Balances independent, nonreactive system

The maximum number of independent equations that can be derived by writing balances on a nonreactive system equals the number of chemical species in the input and output streams ... 

Wlien chemical reactions occur, a new variable sj is introduced into tlie material-balance equationsfor each independent reaction. Furthermore, a new equilibrium relation [Eq. (13.8)] can be written for each independent reaction. Therefore, when chemical-reaction equilibrium is superimposed on phase equilibrium, r new variables appear and r new equations can be written. The difference between the number of variables and number of equations therefore is imchanged, and Duhem s theorem as originally stated holds for reacting systems as well as for nonreacting systems. 

As with nonreactive systems, we can write one total mass balance and, in addition, one mass balance for each component (1,2,. .., p). Since we have p components, we are able to write p + equations in total, but ONLY p of them are independent Why For example, if we sum up all the material balance equations formulated for each component, we will discover that the result is equal to the total mass balance. 

These definitions present convenient and simplifying properties ( ) the dimensions of the system are reduced, simplifying the depiction of equilibrium (figure 3.3) (Frey and Stichlmair, 19996 Barbosa and Doherty, 1987a) (ii) they have the same numerical values before and after reaction (m) they sum up to unity (iv) they clearly indicate the presence of reactive azeotropes when Xi =Yf, (v) the nonreactive hmits are well defined (vi) the number of linear independent transformed composition variables coincides with the number of independent variables that describe the chemical equihbrium problem and vii) the lever rule is valid as the chemical reaction no longer impacts the material balance. 

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