Balancing of equations

Setting f = Tout, H = Hout, and so on, specializes the integral energy balance of Equation (5.14) to a perfectly mixed, continuous-flow stirred tank ... 

Figure AC-2 shows the quantities represented by the mole balance of Equation AC-7. The mole balance is honored only if point M lies on the straight line between points R and S. This can be shown in Figure AC-2 using similar triangles.2...

If the batch reactor operation is both nonadiabatic and nonisothermal, the complete energy balance of equation 12.3-16 must be used together with the iiaterial balance of equation 2.2-4. These constitute a set of two simultaneous, nonlincmr, first-flijer ordinary differential equations with T and fA as dependent variables and I as Iidependent variable. The two boundary conditions are T = T0 and fA = fAo (usually 0) at I = 0. These two equations usually must be solved by a numerical procedure. (See problem 12-9, which may be solved using the E-Z Solve software.)... 

Examples 2.3 to 2.5 are concerned with the balancing of equations for electron acceptors relevant for sewer processes. Example 2.3 shows the procedure for an aerobic process step, Example 2.4 for an anoxic process and Example 2.5 for an anaerobic process. 

Balancing of equations including those for redox equations... 

A balanced chemical equation provides many types of information. It shows which chemical species are the reactants and which species are the products. It may also indicate in which state of matter the reactants and products exist. Special conditions of temperature, catalysts, etc., may be placed over or under the reaction arrow. And, very importantly, the coefficients (the integers in front of the chemical species) indicate the number of each reactant that is used and the number of each product that is formed. These coefficients may stand for individual atoms/molecules or they may represent large numbers of them called moles (see the Stoichiometry chapter for a discussion of moles). The basic idea behind the balancing of equations is the Law of Conservation of Matter, which says that in ordinary chemical reactions matter is neither created nor destroyed. The number of each type of reactant atom has to equal the number of each type of product atom. This requires adjusting the reactant and product coefficients—balancing the equation. When finished, the coefficients should be in the lowest possible whole-number ratio. 

In the total inorganic carbon balance of equation 8.94, we neglected the presence of some species. Table 8.9 shows that this approximation is reasonable although, for accurate calculations, we should also have considered bicarbonates CaHC03 and MgHCO and the soluble carbonate CaCO . Note also that sulfates occur in negligible molar proportions and that carbonate alkalinity coincides with total alkalinity. 

Considering the case of two-phase flow, with constant mass rates, no mass transfer and negligible accelerative effects, the total energy balance of Equation (17) can be rewritten, where Wo/pa = Qo and Wi/pi = Ql, to yield... 

This chapter concerns the application of these four principles to the balancing of equations for electron-transfer reactions. 

When a series of stirred-tanks is used as a chemical reactor, and the reactants are fed at a constant rate, eventually the system reaches a steady state such that the concentrations in the individual tanks, although different, do not vary with time. When the general material balance of equation 1.19 is applied, the accumulation term is therefore zero. Considering first of all the most general case in which the mass density of the mixture is not necessarily constant, the material balance on the reactant A is made on the basis of FA moles of A per unit time fed to the first tank. Then a material balance for the rth tank of volume V (Fig. 1.17) is, in the steady state ... 

Note that two of the reactions (2) and (3) had to be reversed in order to produce the summation reaction. The use of the fractional coefficients is for convenience so that the chlorine and the oxygen will cancel, but also so that we are matching the equation we were given in the problem statement above. The use of fractions in the balancing of equations is common, especially when balancing thermochemical reactions and electrochemical reactions (Chapter 19). 

Runge-Kutta fourth order while components C and D are calculated from the mass balance of Equations 5-130 and 5-132, respectively, at a time increment of h = At = 0.5 min. The computer program BATCH59 calculates the concentrations of A, B, C, and D as function... 

Applying the material balance of Equation 5-1 on species A gives... 

Balancing of equations, including those for redox reactions... 

As in the closed NH3 system, it is important to consider the mass balances correctly. The mass balance of equation viii can be divided by q in order to obtain all concentrations on a per liter water basis ... 

The oxygen in hydrogen peroxide (H2O2) is in an intermediate oxidation state of — 1 some of it is oxidized to O2 and some is reduced to H2O. The balancing of equations for disproportionation reactions is described in the following example. 

The balancing of equations by trial and error is successful if you are organized in your approach. All equations that have the correct formulas for all reactants and products can be balanced. Finally, it is important to understand that subscripts... 

To be meaningful, mi, m2 and ma must have real positive values and in the centre-of-mass system, the kinetic energy balance of equation (33) becomes 0 i.e. the left term of the equation is 0). Then the only way to satisfy equation (33) is for ... 

The radiative energy balances of Equations (7.16) and (7.17) can be represented in a network. Compared with an electric network, 4 and are analogous to me potential, and are analogous to me current, and AiZi and II AiFy are analogous to me resistances. The network analogy... 

A mixed-flow reactor (MFR), also known as the continuous stirred tank reactor (CSTR), is fuUy mixed at the molecular level, and the composition of the exiting stream is identical to that within the reactor. In this case, the material balance of Equation (11.12) is applied for the entire reactor and not just for a differential element as in a PFR. No integration is needed the eqnation becomes... 

This equation is coupled to the component balances of Equation 3.9 and with an equation for the pressure, for example, one of Equations 3.18, 3.19, or 3.21. There are iV + 2 equations and some auxiliary algebraic equations that need to be solved simultaneously. Numerical solution techniques are similar to those used in Section... 

When kmol units are used to characterize the accumulation of a mixture of gases, the mass balance of equation (11.11) is replaced by the molar balance for each component ... 

Equation (13.38) may be combined with the mass balance of equation (13.33) and then with equation (13.36) to give ... 

Masses, mass fractions, and mass ratios can be substituted consistently for moles, mole fractions, and mole ratios in the mass balances of equations (3-41) to (3-48). The following example illustrates this concept. 

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