14UNITPROCESSESINORGANICSYNTHESISaction were tabulated, the standard free-energy change and, thus, K for agivenreaction couldbecalculateddirectly.Calculation of Equilibrium Conversion.In practically all engineeringcalculations,the evaluation of the equilibrium constant is merely ameansto an end.Theultimate goal is the calculation of how far a reaction canproceedthecquilibrium.conversion.Single Isothermal Reaction between Ideal Gases. One of the simplestcasesinvolvingacalculation of equilibrium conversion isforanisothermalreactionbetwecnidealgases.ConsiderthereactionA=R+Swhere A, R,and S are ideal gases.The first'step is to calculate K.The method involving the standardheat of reaction and the standard entropy-change is usually used becausethesedataareavailableformostsubstances.Inthetablesgivingstandardheatsof formation (or standard heats of combustion)and absoluteen-tropies, the standard state is usually specified as unit fugacity for all gasesand is usually stated as the pure gas at I atm pressure.The calculationmustbebaseduponthestandard statespecified bythesetablesand isnotarbitrary,as many people are led to believe.If the standard state foreach component is thatofunit fugacity,theequilibriumequation becomesK-papsPAIt is necessary to express each partial pressure in terms of the samevariabledegree of conversion.If the initial gas consists of 1mole of A,theconversionat equilibriummay be expressed asfollows:A-→R+S1-22BASIS:1MOLEOFAINFEEDConstituentMolesMolefractionPartialpressureAR1-21-2/1+2r(1 -2)/1 +212/1+2/1+2s22/1+22/1+21.0Total.1+zwhere is defined as the total pressure on the system. Thus, the equilib-riumequationbecomesK-/+z)212)1一/+)zorK-1-2Kor★+K
15THERMODYNAMICSIN UNITPROCESSESCorrection for Nomideality.If the pressure were so high that the gasesdid not behave ideally,the equation would have to be corrected for nonidealbehavior. Sincethe standard states are still unit fugacity,the equilibriumequationwouldbeK-lexppsJAVAPAThe fugacity coefficients ()would have to be evaluated.Since in this caseKBPVAtheequationbecomesK.-PapsKPASolvingfor conversicn asinthepreviousexampleK/K2-+K/KThe only difference between the nonideal case and the previous case isthattheratio K/KvreplacesKin theequation forz.Reactions Involving Gases and Solids.We have demonstrated how tocalculatethe equilibrium composition fora reaction involvingall gases.Letus consider thecasewhere agas reactswitha solid such as in thereactionC+CO=2COHereK-'co'cop'coJcovCOsPCoTheterm fc does not appear for carbon because the carbon remains in thesolid stateright up until the time it reacts and, therefore,is present only inits standard state,that is,as thepure solid atunitfugacity.It so happensthat,in thetabulating of enthalpy andentropy datafor solids,the standardstate used is thepure substanceat the standard temperature.The calcula-tionwhich corrects Hand Asfor temperature automatically providesfor the correction of thefugacity of the solid from the standard temperatureto the temperature of the system.Thus, the standard state for solids isthe temperature of the system at one atmosphere pressure.However,thefugacity of solids is almost independent of pressure, and so the fugacityof a solid atthepressure of the system is for all practical purposes thesameas that at 1 atm.Thus, the activity of anysolid (carbon, in thisreaction) is practically unity, and the term does not appear in the equilib-rium equation. It should be noted, however, that the thermal propertiesof carbon must beused in calculating the value of -AGfor the reactionand, hence, thevalueof K
16UNIT PROCESSESIN ORGANIC SYNTHESISSimulaneous Reactions.When twoisothermal reactions take placesimultaneously, the calculation is slightly more involved, but may besolved readily.The solution of this type of problem involves two un-knowns.Theprocedureistosetuptheequationsinvolvingtheequilibriumiconstantforeach reactionand to solvethesimultaneous equationsgraph-ically.Assume that the following two ideal gas reactions occur simultaneouslysndareisothermal:Ki=PRA+B=R(1)PAPBPs(2)A+R=SK,=PAPRCompoundAisthelimitingreactant,Btheexcessreactant.r=moleratioof BtoA inthefeedz=degreeofconversionofAbyreaction(1)y =degree of conversion of A by reaction (2)BASIS:1MOLEOFAINFEEDComponentMole fractionMolesatequilibrium1-z-V41-z-yI+r-2-BT-Zi+r-z-yZ-VR-Vi+r-z-syi+r-z-yTotal...1+r-z-yInthecasewherethetotalpressureis1atm,thepartialpressuresareequaltomolefractionsandthetwoequationsbecomeKt-6-(+r--)()(1-)y+r--)K,s(-)(1--)Sincethe K's are constant and may be calculated from thermal data andr isusually specified,the two equations can be solved simultaneously.The easiestmethod is,generally,toplot y versus zinboth equations, andthe point of intersection gives the desired andy values.Adiabatic Reactions.In the cases thus far considered,we haveshownhowto calculatetheequilibrium conversionforreactionsthattakeplace
17THERMODYNAMICSIN UNITPROCESSESataconstanttemperature.Inmanyindustrialpractices,noheatisaddedorremovedduringtheprocessand theheatof reactionmustoriginatefromorbedispersed in the reacting system itself.Thus, thetemperatureof thereactingmass will change continuouslyduring the reaction, and a calcula-tion of the equilibrium composition will also involve the calculation of thefinal temperature.Thistype of problem is solvedmost easily by agraphicmethod.The method of solution for adiabatic reactions presented here will beforthesimplified casein which itmaybeassumed thatHand Sarerelatively constant over the temperaturerange involved.If this is thecase,aplot of logKversus 1/Twill resultina straightline.Thecalcula-tion involves two relationships between T and z, the degree of conversion.One is a simplified energy balance;the other is the relation involving theequilibriumconstant.Theprocedureisasfollows:1.Bymethodspreviouslydiscussed,calculateKfortwo temperaturesandplotlogKversus1/T.Thiswillbea straightlineif AHandAsareassumed to remain constant.2.Assumeeven values of conversion, z,from O to l, and calculatethecorresponding partial pressure of each gas present for each value of z.3.Usingthese ratios of partial pressures, calculate the values that Kwouldhavefor eachvalue of z.4.UsingthelogKversus1/TtoAdiobalicreactiansplot,evaluateTforeachvalue ofzplofeouilibrumandplot&versusT(lineabin FigConversionT0.81-4)plorodioboticreochionTvsx5.Useasimpleenergybalanceto0.6obtain the other relationshipbe-Equilibrium+tween T and a.Adioboticpoinlemoeralure0.4ZAH-C,(T-T)where C, molal heat capacity0.2H-heatofreactionEouilibriumCurveFromthisequationitisseenthatatT=T.oT20Temperoture,TT-.-andwherez1Fro.1-4.Adiabatic reactions: equilibriumCConversions vs. temperature, adiabatic TAHVB,Z.Ti-C.-T.The line connecting.Tiand Tis drawn in.6.The intersection of the two linesgives the desired values of and T.Thisprocedure is illustrated inFig.1-5
18UNITPROCESSESIN ORGANICSYNTHESIS2,000Thermodynamics and Unit Proc-esses.Themajor.purposeofpre-1,800sentingareviewofthermodynamicsa1principles in this volume is to em-From-Equilibriumpoinphasize the importance of thermo-equilibriumdynamics to a fundamental under-Fromenergy1,400curve-boloncestandingof unitprocesses.Itis,(step4)(step5)therefore, appropriate to discuss1,200somespecificmethodsofapplication1These practical applications gen-1,0000.20.40.60.81.0erally involve three phases of ther-Equilibrium conversion,xmodynamics.They are thermalFra,1-5.Equilibrium converion.effects,chemical equilibrium,andphysical equilibrium.Thermalcal-culations involve only the first law of thermodynamics and are used forcalculating:1. Heat of reaction and the effect of temperature on heat of reaction.2.Sensible heat transferred in preheating and cooling.3.Heatof solutionandadsorption.4.Heat effects in phase transformations (vaporizing,melting,andcrystallizing).Chemical-equilibrium calculations, the subject of this chapter, areprobably themostimportantapplication.Theyinvolve:1.Calculating the equilibrium constants of both themajor and secondaryreactionsof aprocess.2. Calculating the effect of temperature on these constants.3. Calculating how far a reaction can go at a given set of conditions.4. Calculating the concentration of the desired product in the reactoreffuent forvarious process conditions.(This applies tofast reactions.)5. Determining the effects of solvents, inert diluents, or recycle streamsonproductyields.Physical equilibrium is also a very important aspect of thermodynamicswhich applies to the chemical-process industries.It is more often used,however,in those phases of a process which involve the separation and puri.fication of the product once it is formed.Thephysical-equilibrium portionis applied almost entirely to the unit operations. It is used to calculatephase compositions, vapor-liquid equilibria, absorption, adsorption, ex-traction, and distillation and to estimate solubilities. This phase of chemi-cal engineering is covered adequately in other texts.Chemical Equilibrium Applied.The major use of the principles of thischapter is to calculate the equilibrium composition of a system.This application in vapor-phase homogeneous reactions has been discussed above