Chemical Kinetics: The Rates of Reactions

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Chemical Kinetics

Chemc mca al kin etics i s co conce ncerr ne ned d with wi th the rate of che chemi mi ca call r eac acti ti ons . Ø Che Chemi mi ca call ki ne neti tics cs de deal als s wi th Ø Che - how - how r ap apii dly r eac actants tants ar are e co consume nsumed d wnd pr products oducts f or orme med; d; - h ow re - h r eacti action on r ate ates s r espond to change chan ges s i n th e condi conditi ti ons or th the pr esen ce of a catal ys yst; t; - the - th e i de dent ntii f i ca cati tion on of the ste step p by which whi ch a r eac acti tion on take tak es place (r eac acti ti on m echani sm).

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Chemical Kinetics

r eas asons ons f or stu tudyin dying g the r ate ates s of r eacti actions ons Ø T wo re - One is that th - One the e pr prac acti tica call i mport mportance ance of be beii ng able to pr pr edict h ow quickly qui ckly a r eac acti tion on mi xtu xturr e ap approac proache hes s equi l i bri um. ð

T he r ate mi ght depe depend nd on vari var i able un de derr our co cont ntrr ol (T , p, p, catalys ca talyst), t), and we migh t be ab abll e to optimi ze i t by the th e ap appr prop oprr i ate choice choi ce of co condi ndi ti ons ons..

- An othe - An otherr i s that th the e stu tudy dy of r eacti action on r ate ates s l eads to an u n de derr stan tand- d- i ng n g of th the e me mechan chanii sm of a r eacti action on , its i ts an anal alys ysii s i n to a se sequ que en ce of el em en tar y step.

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Chemical Kinetics

, th e study of the eff ect of enzymes on the r ates of Ø Enzyme ki netics reactions , is also an i mportant wi ndow on h ow these macr omolecules wor ks.

Ø We need to cope wi th a wide variety of differ ent r ates and a pr ocess th at appear s to be slow may be the outcome of man y faster steps.

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Empirical Chemical Kinetics Ø Th e f ir st step in the investi gation of the r ate and mechani sm of a reaction is the deter mination of th e over all stoichi ometr y of th e reaction and the identificati on of any side r eactions .

Ø The next step is to deter mi ne how the concentr ations of the r eactants and pr oducts change wi th ti me after the r eaction h as been initiated . - Th e temper atur e of r eacti on mixtu r e mu st be held constant thr oughout the cour se of th e r eacti on , for oth er wi se th e obser ved r ate woul d be a meani ng aver age of the r ate for dif fer ent temperatures.

Ø The method used to moni tor the concentr ations of r eactants and products and their variation wi th time depends on th e substances involved and the acidity. 5

Empirical Chemical Kinetics

- Spectrophotometry - The conductivi ty of the solu ti on - pH meter - Polarimetry - The detection of light emi ssion, ti tr ati on, mass spectr ometer, gas chr omatography, magneti c resonance.

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10.1 Spectrophotometry Ø Th e key resul t for using the intensity of absorption of r adiation at a parti cul ar wavelength to deter mi ne the concentr ation [J] of th e absor bing species is the empir ical Beer -L amber t l aw .

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10.1 Spectropjotometry

A = l og (I /I 0 ) =

[J] L = - log T%

T% = I /I 0 x 100%

- Α : the absorbance - I 0 : the incident i ntensity - I : the tr ansmi tted in tensity - L : the length of th e sample - : the molar absorption coefficient ( (exti nction coeff icient,

)

)

- depends on the wavelength of the incident r eaction and is gr eatest wher e the absorpti on i s most i ntense . 8

10.1 Spectropjotometry

Ø I n a typical spectrophotometer , th e absor bance is plotted as a fun ction of wavelength , so A may be deter mi ned dir ectly f r om the data at a given wavelength .

Α =

[J] L

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10.2 Experimental Techniques , the concentr ation of a system is anal yzed Ø I n a r eal-time analysis while the r eaction i s in progress by dir ect spectr oscopic obser vation of th e r eaction mi xtur e . , the r eactants ar e mi xed as they flow together in Ø I n the flow method a chamber .

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10.2 Experimental Techniques

- Th e r eacti on conti nu es as the thoroughl y mi xed solu ti ons flow -1 thr ough a capil lary outl et tube at about 10 ms , and dif fer ent poin ts along the tube corr esponds to dif fer ent ti mes after the star t of th e r eacti on. - Spectrophotometr ic deter mi nati on of the composition at dif fer ent positi ons along th e tube is equi valent to th e deter mi nati on of the compositi on of the r eaction mi xtur e at dif f er ent times after mi xi ng. - Disadvantage : a large volume of r eactant - Par ticular ly important for r eactions take place ver y quickl y.

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10.2 Experimental Techniques

Ø The stopped-f low techn iques avoids this disadvantage

- The two solu tions are mi xed ver y rapidly (< 1 ms) by injectin g them i nto a mi xi ng chamber designed to ensur e that the fl ow is tur bul ent and that complete mi xi ng occur s ver y qui ckl y. 12

10.2 Experimental Techniques

. Ø Ver y f ast r eactions can be studied by flash photolysis - Th e sample is exposed to a bri ef flash of light th at ini ti ates the r eaction, and th en th e contents of the r eaction chamber are moni tored spectrophotometr ically. -9 -12 -15 - L aser : 10 s (n s), 10 s (pi cosecond), 10 s (f emtosecond), -18 10 s (attosecond)

Ø F ast r eacti ons ar e also studied by pulse r adiolysis in whi ch the flash of electromagneti c radiation i s r eplaced by a shor t bur st of hi gh velocity electrons.

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10.2 Experimental Techniques

Ø I n contr ast to real-tim e analysis, quenching methods ar e based on stopping , or quenchin g , the r eaction af ter it has been al lowed to proceed for a cer tain time and the composition is analysis at l eisur e . - Cooling suddenl y; adding the mi xtu r e to a large volum e solvent; r apid neutr ali zation of an acid r eagent - Th is method is sui table onl y for r eacti ons that are slow enou gh for ther e to be little r eacti on dur ing th e time it takes to quench the mixtures .

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Reaction Rates

Ø Th e r aw data fr om exper im ents to measur e r eaction r ates are quantiti es that ar e propor tional to th e concentr ations or par tial pressur es of r eactants and pr oducts at a ser ies of ti mes after the r eaction i s ini tiated .

Ø I nter mediates can n ot be studied because their exi stence is f leeti ng or their concentr ation i s so low.

Ø M ore inf ormation about th e r eacti on can be extr acted if data are obtain ed at a ser ies of dif f er ent temper atur es .

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10.3 The Definition of Rates Ø Th e r ate of a r eaction taki ng place in a container of f ixed volume is def ined in ter ms of the rate of change of the concentr ation of a designated species . Rate = | [J ]| / t = |d [J ]| / dt - [J ] is the change in th e molar concentr ation of the specied J th at occur s dur ing the time inter val t. - All r ates are positi ve.

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10.3 The Definition of Rates

Ø Th e instantaneous r ate of the reaction ! its r ate at a specif ic in stant. - The in stantaneous rate of consumption of a reactant is th e slope of its molar concentr ation pl otted against the time , with th e slope evalu ated as the tangent to the graph at th e instant of inter est and r eported as a positi ve quanti ty .

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10.3 The Definition of Rates

- Th e instantaneous r ate of f ormation of a product is also the slope of the tangent to th e graph of its molar concentr ation plotted , and also r eported as a positi ve quanti ty . - The steeper th e slope in eith er case, the gr eater th e r ate of th e reaction. 3 -3 -1 -1 ; t : second ; r ate : mol es dm s (M s ) Ø [J] : moles / dm

- Th e instantaneous rate : υ

Ø Th e var ious reactants in a given r eacti on ar e consumed at dif fer ent rates , and the var ious products ar e also formed at dif fer ent r ates . - Th ese r ates are r elated by the stoichiometr y of the reacti on.

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10.3 The Definition of Rates

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10.3 The Definition of Rates

Ø We have to be careful to specify exactl y what species we mean when we r epor t a r eacti on r ate .

Ø Th e most sophisti cated defini ti on of a unique r ate of a r eacti on is in ter ms of the stoichiometric nu mber s , ν J , that appear in the chemi cal equation . - Stoichi ometr ic number s are the stoichi ometr ic coefficients but wr itten as positive for products and as negative f or r eactants .

= (1/ ν ) J d[ J]/dt - The r ate is always positi ve because whenever [J] / t i s negati ve, so is the stoichi ometr ic number . 20

10.3 The Definition of Rates

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10.3 The Definition of Rates

Ø A compli cation : if the r eactants f orm a slowly decayin g intermediate, the pr oducts do not f orm at the same r ate as the r eactants tur n into the inter mediates. - Complication ð advantage : the obser vation th at the consumption and formation r ates are not r elated by the r eacti on stoichi ometr y is a good sign th at a long-lived inter mediate is involved in the r eacti on.

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10.4 Rate Laws and Rate Constants Ø Th e r ate of r eacti on is often found to be propor tional to the molar concentr ation of the r eactants r aised to a simpl e power . - I t may be f ound that the r ate is dir ectly propor ti onal to th e concentr ation s of the r eactants A and B .

] υ = k r [A ] [B - Th e coef ficient k r ate coeff icient ). r is call ed the r ate constant ( - The r ate constant is independent of the concentr ations of th e species taking par t in the r eaction but depends on the temperatur e . " of the Ø An empir ically deter mi ned equati on is call ed the " r ate law

reaction . - A r ate law is an equati on th at expr esses the r ate of r eaction i n ter ms of th e molar concentr ations of r eactants and/or products . 23

10.4 Rate Laws and Rate Constants

Ø Th e un its of k r ar e always to conver t th e product of concentr ations into a r ate expressed as a change in concentr ation di vided by ti me . - Ex.

υ = k r [A] [B] -3 [A ] , [B ] : mol dm (M ) 3 -1 -1 -1 -1 k ) r : dm mol s (M s

- I n gas-phase studies concentr ations are commonl y expr essed i n -3 mol ecul es cm , so the r ate constant f or r eaction above woul d be 3 -1 -1 expr essed in cm molecule s . 24

10.4 Rate Laws and Rate Constants

(Self -test 10.1) 25

10.4 Rate Laws and Rate Constants

Ø Once we kn ow the r ate law and the r ate constant of the r eaction, - we can predict th e r ate of the reacti on f or an given compositi on of the reaction mix tur e ; - we can use a rate law to predict the concentr ation of the r eactants and pr oducts at any time after the start of the r eacti on . - An obser ved rate law is also an impor tant gui de to the mechanism of the r eaction, f or any pr oposed mechanism mu st be consistent with it.

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10.5 Reaction Order - A r ate law provides a basis for the classification of r eacti ons accor ding to their ki netics. - Reactions belongi ng to the same class have simi lar ki neti c behavior - their r ates and the concentr ations of th e r eactants and products var y with compositi on i n a simil ar way.

Ø Th is classification i s based on th eir order , the power to whi ch th e concentr ation of a species is r aised in the r ate law . - F ir st or der (

) in A : υ = k r [A]

- F ir st or der in A and fir st or der in B : υ = k r [A] [B] - Second or der (

Ø

2 ) in A : υ = k r [ A]

Th e over all order of a r eaction with a rate law of the f orm a b c , a+b+c , of th e order s of al l the υ = k r [A] [B] [C] is the sum components.

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10.5 Reaction Order

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10.5 Reaction Order

Ø A r eacti on n eed not h ave an i ntegral order , and man y gas-ph ase r eactions do not . - Ex. ð

1/2 υ = k r [A] [B]

half -or der (1/2) in A ;

f ir st-or der i n B ;

thr ee-hal fs (3/2) or der over all

Ø I f a rate law i s not of the for m

a b c υ = k r [ A] [B] [ C] ##, the

r eaction does not have an over all or der . - Ex.

H 2 (g) + B r (g) 2

2 H Br (g)

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10.5 Reaction Order

- A typical r ate law for the action of an enzyme E on a substr ate .

K M ; a constant

Ø Under cer tain cir cumstances a compli cated r ate law with out an over all order may simpl if y in to a law with a def ini te order . - [S] << K M

/K M [E] [S] υ = k r f ir st-or der in S fi r st-or der in E second-or der over all 30

10.5 Reaction Order

Ø A r ate law is established exper imentally , and cann ot in general be inf er r ed fr om the chemical equation f or the r eaction . - Ex.

H 2 (g) + B r (g) 2

2 H Br (g)

- The r ate law does happen to reflect the r eaction stoichi ometr y. H 2 (g) + I 2 (g)

2 H I (g)

] ] υ = k r [H 2 [I 2

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