4UNIT PROCESSESINORGANIC SYNTHESISFrom heat-of-combustion data:AHrZ(H.)produeuZ(H)resetantc()d(A)(A)(A)It is important that the physical state of all components be the same inall valuesfor heats offormation or combustion.In a combustion reaction,the water formed may be either liquid (the usual standard state) or gas.-H,-372.82kcal/gmoleC,He(g) + 3.50(g) →2CO:(g) +3H,O()CHa(g)+3.50(g)→2CO2(g)+3H,O(g)-AH。-341.26Latent heatof vaporization of 3molesH,O31.56H,O()H,0(g)AH=10.52The heat of combustion when the water formed is in the liquid state isknown as the gross heat of combustion; when the water formed remains asa gas, it is the net heat of combustion.The heat of reaction may also be calculated by combining equations forwhich the heats of reaction are already known, To calculate the heat ofreactionforanyreaction requires merely addingalgebraicallythe equationsfor reactions having known values of H so that their sum gives the re-action desired.This enables the heat of reaction to be calculated forareaction that will not go quantitatively in a calorimeter.In the followingcaseif the heats of reaction of the first two chemical equations areknownthe heat of reaction of the third is the difference between the first two:C(B) + O,→CO;(g)CO(g)+O(0)→CO:(g)C(B)+0:(g)-→CO(g)The usual form in which reaction-heat data are available in the literatureis a tabulation of either the heat of formation or the heat of combustionof the individual compounds in their standard states.For inorganic com-pounds the heat of formation is usually tabulated, while for organic com-pounds the data given are heats of combustion. Sources of data are listedat the end of this chapter.Although both temperature and pressure are specified in designating thestandard state for the reaction, the change of heat of reaction with smallchanges in pressure is generally small and often may be neglected. Forideal gases, the heat of reaction is not affected by pressure.For liquidsand solids,thereissome slight effect,but it is so small thatitmaybeignoredin most cases.The cases in which the effect of pressure upon heat of reaction may be significant are those involving reactions of nonideal gasesat high pressures.Effect of Temperature upon Heat of Reaction.The effect of tempera-ture upon heat of reaction may be quite extensive and cannot be ignored
5THERMODYNAMICSINUNITPROCESSESin most cases. This is especially true in the case of reactions occurring athigh temperatures.Theheat of reaction at anytemperaturemaybe calculated from thefollowing expression:AHTAH-AH+ZHP-ZHRZHRZHPAHawhereHrheatof reactionattemperatureTHsstandard heat of reaction at TsZHp=sum of enthalpies of all products between Ts and TZHr=sum of enthalpies of all reactantsbetween Ts and TZHp and EHr may be evaluated by the most convenient method. Thismaybe donebylooking up valuesfor individual enthalpies in tables,cal-culating them from mean heat capacities, or by integrating heat-capacityequations.H=Hs+ACp(TTs)HH+CpdTTaCpmdifference between meanheatcapacities of all products and allreactantsACp=differencebetween heat capacities of all products and all reactantsACpc(Cp)e+d(Cp)D-a(Cp)-b(Cp)BEntropy Change of aReaction. Let us now consider what makes thereaction proceed.Thesubject of thermodynamics contributesinformationon whyit ispossiblefor aprocess to takeplaceandhowfar itmayproceedas well as on the total energy relations involved when the reaction occurs.Thermodynamics is concerned not alone with the total energy relations ina given system but also with the degree to which this energy can be utilizedtocauseagivenprocesstooccur.Thermodynamic energy terms such as enthalpy and internal energy area measure of the total energy in a system but make no reference to the degree to which that energy is available.There are also terms which are ameasure of the degree to which the energy present in a system will make theprocessgo.ThesetermsarethefreeenergyGand theentropyS.The latter term, entropy, is defined mathematically by the differentialequation relating it (the entropy) to the heat transferred in & reversibleprocess:s-
6UNITPROCESSESINORGANICSYNTHESISA reversible process is regarded as one in which the driving force causingthe process is at all times only infinitesimally greater than that resistingthe process.It is at all times, therefore, at equilibrium.The reversibleprocess is also an ideal or imaginary one from the point of view that allsources of energy dissipation are eliminated.Free-energy Term.Entropy,defined in thismanner and when multi-plied by the absolute temperature, gives a quantity TS which is a measureof that portion of the energy which is unavailable.The term TS subtractedfromtheenthalpy leaves a quantitywhichisthat portion of the enthalpyinaflowprocess,orconstant-pressurebatchprocess,whichisavailableforuseful work.The latter term is called thefree energyand is defined as:G=H-TS.The free energy may be regarded as a property of a system which is adirect measure of that portion of the total energy which will cause the re-actiontoproceed.The total energy that a system possessesmay be rep-The total energy H, can be divided intoresented as shown in Fig.1-1.TSolonK5iouoTS11031FrG. 1-1.Relations of energy terms H, G, A, and U.internal energy U,and flow or external energyPV,orit can be divided intoenergy availableforuseful work G,and unavailable energyTS.A similarfunction is the work function A,definedas:A U-Ts.Basic Energy Relations.The following equations summarize the basicrelationshipsof thermodynamics:
7THERMODYNAMICS IN UNITPROCESSESdUdgdoAU=g4S-dS =dg./Tdg./TH-U+PVAH-AU+A(PV)A-U-TSAA-AU-A(TS)G=H-TSAG=AH-A(TS)Usually an enthalpy changeis a constant-pressure process,changes inwork function arefor a constant-temperature process, and changes in freeenergy arefor a processoccurringat constantpressure and temperature;sotheseequationsareusuallywrittenAH-AU+PAUTSAGAH-TASChemical Equilibrium.Two importantthings that a chemical engineerwishestoknowaboutachemicalreactionare:Can it go?Howlongwill ittake?Thefirst question is one of thermodynamics; the second is one of kinetics.Theprediction of chemical reaction equilibria is oneof the most usefulaspects of thermodynamics.Itispossibleto calculatethe equilibriumconversion of a given reaction from data taken on other reactions orfromthermal data on the individual substances involved.Free Energy As a Criterion of Equilibrium.The decrease in free energyof a system during anyisothermal,isobaric process is ameasureof the netreversiblework(w)thatthesystemcan doupon its surroundings.W=-AGEquilibrium conditionsarethoseinwhichtheforcesresistingtheprocessare just balanced by those which causeit. Therefore,any small changethatwouldtakeplacewouldhavetobeareversibleone if no dissipativeactions are involved.Since a reversible process is one which takes placealways at equilibrium conditions,the criteria of reversibility must includethecriteriaforequilibriumconditionsatconstantpressureandtemperature.Sinceforareversibleprocessatconstantpressureandconstanttempera-turedG-pyand sincef0when only the work of expansion is involved,then if the process is at equi-libriumfora differential changewhichitmightundergo,dG=0
8UNITPROCESSESINORGANICBYNTHESISAs most chemical reactions of industrial importance are restricted to con-stant pressure and are not harnessed to produce useful work,the free energyis useful in calculating the composition of the equilibrium mixture.EquilibriumConstantforIdealGases.Whenachemicalreactiontakesplace at constant temperature and pressure, the free energy of the systemcontinues to decrease as long as the reaction proceeds spontaneously.When the free energy has'reached the lowest value possible for the systemat that temperature and pressure, the reaction has come to equilibrium.Any further reaction in the same direction would have to be accompaniedby an increase in free energy.Therefore, it could not occur unless someextra force (such as, forinstance, electromotive) were applied to the system.Inmostreactions there is no extraforceapplied, and thereaction stops atthe pointwhere the free energyreaches the minimumvalue.The composi-tion of the mixture of reactants and products is the equilibrium compasition.It is this compasition that chemical engineers are interested in calculatingforthepurpose of estimatingthemaximum possibleyieldof aprocessDevelopment of the EquilibriumEquation.The actual value of the freeenergy at this point has little practical significance.However, we shall seethat through use of the free-energy relationships it is possible to calculatethe equilibriumcomposition.Let us consider the application of these principles to a specific chemicalreaction.The.watergasshiftreactionCO(o) +H;O(g) =CO:(g) +H,(g)is one of universal interest to engineers.A chemical reaction may begeneralized asfollows:aA+bB=cC+dDThe standard free-energy change for this system may be calculated fromthestandard freeenergiesof formation (Gg)of the individual.components:G=Z(G)prodoetuZ(G7)resetastAll chemical thermodynamic textsl derive the relationships between thestandard free-energy change and the equilibrium constant K, which is-AG°-RTInKThe equilibrium constant for the generalized reaction may be writtenintermsofpartial pressurepifthecomponents arebehaving as idealgasesor thermodynamic functions as activity a or fugacity J may beused fornonideal systems.K-popsfor ideal gaseepipiSeefootnote1,p.1