Thermodynamics

794 | ThermodynamicsCO 2 CO 2COO 2COO 2O 2COCO 2FIGURE 16–1A reaction chamber that contains amixture of CO 2 , CO, and O 2 at aspecified temperature and pressure.SdS > 0dS = 0Violation ofsecond lawdS < 016–1 ■ CRITERION FOR CHEMICAL EQUILIBRIUMConsider a reaction chamber that contains a mixture of CO, O 2 , and CO 2 ata specified temperature and pressure. Let us try to predict what will happenin this chamber (Fig. 16–1). Probably the first thing that comes to mind is achemical reaction between CO and O 2 to form more CO 2 :CO 1 2 O 2 S CO 2This reaction is certainly a possibility, but it is not the only possibility. It isalso possible that some CO 2 in the combustion chamber dissociated into COand O 2 . Yet a third possibility would be to have no reactions among thethree components at all, that is, for the system to be in chemical equilibrium.It appears that although we know the temperature, pressure, andcomposition (thus the state) of the system, we are unable to predict whetherthe system is in chemical equilibrium. In this chapter we develop the necessarytools to correct this.Assume that the CO, O 2 , and CO 2 mixture mentioned above is in chemicalequilibrium at the specified temperature and pressure. The chemical compositionof this mixture does not change unless the temperature or the pressureof the mixture is changed. That is, a reacting mixture, in general, has differentequilibrium compositions at different pressures and temperatures. Therefore,when developing a general criterion for chemical equilibrium, weconsider a reacting system at a fixed temperature and pressure.Taking the positive direction of heat transfer to be to the system, theincrease of entropy principle for a reacting or nonreacting system wasexpressed in Chapter 7 as100%reactantsEquilibriumcomposition100%productsFIGURE 16–2Equilibrium criteria for a chemicalreaction that takes place adiabatically.REACTIONCHAMBERδ QControlmassT, PW bFIGURE 16–3A control mass undergoing a chemicalreaction at a specified temperature andpressure.δ(16–1)A system and its surroundings form an adiabatic system, and for such systemsEq. 16–1 reduces to dS sys 0. That is, a chemical reaction in an adiabaticchamber proceeds in the direction of increasing entropy. When the entropyreaches a maximum, the reaction stops (Fig. 16–2). Therefore, entropy is avery useful property in the analysis of reacting adiabatic systems.When a reacting system involves heat transfer, the increase of entropyprinciple relation (Eq. 16–1) becomes impractical to use, however, since itrequires a knowledge of heat transfer between the system and its surroundings.A more practical approach would be to develop a relation for theequilibrium criterion in terms of the properties of the reacting system only.Such a relation is developed below.Consider a reacting (or nonreacting) simple compressible system of fixedmass with only quasi-equilibrium work modes at a specified temperature Tand pressure P (Fig. 16–3). Combining the first- and the second-lawrelations for this system givesdQ P dV dUdS dQ TdS sys dQ T dU P dV T ds 0(16–2)