24UNITPROCESSESINORGANIC SYNTHESISwhere I is integration constant.Thus, if the reaction is first order, a plotof theterm ln Caversus timewill givea straight line of negative slopeSecond-order Reaction.If a chemical reaction has a rate equation ofthefollowingform, it is of second order:acA-kci(3)dtAplot of Ca/tagainst Cis a straight line.It isbetterto use theintegral form of Eq. (3):无=m+c11-1.-kt(4)orcCThus,a plot of 1/Caagainst t will give a straight line with a slope equalto k.Forareaction of the formA+B-→C+Dwith therateequationdCAkCACs(5)dthe integral form may be expressed in terms of conversion ()and initialconcentrations;thus'1n--(6)aina6-)A plot of theterm 1/(a-b)lnb(a-z)/a(b-z)against t will give astraight linewitha slopeequal to-k.If a and bare equal, theequationrevertstotheintegratedform(7)-kta(a-)Thus, a plot of r/a(az) against t would give a straight line with aslope of k.Third-orderReaction.IfthereactionA→Bwere a third-order reaction, the rate equation would bedCAkcdtIntermsof conversion,therateequation isnow些-(-)(8) FROBT and PEARSON, op.cil
25CHEMICAL EINETICSandtheintegrated form is20-(9)2a(a-2)-kAplot of the quantity (2ar-°)/2a'(a-z)"againsttwould be a straightline.Zero-order Reaction.In some chemical reactions the rate of reactionis independent of the reactant concentration. The rate equation would bedcAk(10)dand a plot of reactant concentration against time would be a straight line.General Case.The general rate equation for a reaction involving asinglereactantisdCA=kCidtdz-k(a-2)ordwhere n may be any positivenumber.In most cases, n is a fraction.Theintegral form of this equation'is11-k(11)(n-)( -2)Limitations of Methods.All the plots discussed above for determiningthe order of a reaction are valid either for nonreversible reactions or atlowvaluesof conversion.The methods which can be used to determine the order of reaction maybe summarized as follows:1.PlottingC/Atversusconcentration2. Calculating k from the data and taking the order which gives themost nearly constant value of k.3. Plotting the proper integral function for each order and selecting theOne which gives a straight line.Table 2-1 is a summary of the differential and integral equations foreach order of reaction.Effect of Temperature on Chemical Reactions. The basic reaction-rateequations discussed above are defined only by concentration and time.The effect of temperature appears only in the variation of k.The relationship between the reaction-rate constant (e)and temperaturewasfirstobservedbyArrheniustobeh-8e8/arI LAIDLER, op.cil
TABLE2-1.SUMMARYOFEQUATIONSPORORDEROFREACTIONOrderChemicalequntionUnits of k!RateequationIntegratedequation0A-productsdz/dtkz-ktconc./time11/timeA→productsd/dt =k(a -z)In a/(a-z) =kt2A→productsdz/dt=k(a-z)/a(a-z) kt1/(time)(conc.)1lnba-起)2= ktA+Bproducts1/(time) (cone.)dz/dl =k(a-z) (6 -z)Q-6a(6-z)2az-&3A→ products1/(time) (conc.)dz/dl k(a z)a20(a-zjt1b(a-z)3A+B→produets1/(time)(conc.)sdz/dt m k(a z) (6 - z)(a-bjlna(6-2)11/a-1=kta-6a-z-11FrsctionalA→productsd/dt =k(a-z)1=ktQ[a(time) (cone.)---orgeneral
27CHEMIEAL KINETICSWhen In k is plotted against 1/T, the values of E/R and of s may bedetermined from the slope and intercept of the line.Types of Chemical Reactions.Some of the classifications of reactionsdeal only with the chemistry of the reactions, and some are concermedwith the environment in which the reaction takes placeSomeof the criteria whichare used in classifying reactions are:I.Heterogeneous orhomogeneous reactionsThis classification refersto the number of phascs in the reacting system.A homogeneous reactionis one which takes place in only one phase.A heterogeneous reaction in-volves morethan onephase.2. Mechanism of reaction, such as chain reactions, regular molecularreactions,orphotochemicalreactions.3.Catalyticornoncatalyticreactions.4. The method of operating the reactor, such as adiabatic, isothermalornonadiabatic-nonisothermal.5.The stoichiometric chemical equation. Reactions maybe divided inthis manner into five major types: simple reactions, parallel reactions,series reactions,complex series reactions,and reversiblereactions.SimpleReactions.A simple rcactioniswhere onlyone reaction is consideredtotakeplace.Themorecommonsimplereactionsarerepresentedby the following types:A-RA+B-RA-R+SA+B-R+S2A-RA-2RA typical concentration-time curve is shown in Fig.2-2 on page 30.Some industrially important examples of simple reactions are:1.A-R.Isomerization of butanewhich is discussed in Chap.14.2.A+B-→R+S.Acylationofamines.RNH,+RCOOH-RNHCOR+HORNH,+RCOCI→RNHCOR+HCI3.A-R+S.Production of vinyl chloridefromethylenedichlorideCICHCHCI→CHCHCI+HCIWhen only one reaction is taking place, the only variables to be con-sidered are time and conversion.Thereaction AR isthesimplest ofthis type. It represents a molecular rearrangement. The basic rate equa-tion for this reaction i-_dCA-kCA(12)dt1ConRrGAN,Chem.Eng.,61,September,1954
28UNIT PROCESSESINORGANIC SYNTHEBISwhere n is the order of reaction.The integrated forms of the equationfor various reaction orders are given in the accompanying table.OrderDifferentialformIntegral form0-dCa/dtmkCo-Ca-k1-dCa/-CInCh/CAkt2dca/du-kCt(1/CA)-(1/CA)-dCa/d=kcl2(Cl.-Ch) =ktndCadC111n-icr-1C2-1If the rate for a reaction involving two reactant molecules, such as thereactionA+B+R,isgivenbytheequationdCA-kCACsdtthe equation can be integrated into one in terms of conversion and timeonly,as shown in Eq. (6)Parallel Reactions.Parallel reactions are those in which more than oneproduct is formed by separate reactions and where the products, onceformed, do not react again.Some typical parallel reactions are(ARA-→8JA+B-RA+B-SA→RA+B-SAn example of a set of parallel reactions of the typeA+B-RA+B-SA+B-Tis in the nitration of toluene, which is discussed fully in Chap. 4.CH,HNO+HNO,CH+HNOCHH+HNO,NO