Mole balances multiple reactions

Balancing chemical reactions is an application of solving multiple simultaneous linear equations. Consider, for example, the complete combustion of one mole of methane to produce carbon dioxide and water ... 

There are a number of instances when it is much more convenient to work in terms of the number of moles (iV, N-g) or molar flow rates (Fj, Fg, etc.) rather than conversion. Membrane reactors and multiple reactions taking place in the gas phase are two such cases where molar flow rates rather than conversion are preferred. In Section 3.4 we de.scribed how we can express concentrations in terms of the molar flow rates of the reacting species rather than conversion, We will develop our algorithm using concentrations (liquids) and molar flow rates (gas) as our dependent variables. The main difference is that when conversion is used as our variable to relate one species concentration to that of another species concentration, we needed to write a mole balance on only one species, our basis of calculation. When molar flow rates and concentrations are used as our variables, we must write a mole balance on each species and then relate the mole balances to one another through the relative rates of reaction for... 

In this chapter we discuss reactor selection and general mole balances for multiple reactions. There are three basic types of multiple reactions series, parallel, and independent. In parallel reactions (also called competing reactions) the reactant is consumed by two different reaction pathways to form different products ... 

Having written the mole balances, the key point for multiple reactions is to write the net rate of formation of each species (e.g.. A, B). That is, we have to sum up the rates of formation for each reaction in order to obtain the net... 

These are die forms i of the mole balances we will use for ll multiple reactions... 

Example 6-S Combining Mole Balances, Rate Laws, and Stoichiometry for Multiple Reactions... 

We see tliiu conversion is not used in this sum. The molar flow rates, Fj, are found by solving the mole balance etjuations. Equation (.1-42) will be u.seci for measures other than ctmversion when we discuss nienibrane reactors (Chapter 4 Part 2) and multiple reactions (Chapter 6). We will use this form of the concentration equation for multiple gas-phase reactions and for membrane reactors. 

We divide the chapter into two parts Part 1 Mote Balances in Terms of Conversion, and Part 2 Mole Balances in Terms of Concentration, C,. and Molar Flow Rates, F,." In Pan 1, we will concentrate on batch reactors, CSTRs, and PFRs where conversion is the preferred measure of a reaction s progress for single reactions. In Part 2. we will analyze membrane reactors, the startup of a CSTR. and semibatch reactors, which are most easily analyzed using concentration and molar How rates as the variables rather than conversion. We will again use mole balances in terms of these variables (Q. f,) for multiple reactors in Chapter 6. 

Chemical Reaction Engineering. There is a greater emphasis on the use of mole balances in terms of concentrations and molar flow rates rather than conversion. It is introduced early in the text so that these forms of the balance equations can be easily applied to membrane reactors and multiple reactions, as well as PFRs. PBRs. and CSTRs. 

When multiple reactions occur in the gas phase, the mass balance for component i is written for an ideal tubular reactor at high mass transfer Peclet numbers in the following form, and each term has units of moles per volume per time ... 

Notice that the molar density of key-limiting reactant A on the external surface of the catalytic pellet is always used as the characteristic quantity to make the molar density of component i dimensionless in all the species mass balances. effective is the effective intrapellet diffusion coefficient of species i. If there is only one chemical reaction, or one rate-limiting step in a multiple reaction sequence, that is characterized by nth-order irreversible kinetics, then the rate constant in the numerator of the Damkohler numbers is the same for each A -. Hence, kj is written as k , which signifies that has units of (volume/mole)" /time for... 

In the case of multiple reaction equilibria, the number of moles of all reactive compounds in chemical equilibrium can be determined with the help of nonlinear regression methods [11]. But at the same time, the element balance has to be satisfied this means the amount of carbon, hydrogen, oxygen, nitrogen has to be the same before and after the reaction. This can either be taken into account with the help of Lagrange multipliers or using penalty functions [11], as shown in Example 12.8. 

We will again use mole balances in terms of these variables (Afj. F,) for multiple reactions in Chapter 8 and for heat effects in Clusters 11 through 13. 

The multiple reaction algorithm can be applied to parallel reactions, series reactions, complex reactions, and independent reactions. The availability of software packages (ODE solvers) makes it much easier to solve problems using moles or molar flow rates Fj rather than conversion. For liquid systems, concentration is usually the preferred variable used in the mole balance equations. 

Equation (12-5) is coupled with llte mole balances on each species [Equation (11 -33)]. Next, we express as a function of either the concentrations for liquid systems or molar flow rates for gas systems, as desenbed in Chapter 4. We will use the molar flow rate form of the energy balance for membrane reactors and also extend this form to multiple reactions. 

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