegred re equion for frcionl order recions The inegred re epression for he n h order recion is pplicble o he of frcionl order recions [ ] ( n ( n ( n ( when n = 3/, (4
4 [ ] / / ( when n = 5/, [ ] ec 3 / 3 / 3 ( Time for frcionl chnge: The inegred re epression for he n h order recion [ ] ( n ( n ( n ( Suppose i is required o clcule he ime for he compleion of hlf of he recion ie, = /, = / Subsiuing hese vlues in he bove eqn ( n ( n / ( n ( / ( n ( n ( n / ( n / ( n ( n or / ( n Similrly, i cn be proved h 3 / 4 ( n Thus, he ime required o complee definie frcion of he n h order is inversely proporionl o he (n- h power of he iniil concenrion SUMMARY Order of recions Inegred re equion Hlf-life period Zero K = / / Firs Second 303 log 303 log ( OR / / 0693 [ ]
5 303 b( log ( b ( b Third ( ( OR / 3 ( [ ] n h ( n ( [ ( n ( n ] / ( n ( n ( n Elemenry nd comple recions Elemenry recions (or isoled recions re simple recions in which he recns re direcly rnsformed ino producs wihou ny inermedie sep Comple recions do no occur in single sep, bu compliced by inermedie sges or by side nd reverse recions Moleculriy of recion The moleculriy of recion is defined s he number of molecules, oms or ions h mus collide wih one noher simulneously so s o resul ino chemicl recion ( For relively simple recions: Erlier, no disincion ws mde beween mloeculriy nd order of recion Recions of firs, second nd hird order were clled unimoleculr, bimoleculr nd rimoleculr recions This prcice is, however, no followed now The moleculriy is simply he sum of he molecules of differen recns s represened by he blnced chemicl equion Emples: (i (ii (iii Decomposiion of FO FO F + O Unimoleculr Dissociion of HI HI H + I Bimoleculr Oidion of niric oide o nirogen dioide NO + O NO Trimoleculr In severl recions, he order of rcion is differen from moleculriy Eg, Pseudo-order recions (Pseudo-moleculr recions A recion in which one of he recns is presen in lrge ecess, showing n order differen from he cul order is clled pseudo-order recion (Such recions in old dys re menioned s pseudo-moleculr recions, since moleculriy nd order re sme for elemenry recions (i Pseudo- firs order recions (Pseudo-unimoleculr recions
6 A recion in which one of he recns is presen in lrge ecess, showing firs order ineics differen from he cul order is clled pseudo- firs order recion Acully, more hn one molecule is involved in he chemicl recion Emples: ( Hydrolysis of n eser: Ehyl cee upon hydrolysis in queous soluion forms ceic cid nd ehyl lcohol CH3-COOCH5 + HO CH3-COOH + CH5OH Ehyl cee (ecess ceic cid ehyl lcohol Since i is n elemenry recion, he re lw cn be wrien s, Re = [CH3-COOCH5] [HO] As HO is presen in lrge ecess, is concenrion remins prciclly consn in he course of recion Then, Re = [CH3-COOCH5] where = [HO] Therefore he recion is sid o hve pseudo-firs order, bu he recion is bimoleculr (b Hydrolysis of sucrose (Inversion of cne sugr: queous soluion forms glucose nd frucose Sucrose upon hydrolysis in CHO + HO C6HO6 + C6HO6 sucrose (ecess glucose frucose Since i is n elemenry recion, he re lw cn be wrien s, Re = [CHO] [HO] As HO is presen in lrge ecess, is concenrion remins prciclly consn in he course of recion Then, Re = [CHO] where = [HO] Eperimenlly his recion will be firs- order Therefore i is pseudo-firs order recion, bu i is bimoleculr (b For comple recions: Those recions which occur in wo or more seps re clled comple recions The moleculriy of he overll recion hs no significnce Bu every sep or elemenry process involved in comple recion hs is own moleculriy The sepwise sequence of recions h conver recns o producs is clled he mechnism of he recion In ny mechnism, some of he seps will be fs, ohers will be slow The slowes sep is he re-deermining sep of he recion nd i deermines he order of he recion The reducion of bromic cid o hydrobromic cid by hydriodic cid is n emple of comple recion I is soichiomericlly represened s: HBrO3 + 6HI HBr + 3HO + 3I I is believed o hve he following mechnism involving hree seps, (i HBrO3 + HI HBrO + HIO (slow (ii HBrO + 4HI HBr + HO + I ( fs (iii HIO + HI HO (fs Overll recion HBrO3 + 6HI HBr + 3HO + 3I
7 The moleculriies of seps (i, (ii nd (iii re, 5 nd respecively I is no desirble o epress moleculriy for he overll recion Seps ( (ii nd (iii re fs while sep (i is slow According o he sep (i, he recion is of second order Thus here is lso no correlion beween he order nd moleculriy of recion Differences beween order nd moleculriy Order Moleculriy I is he sum of he powers of concenrion erms in he re lw epression I is n eperimenlly deermined vlue 3 I cn hve frcionl number nd zero vlues besides whole number vlues 4 I is lwys sme for he overll recion, wheher he recion is comple or simple 5 Order of recion cn chnge wih he condiions such s pressure, emp nd concenrion I is he number of molecules, oms or ions h mus collide wih one noher simulneously so s o resul ino chemicl recion I is heoreicl concep I cn hve only whole number vlues I hs no significnce for comple recion nd cn be epressed for ech sep in cse of comple recion Moleculriy is invrin for chemicl equion Mehods of deermining he order of recion There re vrious mehods for deermining he order of recion Inegrion mehod Anlyicl or inegred re equion mehod b Grphicl mehod Hlf-life mehod 3 Vn Hoff Differenil mehod 4 Rio vriion mehod 5 Oswld s Isolion mehod Inegrion mehod Anlyicl or inegred re equion mehod In his mehod he iniil concenrion of ll he recns ing pr re deermined The progress of he recion cn be noed by deermining he concenrion of he recing subsnces differen inervls of ime These vlues re hen subsiued ino he inegred equions for he firs, second, hird order recions ec For zero order recion, For firs order recion, For Second order recion, = / 303 log (
8 ( For Third order recion, ( The re equion which yields consn vlue of he re consn for series of inervls of ime gives he correc order of he recion As his mehod involves of he ril of differen equions, i is usully clled s he hi nd ril mehod b Grphicl mehod using inegred re equion In his mehod he iniil concenrion of ll he recns ing pr re deermined The progress of he recion cn be noed by deermining he concenrion of he recing subsnces differen inervls of ime Then he suible concenrion funcion for he firs, second, hird order recions ec is ploed gins ime The grph, which gives srigh line, corresponds o he correc order of he recion log (- Firs order Second order Time Time If he plo of log(- gins ime is srigh line, he recion is of he firs order b If he plo of /(- gins ime is srigh line, he recion is of he second order, nd so on Hlf-life mehod (Frcionl chnge mehod The ime en for hlf of he recion o be compleed is clled hlf-life period I is found h he hlf life period or ny frcionl chnge is consn for firs order recion, inversely proporionl o he iniil concenrion for he second order recion nd inversely proporionl o squre of he iniil concenrion nd so on In generl, he hlf life period of n n h order recion is inversely proporionl o he (n- h power of he iniil concenrion Thus for he n h order recion, / is given by / ( n Consider wo sepre eperimens wih differen iniil concenrion Le nd le (/ nd (/ re heir respecive hlf-life periods ( / ( n ( ( / ( n (
9 On dividing, ( ( / / ( n ( n ( n ` Ting logrihm, ( / log ( n log ( / log(( / log( / ( n (log log n log(( / (log log( / log log(( / log( / n (log log By subsiuing he eperimenl d in his equion, he order of he recion cn be clculed 3 Vn Hoff Differenil mehod The re of he recion of n h order is proporionl o he n h power of concenrion dc n C, where c is he concenrion of he recn On ing logrihm, dc log log n logc Consider wo sepre eperimens wih differen iniil concenrions, C nd C Then we cn wrie, dc log log nlogc dc log log nlogc On subrcion,
0 dc log dc log n logc dc log n logc dc log logc logc dc The vlues of dc nd cn be deermined by ploing he concenrion of recns gins ime nd hen ing he slope of he srigh line By subsiuing hese vlues in he bove equion, he order of he recion cn be clculed 4 Rio vriion mehod (Iniil re mehod In his mehod, he re he beginning of he recion (ie, iniil re is mesured Then he iniil concenrion of only one of he recns is vried by nown fcor while eeping he concenrions of he oher recns consn The recion re is mesured gin From he recion res, he order wih respec o his priculr recn is clculed The procedure is repeed wih respec o every oher recn nd hus he order wih respec o ech of hem is clculed Then he sum of he individul orders gives he overll order of he recion This mehod cn be illusred s follows, Consider he recion, A + B Producs Iniil concenrion b 0 b y If he concenrion of A is doubled, eeping h of B consn Dividing, we ge On ing logrihm, y b log log
log log Thus he order, wih respec o recn A is clculed The procedure is repeed wih he oher recn B o clcule is order, y hen he overll order of he recion is given by, n = + y 5 Oswld s Isolion mehod In his mehod, ll he recns ecep one re en in lrge quniies so h he concenrions of hese recns remin consn hroughou he recion Thus he order of he recion wih respec o h isoled recn, which is no en in lrge quniy The eperimen is repeed by isoling ech recn in urn The ol order of he recion will be given by he sum of he order of isoled recions For emple, suppose recion involves hree recns A, B nd C In he firs cse B nd C re en in ecess so h A is isoled The order hus observed is he order wih respec o A Similrly by ing A nd C in ecess, he order wih respec o B cn be found nd by ing A nd B in ecess, he order wih respec o C cn be found If n A, n B nd n C re he orders wih respec o A, B nd C respecively, hen he overll order of he recion n will be given by he epression: n = n A + n B + n C