Solving Material Balance Problems Involving Simultaneous Equations

4 SOLVING MATERIAL BALANCE PROBLEMS INVOLVING SIMULTANEOUS EQUATIONS 

Your objectives in studying this section are to be able to  

Write a set of independent material balance equations for a process. 

Apply the 10-step strategy to solve steady-state problems (with or without chemical reaction) that require the solution of simultaneous equations. 

In Sec. 2.3 you learned how to formulate uncoupled material balances that could be solved one equation at a time for the values of the unknown variables. All the equations were quite simple, and you did not have to solve two or more equations (called irreducible equations because of the nature of their coupling) simultaneously. You should have observed in Sec. 2.3 that the information provided with respect to the problems such as flows and concentrations was of a special structure that led to the 

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Another class of problems involves processes for which the heat input and outlet temperature are specified but the extent of reaction and product composition are not. Solving such problems requires the simultaneous solution of material and energy balance equations, as the next example illustrates. 

Solving problems that involve the electrostatic adsorption models requires the solution of a number of simultaneous equations. These include intrinsic constant adsorption expressions (mass-action equations) such as just described, and mass- and material-balance and charge-balance equations that account for total surface sites and sorbate species associated with the surface and the solution (cf. Davis et al. 1978 Dzombak and Morel 1987 Allison et al. 1991). These equations are considered in more detail in discussions of the three models. 

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