Form of the Balanced Equation

The value of from Example 17-1 is much different from the value given earlier for the same reaction at 2 5°C. For is reaction, products are favored at the lower temperature (K, = 3.6 X 10 at 25°C), whereas reactants are favored at the higher temperature (i = 0.286 at 500°C). You may recall from Chapter 16 that the rate constant, k, for any reaction increases with increasing temperature. But the value of for different reactions responds differently to temperature changes for some reactions, increases with increasing temperature, whereas for others decreases with increasing temperature, as we will see in Sections 17-6 and 17-13. 

The small value ofK Indicates that the equilibrium lies to the left, that is, the forward reaction is nonspontaneous (reactant-favored). 

We put 10.0 moles ofN20 into a 2.00-L container at some temperature, where it decomposes according to 

At equilibrium, 2.20 moles of N2O remain. Calculate the value of for the reaction. 

We express all concentrations in moles per Uter. The mole ratio from the balanced chemical equation allows us to find the changes in concentrations of the other substances in the reaction. We use the reaction summary to find the equilibrium concentrations to use in the expression. 

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A dimensionless form of the balance equation, can be obtained by substituting the following dimensionless variables... 

The gas is at high concentration and therefore the column component balance equations are based on mole ratio concentration units. The form of the balance equations follow those of Sec. 4.4.1. 

The concepts of structural observability are the basic tools for developing variable classification strategies. Some approaches presented in Chapter 3 are based on the fact that the classification of process variables results from the topology of the system and the placement of instruments and has nothing to do with the functional form of the balance equations. Thus, the linearity restriction will be removed and efficient reduction of the large-scale problem will be accomplished. 

By taking xf = mv, we can obtain the local form of the balance equation of the linear momentum as... 

As Steward (13) has proved, all the unmeasured variables will be assigned to every possible output set assignment if they are determinables, i.e. if there is no structural singularity. This result is general and does not depend on the functional form of the balance equations. Consequently, except for isolated numerical singularities the determinability of an unmeasured parameter is specified from whether it can be assigned in an output set assignment or not. 

If a total material balance is performed, the above form of the balance equation must be used if the amounts or flowrates are expressed in terms of moles, e.g., Ibmol or gmol/h, since the total number of moles can change during a chemical reaction. If,... 

Basic Concepts 17-2 The Equilibrium Constant 17-3 Variation of with the Form of the Balanced Equation 17-4 The Reaction Quotient 17-5 Uses of the Equilibrium Constant,... 

The value of depends on the form of the balanced equation for the reaction. We wrote the equation for the reaction of SO2 and O2 to form SO3, and its equilibrium constant expression as... 

Consider the generic transport equation for the property -0 and assume that the velocity held and the fluid properties are known. The starting point for the FVM is the integral form of the balance equation ... 

Both methods lead to the correct form of the balanced equation. The ion-eietron method has two advantages ... 

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. 

Notice that Eq. 2.1-1 is concerned with an instantaneous rate of change, and it requires data on the rates at which flows occur. Equation 2.1-2, on the other hand, is for computing the total change that has occurred and requires data only on the total flows over the time interval. These two equations, one for the instantaneous rate of change of a system property (here the amount of water) and the other for the change over an interval of time, illustrate the two types of change-of-state problems that are of interest in this book and the forms of the balance equations that are used in their solution. 

The differential form of the multicomponent mass, energy, and entropy balances can be integrated over time to get difference forms of the balance equations, as was done in Chapters 2, 3, and 4 for the pure-component equations. The differential and difference forms of the balance equations are.listed in Tables 8.4-1 and 8.4-2, respectively. It is left to the reader to work out the various simplifications of these equations that arise for special cases of closed systems, adiabatic processes, and so forth. 

Since the form of the balance equations is unchanged, we can use, without modification, the analysis of the last chapter to establish that the equilibrium criteria for a closed multicomponent mi.xture are (Problem 8.23)... 

In the chemical processing industries, steady-flow systems are common, so the accumulation terms on the left sides of (12.3.1) and (12.3.2) are normally zero, and the rate forms of the balance equations can be used. Then the material and energy balances can be expressed as... 

By observing the dimensionless form of the balance equations (Eqs. 22, 23a) and bearing in mind the dimensionless groups that can be introduced by the boundary conditions, it is easy to demonstrate that the average Nusselt number in the laminar regime can be considered, for a fixed cross-sectional geometry, as a function of the following dimensionless quantities ... 

Generally, it is preferable to avoid using fi actional coefficients because they could be interpreted as implying the existence of fractional molecules. But we can easily eliminate any fractions by multiplying the entire equation by a factor that removes them. In this case multiplying by 2 will do the trick, converting the 1/2 to 1. This brings us to a final form of the balanced equation ... 

Substituting Eqns (14.31) and (14.35) in the general form of the balance equations of entropy... 

Considering a kinematically admissible variation" h = (8p, 50) of the pair p, A), taking the dot product with Eqs. (5a) and (5b), integrating over the length of the curved reference beam and integrating by parts, we obtain the nonlinear functional G p, A, h) corresponding to the weak form of the balance equations, Ibrahimbegovic (1995) and... 

Since this relation should be valid for an any volume, we can equate the integrands. This gives us the differential form of the balance equation for Y ... 

It should be noted that the exact form of the balance Equation 3.22 cannot be directly applied to the equilibrium reactor, since R = 0 in equilibria but 0. 

According to the guidelines set in Equations 5.18 through 5.20, the alternative forms of the balance equations, expressed with the extents of reactions, the molar flows of the key components, and the relative conversions, are obtained ... 

In particular, the form of the balance equations obtained is quite characteristic and sufficiently general to be considered as the basis for treating a wide variety of cases. We remain, however, less satisfied as far as the constitutive relations are concerned, since their determination implies the study of a three dimensional medium each time, over the thickness of the interface. There would be no gain in time or simplicity if this work had to be repeated in each case. 

Another form of the balance equation is derived from the above equation, using the conservation of mass equation ... 

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