29CHEMICALKINETICSThebasicrateequationsforthereactionSA-RA-SaredCxkCsdtdCs=kcrdtdC - kca + kcr(13)dtIfthereactionsareboththesameorder,dCA = -(kn + k) Ci(14)dtIf both reactionsare first order,(15)CA=CA,e-ki(16)CR-CRg=ki+kiCa,(1 eb)ke(17)Ca-Cs,"h+CA,(1--)wherebm(h+k)tThe concentrations of R and S are related by the simple ratio of therateconstantsCR-Cno_kiCs-Cso"KFigure2-3shows a concentration-time curvefor aparallel reactionSeriesReactions.Seriesreactionsarethoseinwhichtheproductofthereactiongoes on to react further.The simplest example isA-R-→S1An example of commercial interest is.the liquid-phase chlorination ofbenzene.From a typical plot of concentration versus holding time, it can be seenthat theconcentration of Rpassesthrough-a maximum valueandalsothat there is an inflection point in the curve for the concentration of S(Fig. 2-4).Therateequationsforreactionsof thistypeareaCA=kCAdidCr - kCh -kCn(18)dldCskcmdt
30UNITPROCESSESINORGANICSYNTHESISIntegral reaction-rate equations have been worked out forthe case offirst-order reactions.These are discussed in the standard texts on physicalchemistry.Thefirst-order rate equationsareDifferentialIntegralSimpledcA-kCaRorsCaChe-h,edtCAedCa-kCA-kCnCn"-k(-)dtAwhere kka/k,for thecasewhereneitherTime-Rnor Sis recycled.The concentration ofFig.2-2S is determined by material balanceCs-CAg-CA-CRRPorolle!ComplerSeriesReactions.Complexseriessreactions are those in which there is furtherreaction between one of the reactants andAone of theproducts so that bothseriesandTime-parallel reactions take place simultaneously.Fig.2-3Anexampleof thisisA+B-RA+R-SSerlesA+8-TThis is a series reaction with respect to B,R, and S, but it is a parallel reaction withrespect to A.A concentration-time curveTime-isshownin Fig.2-5.Fig.2-4An industrial operation exemplifying aFiGs.2-2to2-4.Time-concen-complex series liquid-phase reaction is intration curves for simple, paral-the conversion of alkylene oxides to the al-lel, and series reactions.kanolamines,whichis discussed in Chap.8.CH,+NH,→HOCHCH,NHH,C(Ethanolamine)CH,CH.OHCH,+CHOHCH,NH→HNH.CCH,CH,OH(Diethanolamine)CHCH,OHCH,CH,OHCH.CH,OHHCCH+HNCH.CH.OHCH.CH.OH(Triethanolamine)
31CHEMICAL KINETICSAmong many similar liquid-phase reactions of the complex series type, thefollowingareshownlaterinthisbook:1.Glycol ethers,2.Dimethylol urea,3. Glycines.An example of a vapor-phase complex series reaction is the chlorinationof propane,whichisdiscussed in Chap.6.A complex series reaction, such as the one above, is more complicatedthan the corresponding series reaction. The reactant ratio CBo/Ca,is anadded variablewhich is not present in the straight series reaction.Thefact that A reacts with each of the products as well as with B results in amore complicated relationship between Caand time.Thepresence of tworeactantsmakesthe control of thereaction easierthanfora series reactionbecause in both cases, if R is the desired product and S is valueless, thebest way to obtain the highest yield of R would be to run the reactor soas to obtain a fairly low conversion in each pass and to recycle the unre-acted A.If this were the case,the lower limit to the conversion of A perpass in either case would be regulated only by the economics of the reactorand recovery equipment cost.However,a high yield could be obtainedfor eithertype of reactionIf reactant A happens tobeamaterialwhichis so easilyComplex Seriesdecomposedthatitcannotberecoveredinarecycle system,8nothing can be done to ob-tain ahigh yieldof the desiredTimiproduct in the case of the.Fig.2-5straight series reaction.Inthe case of thecomplex seriesreaction, the yield of R canbe increased by using a highReversibleratio of B to A in the feed.Thus,higher yields of R canRbe obtained for the complexseriesreaction if B can berecoveredand recycled.IfBcannot be recycled, the sameTime--problemholds forthecomplexFig.2-6seriesreaction asfortheseriesFiGs,2-5and 2-6.Time-concentration curvesreaction.forcomplexseries and reversiblereactions,Fortunately, in the com-mercial reactions listed above, the compound B either can be recoveredand recycled (as in the reaction of alcohols with ethylene oxide) or is oflow value (such as in the reaction of water and ethylene oxide)
32UNITPROCESSESINORGANICSYNTHESISReversible Reactions.Reversible reactions are those in which the for-ward and reversereactions takeplace simultaneously.Any of theabovetypes of reactions can also be reversible (Fig.2-6).If the reuction is re-versible,this is taken into account in therate equation.For a simple-orderreversiblereaction of thetypeA+B=R+Sthe net rate equation can bewritten=k(CAC-CRCs)(19)where K is the equilibrium constant.The numerical value of K corre-spondingto concentration must be used in this equation.Examples of the reversible reactions are:I.Nitration of cellulose.2. Water-gas shift reaction.3.Sulfonation of naphthalene.4.Esterificationof ethyl alcohol5.Alkylation of benzene.Calculation of Conversion and Reactor Size.I The most important useof kinetics for the engineer is in the calculation of reactor size.In thebatch-reactor calculations,the typical kinetic equations involving con-centration terms can be used without alteration.In this type of calcula-tion it is usually desirable to calculate either the length of time perbatchfor a reactor of a given size or the amount of initial charge needed if theproduction rate is specified for a given degree of conversion.HeterogeneousReactions.Heterogeneous reactions arethose in whichmorethanone phaseis involved.Some importanttypes of heterogeneousreactions of industrial interest are:1.Gas-phasereactionspromotedbysolid catalysts.2.Noncatalytic reactions involving gases and solids.3.Reactions between gases and liquids.4.Two-(ormore)phase liquidreactions.5.Reactions between liguids and solids.The first of these is particularly important to the chemical-process andpetroleum-refining industries.An example is in vapor-phase catalyticcracking.The second type is particularly important in fuel technologysince the combustion of any solid fuel falls in this category. The thirdtype is very important in the chemical-process industries.An examplewould be the chlorination of a liquid hydrocarbon.Since the degree ofcontactof thetwophasesis ofmajor importance,reactorsaredesigned bythe same methods used for absorption processes.1ConRIGAN,Chem.Eng.,61,October,1954
33CHEMICALKINETICSVapor-phase Catalytic Reactions.When a gaseous reaction is promotedby a catalyst, the reactants are first adsorbed upon the catalyst surface.Theactual transformationfrom reactants toproducts takes place in theadsorbed phase.Therefore, the adsorption characteristics of the catalysttoward each of the reactants and products are important factors in ratedetermination.Adsorption may be either physical or chemical. The theory of physicaladsorption assumes that the adsorbed phase is a condensed liquid-phaselayer of molecules of the vapor on the solid surface,Chemical adsorptionisthechemical combinationof avapormoleculewith aportionof catalystsurface.This portion of surface is called an active center.In the applica-tion of adsorption to catalysis, chemical adsorption is of major importance.Adsorption Equations.2There are three important equations relatingthe concentration of adsorbate on the solid with its partial pressure in thegas phase.One of these is entirely empirical, while the other two have atheoretical basis.Freundlich's isotherm is the empirical relationship and iscA-apAwherepapartial pressureof AinvaporphaseCa = concentration of adsorbed material on solidaandnareempirical constantsAn equation of more interest in catalytic kinetics is Langmuir's isothermkipa.Ca"T+kapawhich was derived for the simplest possible case of chemical adsorption.Other isotherms of a similar nature,but more complicated, can also bederivedforsimilarcases.A general equation for a single adsorbate has been derived by R. A.Koble’and can be written in general terms:L'K'piCAMI+K'piwhere L'and K'are constants related to K and L (see below) and n isan exponentwhichmaybefractional,l,orgreaterthan1.Thespecialcase where n equals l.0 is the Langmuir isotherm.Catalytic Rate Equations. Catalytic rate equations based upon theorder-of-reaction conceptarenotrecommendedbecausetheydonotac-1HouGEN and WArsoN,"Chemical Process Principles,"John Wiley &Sons,Ino.New York, 1947.CoRRIGAN, Chem.Eng., 61,November,1954.CoRRIGAN,Chem.Eng.,61,December,1954; KonLE andConRIGAN,Ind.Eng.Chem,44,February,1952.CoRRiGaN,Chem.Eng.,62,January1955;62,February,1955