Thermodynamics

804 | ThermodynamicsTheny 3 x 0.246z 2.5 x 2 1.123Therefore, the equilibrium composition of the mixture at 2600 K and 5 atm is2.754CO 2 0.246CO 1.123O 2 8N 2Discussion Note that the inert gases do not affect the K P value or the K Prelation for a reaction, but they do affect the equilibrium composition.Composition: CO 2 , CO, O 2 , ONo. of components: 4No. of elements: 2No. of K p relations needed: 4 – 2 = 2FIGURE 16–14The number of K P relations needed todetermine the equilibrium compositionof a reacting mixture is the differencebetween the number of species and thenumber of elements.16–4 ■ CHEMICAL EQUILIBRIUMFOR SIMULTANEOUS REACTIONSThe reacting mixtures we have considered so far involved only one reaction,and writing a K P relation for that reaction was sufficient to determine theequilibrium composition of the mixture. However, most practical chemicalreactions involve two or more reactions that occur simultaneously, whichmakes them more difficult to deal with. In such cases, it becomes necessaryto apply the equilibrium criterion to all possible reactions that may occur inthe reaction chamber. When a chemical species appears in more than onereaction, the application of the equilibrium criterion, together with the massbalance for each chemical species, results in a system of simultaneous equationsfrom which the equilibrium composition can be determined.We have shown earlier that a reacting system at a specified temperatureand pressure achieves chemical equilibrium when its Gibbs function reachesa minimum value, that is, (dG) T,P 0. This is true regardless of the numberof reactions that may be occurring. When two or more reactions areinvolved, this condition is satisfied only when (dG) T,P 0 for each reaction.Assuming ideal-gas behavior, the K P of each reaction can be determinedfrom Eq. 16–15, with N total being the total number of moles present in theequilibrium mixture.The determination of the equilibrium composition of a reacting mixturerequires that we have as many equations as unknowns, where the unknownsare the number of moles of each chemical species present in the equilibriummixture. The mass balance of each element involved provides one equation.The rest of the equations must come from the K P relations written for eachreaction. Thus we conclude that the number of K P relations needed to determinethe equilibrium composition of a reacting mixture is equal to thenumber of chemical species minus the number of elements present in equilibrium.For an equilibrium mixture that consists of CO 2 , CO, O 2 , and O,for example, two K P relations are needed to determine the equilibriumcomposition since it involves four chemical species and two elements(Fig. 16–14).The determination of the equilibrium composition of a reacting mixture inthe presence of two simultaneous reactions is here with an example.