Multiple reactions and stoichiometric balances

Before an expression such as Eq 2.26 can be integrated, the RHS must be expressed in terms of the single variable Ca. From the stoichiometric Eq 2.5, 

When a substance participates in several reactions at the same time, its net rate of decomposition is the algebraic sum of its rates in the individual reactions. The rates of the individual steps are identified with subscripts (dC/dt)1( (dC/dt)2,.. . . Take this group of reactions  

The number of independent rate equations is the same as the number of independent stoichiometric relations. In the present example, reactions 2 and 3 are reversible and are not independent. 

Some reactions apparently represented by single stoichiometric equations are in reality the result of a number of other reactions, often involving short lived intermediates such as free radicals. After a set of such elementary reactions is postulated by experience, intuition and exercise of judgement, a rate equation is deduced and checked against rate data. Problem Secion 3 of this chapter has a number of real examples. 

The amounts of all participants of a group of reactions can be expressed in terms of a number of key components equal to the number of independent stoichiometric relations. The independent rate equations then will involve only the key components and can be integrated. Problem Section 1 of this chapter develops several examples. 

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Stoichiometry (from the Greek stoikeion—element) is the practical application of the law of multiple proportions. The stoichiometric equation for a chemical reaction states unambiguously the number of molecules of the reactants and products that take part from which the quantities can be calculated. The equation must balance. 

Finally, when you are using either molecular species balances or extents of reaction to analyze a reactive system, the degree-of-freedom analysis must account for the number of independent chemical reactions among the species entering and leaving the system. Chemical reactions are independent if the stoichiometric equation of any one of them cannot be obtained by adding and subtracting multiples of the stoichiometric equations of the others. 

In order to quantify the rate of a chemical transformation, we need to introduce some definitions. First, we distinguish between different types of reactions based on the form used to describe eventual chemical transformation, as single or multiple reactions. Usually this can be done from material balance after examining the stoichiometry between reacting materials and products. If a single stoichiometric equation can present the transformation, this is a single reaction. If more than one equation is necessary to present all observed components and their transformations, this it is a case of multiple reactions. The examples are as following ... 

In the previous section, we have seen that, for a single reaetion, the rates of reaction for different components can all be expressed in terms of the rate of reaction of one component (together with the stoichiometric numbers), or the conversion of one of the reactants, or the yield of one of the produets (of course, together with the stoichiometric numbers). These information and relations for the single reaction are adequate for the solution of any mass balance problem with a single reaction and can be easily extended to multiple reaction systems, as will be shown later. However, in this section, we will try to make the calculations even more systematic. This will require, first, that we introduce the sign convention for the stoichiometric numbers, as we... 

Aspen is capable of modeling chemical reactions. It can handle single and multiple reactions. Material balance can be done in the stoichiometric reactor, Rsto/c from Reactors in the model library. Click on Material Streams, and connect the inlet and product streams. Click on Components and choose the components involved. Peng-Robinson EOS is selected as the thermodynamic fluid package. Doubleclick on the conversion reaction block. Click on the Specification tab enter pressure as 1 atm and temperature as 25°C. Then click on the Reactions tab, click on New and enter the components involved in the reaction, stoichiometric coefficient, and fractional conversion as shown in Figure 3.13. Close the stoichiometric windows and then double click on the inlet stream, specify temperature, pressure, flow rate, and composition. Click Run and then generate the stream table as shown in Figure 3.14. 

In general, concentrations of the products are divided by the concentrations of the reactants. In the case of gas-phase reactions, partial pressures cire used instead of molar concentrations. Multiple product or reactant concentrations are multiplied. Each concentration is raised to an exponent equal to its stoichiometric coefficient in the balanced reaction equation. (See Chapters 8 and 9 for details on balanced equations and stoichiometry.)... 

You can calculate the equilibrium constant for a reaction, from the concentrations of reactants and products at equilibrium. In the following reaction, for example, A and B are reactants, C and D are products, and a, b, c, and d are stoichiometric coefficients (numbers showing mole multiples in a balanced equation) ... 

If a reduction in the number of molar balances is desired for the calculations, the stoichiometric relationships developed in the previous section must be utilized. We can thus reduce the number of necessary balance equations from N to S one should keep in mind that the number of chemical reactions is usually much lower than the number of components in a system. The molar flows, /, can be replaced by expressions containing reaction extent, specific reaction extent, and reaction extent with concentration dimension or conversion (, I, I", or tia) in a system containing a single chemical reaction. For systems with multiple chemical reactions, h is replaced by an expression containing or i). ... 

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