Chemical equations material balance equation

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... 

The Flory principle allows a simple relationship between the rate constants of macromolecular reactions (whose number is infinite) with the corresponding rate constants of elementary reactions. According to this principle all chemically identical reactive centers are kinetically indistinguishable, so that the rate constant of the reaction between any two molecules is proportional to that of the elementary reaction between their reactive centers and to the numbers of these centers in reacting molecules. Therefore, the material balance equations will comprise as kinetic parameters the rate constants of only elementary reactions whose number is normally rather small. 

From the material balance (equation 14.3-5) applied to C2H4(A), together with the rate law, and the fact that cA = cB, since PAo FB o and vA = Pg in the chemical equation,... 

Chemical production rates are often expressed on a molar basis but can be easily converted to mass flow quantities (kg/s). The material balance equation can then be expressed as... 

Fermentation systems obey the same fundamental mass and energy balance relationships as do chemical reaction systems, but special difficulties arise in biological reactor modelling, owing to uncertainties in the kinetic rate expression and the reaction stoichiometry. In what follows, material balance equations are derived for the total mass, the mass of substrate and the cell mass for the case of the stirred tank bioreactor system (Dunn et ah, 2003). 

Petersen [12] points out that this criterion is invalid for more complex chemical reactions whose rate is retarded by products. In such cases, the observed kinetic rate expression should be substituted into the material balance equation for the particular geometry of particle concerned. An asymptotic solution to the material balance equation then gives the correct form of the effectiveness factor. The results indicate that the inequality (23) is applicable only at high partial pressures of product. For low partial pressures of product (often the condition in an experimental differential tubular reactor), the criterion will depend on the magnitude of the constants in the kinetic rate equation. 

In the Inflow and Outflow terms (1) and (2), the heat flow may be of two kinds the first is transfer of sensible heat or enthalpy by the fluid entering and leaving the element and the second is heat transferred to or from the fluid across heat transfer surfaces, such as cooling coils situated in the reactor. The Heat absorbed in the chemical reaction, term (3), depends on the rate of reaction, which in turn depends on the concentration levels in the reactor as determined by the general material balance equation. Since the rate of reaction depends also on the temperature levels... 

The basic developments reported herein can be used to predict multicomponent adsorption rates in different types of contacting units, such as slurry adsorbers, moving bed units and columnar operation. The adsorption rate and equilibrium equations would remain the same, but the reactor material balance equation would be different depending on the reactor type and geometry. Thus, the multicomponent adsorption model can be utilized in practical processing applications in the chemical industry, air pollution control, and water and wastewater treatment. 

As mentioned in Chapter 2, chemical conjugation is absent in initiated processes. Moreover, initiated parallel chain processes (3.29) and (3.30) display the main reaction paths for reagent transformation to final products no matter what the manner of initiation. As shown by scheme (3.28), at chemical conjugation the first stage of the primary process in the mechanism and material balance equation must be taken into account by both reactions. 

Consider such a system containing a total of one mole of chemical sped and having an overall composition represented by the set of mole fractions Z Let L be the moles of liquid, with mole fractions xf, and let V be the moles vapor, with mole fractions. The material-balance equations are... 

If the system is closed and formed from specified aihounts of the chemical species present, then we can write a material-balance equation for each of the N chemical species. These in addition to the (ir - 1 )N phase-equilibrium equations provide a total number of independent equations equal to... 

Material Balance Equation for a Constant Volume Reservoir and with No Initial Gas Cap. Reservoir material balances are based on the principle of conservation of mass which asserts that the total mass of a system remains constant during a chemical or physical change. Before applying this principle to a constant volume reservoir with no gas cap the following terms need to be defined. 

A distillation process is shown in Fig. P2.59. You are asked to solve for all the values of the stream flows and compositions. How many unknowns are there in the system How many independent material balance equations can you write Explain each answer and show all details whereby you reached your decision. For each stream, the only components that occur are shown below the stream. Metallurgical-grade silicon is purified to electronic grade for use in the semiconductor industry by chemically separating it from its impurities. Si metal reacts in varying degrees with hydrogen chloride gas at 300°C to form several polychlorinated... 

The system is closed and without chemical reaction material balances therefore require that dni = -dn , reducing the preceding equation to... 

Chemical engineers develop mathematical models of systems of interest that usually include parameters. This chapter describes methodology that can be used to determine these parameters, which usually appear in a nonlinear manner. For example, the material balance equation for the reaction... 

A model for multistage separation accompanied by chemical reactions must include a term in the component material balance. Equation 13.2 or 13.49, to represent the change in the number of moles of component i on stage j due to chemical reaction. This term is expressed as... 

The equation of state for the mixture is obtained by the minimization procedure discussed previously. The result is an equation of state identical in form to Equation 2.A38. Similarly, the quasi-chemical condition for the mixture is identical in form to Equation 2.A39, and the material balance equations are identical in form to Equations 2.A34 or 2.A35. Of course r, s, e, and p in these equations are now quantities pertinent to the mixture. 

In order to explore the dynamics of open systems, it is necessary to formulate a material balance equation that accounts for all processes that work to elevate or depress the concentrations of chemical species of interest. Physical and chemical processes have been included in Eq. 65 (biological processes have not been considered) (Imboden and Schwarzenbach, 1985) ... 

In addition to the material balance Equation 18.38 that one normally encounters in design problems involving chemical reactions with no charge transfer, for the case of an electrochemical reaction, one must consider a charge balance equation that governs the distribution of the electric potential across the particle or the pores. For the particle in itself, such a conservation equation is usually presented in the form of Ohm s law given as follows ... 

Equilibrium compositions of the simulated exhaust were calculated as a function of temperature for several assumed reaction models. The calculations consisted of solving simultaneously, by the Newton iteration procedure, a set of material balance equations and chemical equilibrium... 

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