Chemical species balances

Chemical Species Balances Decay Factors for Reactive Species The CEB method can be extended to families of chemical compounds, such as polycyclic aromatic hydrocarbons (PAH), while taking chemical reaction into account. Formally this can be done by writing chemical species balances in a somewhat different fashion from the CEB formulation ... 

The chemical species balance method can be extended to first-order chemical decay processes as follows ... 

Duval, M.M., (1980) "Source Resolution Studies of Ambient Polycyclic Aromatic Hydrocarbons in the Los Angeles Atmosphere Application of a Chemical Species Balance Method with First Order Chemical Decay", Thesis, Master of Science in Engineering, UCLA. 

To determine the thickness of the silicon film as a function of radius, both the Navier-Stokes equations and the chemical species balances are written and solved. Then, the volumetric flow rate of the feed stream, and its distribution through the showerhead holes, is adjusted to obtain a more uniform film. 

In the previous chapter, we have dealt with single-component balances, thus with the case when only one quantity is balanced around each node. A multicomponent balance is a set of several component balances. In chemical process networks, the components are certain chemical species present in the streams as the components of a mixture. Generally, the species can be transformed into one another by chemical reactions so their quantities may not be conserved individually. The individual balances are then not independent, as they must obey stoichiometric laws. This chapter deals mainly with steady-state chemical species balancing where chemical reactions are admitted the wording steady state is explained below. Formally precise unsteady-state balancing brings some problems, mainly because the holdup (accumulation) of a component in a unit is difficult to identify, due to spatial variability of the concentrations. See Section 4.7. 

Madron, F. and V. Veverka (1991), Invariants of the chemical species balances of a reacting system, Chem. Eng. Sci. 46, 2633-2637... 

The complete set of balance equations comprises the component (chemical species) balances and the energy balance. In an analogous manner as in Section 3.3, having measured or otherwise fixed certain variables values, the variables can be classified into measured and unmeasured the latter are to be computed as unknowns in a system of equations. A finer classification as in Section 3.3 is, however, less obvious. 

The minimal set of balance constraints (multicomponent chemical species balance and energy balance) will be formulated and analyzed in Chapter 8, Section 8.3 it is a set of independent scalar equations taking still account of all the available information. Solvability problems arise when certain variables values are given a priori see again Chapter 8. For the moment, let us only recall Section 5.5 as example of a complication. 

If the T and P of a multiphase system are constant, then the quantities capable of change are the iadividual mole numbers of the various chemical species / ia the various phases p. In the absence of chemical reactions, which is assumed here, the may change only by iaterphase mass transfer, and not (because the system is closed) by the transfer of matter across the boundaries of the system. Hence, for phase equUibrium ia a TT-phase system, equation 212 is subject to a set of material balance constraints ... 

If the source fingerprints, for each of n sources are known and the number of sources is less than or equal to the number of measured species (n < m), an estimate for the solution to the system of equations (3) can be obtained. If m > n, then the set of equations is overdetermined, and least-squares or linear programming techniques are used to solve for L. This is the basis of the chemical mass balance (CMB) method (20,21). If each source emits a particular species unique to it, then a very simple tracer technique can be used (5). Examples of commonly used tracers are lead and bromine from mobile sources, nickel from fuel oil, and sodium from sea salt. The condition that each source have a unique tracer species is not often met in practice. 

Formulate the constraining material-balance equations, based on conservation of the total number of atoms of each element in a system comprised of w elements. Let subscript k identify a particular atom, and define Ai as the total number of atomic masses of the /cth element in the feed. Further, let a be the number of atoms of the /cth element present in each molecule of chemical species i. The material balance for element k is then... 

If species i is an element, AG/ is zero. There are N equilibrium equations (Eqs. [4-355]), one for each chemical species, and there are w material-balance equations (Eqs. [4-353]), one for each element—a total of N + to equations. The unknowns in these equations are the (note that y, = of which there are N, and the Xi, of which... 

For each stage J, the following 2C -1- 3 component material-balance (M), phase-equilibrium (E), mole-fraction-summation (S), and energy-balance (H) equations apply, where C is the number of chemical species ... 

The formation of the combination of defects may be described as a chemical reaction and thermodynamic equilibrium conditions may be applied. The chemical notations of Kroger-Vink, Schottky, and defect structure elements (DSEs) are used [3, 11]. The chemical reactions have to balance the chemical species, lattice sites, and charges. An unoccupied lattice site is considered to be a chemical species (V) it is quite common that specific crystal structures are only found in the presence of a certain number of vacancies [12]. The Kroger-Vink notation makes use of the chemical element followed by the lattice site of this element as subscript and the charge relative to the ideal undisturbed lattice as superscript. An example is the formation of interstitial metal M ions and metal M ion vacancies, e.g., in silver halides ... 

A balanced chemical equation lists the initial chemical species (substrates) present and the new chemical species (products) formed for a particular chemical reaction, all in their correct proportions or stoichiome-try. For example, balanced equation (1) below describes the reaction of one molecule each of substrates A and B to form one molecule each of products P and Q. 

Both proposed mechanisms for NO2 decomposition contain chemical species produced in the first step and consumed in the second step. This is the defining characteristic of an intermediate. An intermediate is a chemical species produced In an early step of a mechanism and consumed in a later step. Intermediates never appear in the overall chemical equation. Notice that neither the O atoms of Mechanism I nor the NO3 molecules of Mechanism II appear In the balanced chemical equation for NO2 decomposition. 

The effect of concentration on the rate of a particular chemical reaction can be summarized in an algebraic expression known as a rate law. A rate law links the rate of a reaction with the concentrations of the reactants through a rate constant (jt ). In addition, as we show later in this chapter, the rate law may contain concentrations of chemical species that are not part of the balanced overall reaction. 

Unfortunately, chemical species produced by humans can react in ways that reduce the O3 concentration. For example, NO changes the oxygen balance through the following reactions NO + 03 NO2 + O2... 

When half-reactions are combined, there is often a duplication of some chemical species, particularly H2 0 and H3 O or OH. The overall equation is cleaned up by combining species that appear twice on the same side. Also, when a species appears on both sides of the balanced equation, equal numbers of the species are subtracted from each side. 

The coefficients of any balanced redox equation describe the stoichiometric ratios between chemical species, just as for other balanced chemical equations. Additionally, in redox reactions we can relate moles of chemical change to moles of electrons. Because electrons always cancel in a balanced redox equation, however, we need to look at half-reactions to determine the stoichiometric coefficients for the electrons. A balanced half-reaction provides the stoichiometric coefficients needed to compute the number of moles of electrons transferred for every mole of reagent. 

Each chemical species, in the system, can be described by means of a component balance around an arbitrary, well-mixed, balance region, as shown in Fig. 1.16. 

For a steady-state process the accumulation term will be zero. Except in nuclear processes, mass is neither generated nor consumed but if a chemical reaction takes place a particular chemical species may be formed or consumed in the process. If there is no chemical reaction the steady-state balance reduces to... 

Algebraic symbols are assigned to all the unknown flows and compositions. Balance equations are then written around each sub-system for the independent components (chemical species or elements). 

In addition to the total mass balance, equations can be written to describe changes in each of the individual chemical species, or components, that are present. As with the total mass, the mass of a component can be altered by exchange with the surroundings. However, it can also be affected by chemical reactions occurring within the system, converting one component to another. The total mass of the system is not affected by such interconversions, since the mass of reactants consumed is exactly equal to the mass of products formed. In verbal form, the component mass balance for a particular component A in the system is... 

When fluid velocity is constant, a component mass balance for a chemical species A in plug flow can be written as... 

Here the square brackets indicate the concentration of the chemical species within the bracket. That is, [A] means the concentration of A, and so forth. [A]" means the concentration of A raised to the a power, where a is the value of the coefficient of A in the balanced equation for the chemical equilibrium. The value of the ratio of concentration terms is symbolized by the letter K, called the equilibrium constant. For example, for the reaction of nitrogen and hydrogen referred to in Sec. 19.3,... 

The number of chemical species involved in a single elementary reaction is referred to as the molecularity of that reaction. Molecularity is a theoretical concept, whereas stoichiometry and order are empirical concepts. A simple reaction is referred to as uni-, bi-, or termolecular if one, two, or three species, respectively, participate as reactants. The majority of known elementary steps are bimolecular, with the balance being unimolecular and termolecular. 

Our discussion of multiphase CFD models has thus far focused on describing the mass and momentum balances for each phase. In applications to chemical reactors, we will frequently need to include chemical species and enthalpy balances. As mentioned previously, the multifluid models do not resolve the interfaces between phases and models based on correlations will be needed to close the interphase mass- and heat-transfer terms. To keep the notation simple, we will consider only a two-phase gas-solid system with ag + as = 1. If we denote the mass fractions of Nsp chemical species in each phase by Yga and Ysa, respectively, we can write the species balance equations as... 

Equation 1.5-1 used as a mass balance is normally applied to a chemical species. For a simple system (Section 1.4.4), only one equation is required, and it is a matter of convenience which substance is chosen. For a complex system, the maximum number of independent mass balance equations is equal to R, the number of chemical equations or noncomponent species. Here also it is largely a matter of convenience which species are chosen. Whether the system is simple or complex, there is usually only one energy balance. 

The Law of Conservation of Mass states that the total mass remains unchanged. This means that the total mass of the atoms of each element represented in the reactants must appear as products. In order to indicate this, we must balance the reaction. When balancing chemical equations, it is important to realize that you cannot change the formulas of the reactants and products the only things you may change are the coefficients in front of the reactants and products. The coefficients indicate how many of each chemical species react or form. A balanced equation has the same number of each type of atom present on both sides of the equation and the coefficients are present in the lowest whole number ratio. For example, iron metal reacts with oxygen gas to form rust, iron(III) oxide. We may represent this reaction by the following balanced equation ... 

As we mentioned previously, the balanced chemical equation not only indicates what chemical species are the reactants and what the products are, but it also indicates the relative ratio of reactants and products. Consider the balanced equation for the rusting of iron ... 

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