Complex reactions mole balances

Macroscopic chemical techniques can be used to characterize overall reactions like those in Eqs. 1.3, 1.8, and 1.9. Given the complexity of reaction mechanisms, however, measurements of the composition of the aqueous system in which an overall reaction occurs over the course of time may not always yield data that conform to the expected stoichiometry. For example, if the reaction of carbon dioxide and water to produce protons and bicarbonate ions is initiated at high pH (very low proton concentration), the disappearance of 1 mol C02 need not be accompanied by the disappearance of 1 mol H20 (because of Eq. 1.5) or by the appearance of 1 mol H+ (because of Eq. 1.1).2,7 The unaccounted-for presence of intermediate species (like H2COj in Eq. 1.1) can lead typically to a delay in the formation of one or more final product species relative to the others, such that the expected stoichiometry in an overall reaction is violated when the reaction progress is monitored. This transient feature of mole balance in overall reactions has important ramifications when the kinetics of soil chemical processes are investigated (Section 1.3). 

Of course, redox reactions do not occur in isolation but are coupled through complexation reactions to other species. For example, Eq. 2.30 could include terms for nitrate and amine complexes, in addition to those for free nitrate, nitrite, and ammonium ions, if a typical soil solution were under consideration. The calculation of nitrogen speciation then would proceed just as described above. Indeed, redox reactions introduce no new mathematical elements into a speciation computation, any more than would the consideration of, for example, C02 reactions. The only new item brought in is an additional variable, the pE value, which, like the partial pressure of C02(g), must be specified in order to solve mole balance equations for distribution coefficients. 

The formal similarity between adsorption and complexation reactions can be exploited to incorporate adsorbed species into the equilibrium speciation calculations described in Sections 2.4 and 3.1. To do this, a choice of adsorbent species components (SR r in Eq. 4.3) must be made and equilibrium constants for reactions with aqueous ions must be available. A model for computing adsorbed species activity coefficients must also be selected.8 Once these choices are made and the thermodynamic data are compiled, a speciation calculation proceeds by adding adsorbent species and adsorbed species (SR Mp(OH)yHxLq in Eq. 4.3) to the mole-balance equations for metals and ligands, and then following the steps described in Section 2.4 for aqueous species. For compatibility of the units of concentration, njw) in Eq. 4.2 is converted to an aqueous-phase concentration through division by the volume of aqueous solution. 

In complex reaction systems consisting of combinations of parallel and series reactions the availability of software packages (ODE solvers) makes it much easier to solve problems using moles Nj or molar flow rates Fj rather than conversion. For liquid systems, concentration may be the preferred variable used in, the mole balance equations. The resulting coupled differential equations can be easily solved using an ODE solver. In fact, tltis section has been developed to take advantage of the vast number of computational techniques now available on mainframe (e.g., Simulsolv) and personal computers (POLYMATH). 

Table 6-1 gives the forms of the mole balances we shall use for complex reactions where and fg are the net rates of reaction. 

Sec. 6.3 Algorithm tor Solution to Complex Reactions (2) Mole balance on NHj ... 

In this chapter, we discuss reactor selection and general mole balances for multiple reactions. First, we describe the four baste types of multiple reactions series, parallel, independent, and complex. Next, we define the selectivity parameter and discuss how it can be used to minimize unwanted side reactions by proper choice of operating conditions and reactor selection. We then develop the algorithm that can be used to solve reaction engineering problems when multiple reactions are involved. Finally, a number of examples are given that show how the algorithm is applied to a number of real reactions. 

We begin by writing mole balance equations in varitdiles other than conversion. Nf, C , Fi- Table 6-1 gives the forms of the mole balance equation we shall use for complex reactions where and tb are the net rates of formation of A and B. 

The algorithm for solving complex reactions is applied to a gas-pha.se reaction in Figure 6-5. This algorithm is very similar to the one given in Chapter 4 for w riling the mole balances in terms of molar flow rates and concentrations (i.e.. 

Based on the experimental mole ratio of reactants in part C, write a balanced chemical equation describing the complexation reaction you observed assuming all reactants used (neglecting NH20H HC1 and buffer) actually formed complex. 

The more complex case of the continuous stirred-tank reactor (CSTR) can be analyzed in a similar way as that of the plug-flow reactor (Section 6.2.3.2). Again considering the reversible exothermic reaction A B, the mole balance equation for component A at steady-state conditions is... 

Although this particular problem could he solved using conversion, we shall illustrate how it can also be solved using molar flow rates as the variable in the mole balance. Why do we do this We do this to give practice using molar flow rates as the variables in order to help prepare the reader for the more complex problems where conversion cannot be used as a variable. We first write the reaction in symbolic form and then divide by the stoichiometric coefficient of the limiting reactant. NOCl. 

Gadewar, S.B., Doherty, M.F., Malone, M.F. A systematic method for reaction invariants and mole balances for complex chemistries. Comput. Chem. Eng. 25, 1199-1217 (2001)... 

The characteristic features of parameter estimation in a molecular model of adsorption are illustrated in Table 9.9, taking the simple example of the constant-capacitance model as applied to the acid-base reactions on a hydroxylated mineral surface. (It is instructive to work out the correspondence between equation (9.2) and the two reactions in Table 9.9.) Given the assumption of an average surface hydroxyl, there are just two chemical reactions involved (the background electrolyte is not considered). The constraint equations prescribe mass and charge balance (in terms of mole fractions, x) and two complex stability constants. Parameter estimation then requires the determination of the two equilibrium constants and the capacitance density simultaneously from experimental data on the species mole fractions as functions of pH. 

A 1-1. three-necked round-bottomed flask is fitted with a dropping funnel, a reflux condenser attached to a hydrogen chloride absorption trap, and a very sturdy mechanical stirrer (Note 1), which may be of the mercury-sealed or rubber-sleeve tjtpe. In the flask are placed 350 ml. of dry carbon disulfide and 80 g. (0.48 mole) of fluorene (Note 2). The stirrer is started, and, after the fluorene has dissolved, 128 g. (0.96 mole) of anhydrous aluminum chloride is added in one portion. In the dropping funnel is placed 49.4 g. (0.48 mole) of redistilled acetic anhydride, and about 1 ml. of it is added dropwise to the vigorously stirred dark red reaction mixture. If the reaction does not start immediately it is initiated by warming the reaction flask in a water bath (Note 3). After the reaction has started, the balance of the acetic anhydride is added at such a rate that the carbon disulfide refluxes gently about 45-55 minutes is required. When approximately one-half of the acetic anhydride has been added an addition complex sepa-... 

Mole-mole problems are sort of like introductory, or skill-building, problems that will help you practice using the molar ratios given by balanced chemical reactions. The harder stoichiometry problems, which we will begin in the next lesson, all make use of mole-mole problems as a step in the problem-solving process. This lesson will give you an opportunity to become comfortable with the molar ratio without worrying about more complex problems at the same time. 

The first category includes systems in which the number of independent balance relationships is equal to the number of elements or basic species and where, moreover, conversion of the initial to the equilibrium mixture involves a change in the overall number of moles. The two conditions are usually satisfied when the initial mixture includes at least two constituents and the equilibrium mixture is rather complex. In such cases, there is usually at least one reaction among the many possible ones, the sum of stoichiometric coefficients of which is non-zero. For a system thus defined, the set (5.121) may be used unchanged. 

The simplest approximation for treating a complex flame system corresponds to assuming the pseudo-stationary state concentration for each of the chemical intermediates in the expressions for the net rate of production of the fuel and product molecules, and setting the mole fractions and fractions of the mass rate of flow for each of these intermediates equal to zero in the diffusion, energy balance, and motion equations. The resulting equations correspond to a simple one step chemical reaction system with only a single linearly independent and the solution of these equations presents no difficult mathematical problems. 

Balancing electrode reactions. In any stoichiometric half-cell (electrode) reaction, the charge on both sides is balanced explicitly by electrons. The balanced equation gives the ratio of moles of electrons to moles of other species, and the number of moles of electrons can be converted into coulombs using the Faraday. In aqueous solutions these reactions may be complex because the solvent water can become involved in the reaction. In acidic aqueous solution, an electrode reaction is most easily balanced by carrying out the following steps in order ... 

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