Examples balancing equation

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. 

EXAMPLE Balancing Equations by the Half-Reaction Method (Acidic Solution)... 

Reservoir engineers describe the relationship between the volume of fluids produced, the compressibility of the fluids and the reservoir pressure using material balance techniques. This approach treats the reservoir system like a tank, filled with oil, water, gas, and reservoir rock in the appropriate volumes, but without regard to the distribution of the fluids (i.e. the detailed movement of fluids inside the system). Material balance uses the PVT properties of the fluids described in Section 5.2.6, and accounts for the variations of fluid properties with pressure. The technique is firstly useful in predicting how reservoir pressure will respond to production. Secondly, material balance can be used to reduce uncertainty in volumetries by measuring reservoir pressure and cumulative production during the producing phase of the field life. An example of the simplest material balance equation for an oil reservoir above the bubble point will be shown In the next section. 

Derivation of the working equations of upwinded schemes for heat transport in a polymeric flow is similar to the previously described weighted residual Petrov-Galerkm finite element method. In this section a basic outline of this derivation is given using a steady-state heat balance equation as an example. 

Besides equilibrium constant equations, two other types of equations are used in the systematic approach to solving equilibrium problems. The first of these is a mass balance equation, which is simply a statement of the conservation of matter. In a solution of a monoprotic weak acid, for example, the combined concentrations of the conjugate weak acid, HA, and the conjugate weak base, A , must equal the weak acid s initial concentration, Cha- ... 

Note that the concentration of Ca + is multiplied by 2, and that the concentrations of H3O+ and OH are also included. Charge balance equations must be written carefully since every ion in solution must be included. This presents a problem when the concentration of one ion in solution is held constant by a reagent of unspecified composition. For example, in many situations pH is held constant using a buffer. If the composition of the buffer is not specified, then a charge balance equation cannot be written. 

Example This equation is obtained in distillation problems, among others, in which the number of theoretical plates is required. If the relative volatility is assumed to be constant, the plates are theoretically perfect, and the molal liquid and vapor rates are constant, then a material balance around the nth plate of the enriching section yields a Riccati difference equation. 

Microscopic Balance Equations Partial differential balance equations express the conservation principles at a point in space. Equations for mass, momentum, totaf energy, and mechanical energy may be found in Whitaker (ibid.). Bird, Stewart, and Lightfoot (Transport Phenomena, Wiley, New York, 1960), and Slattery (Momentum, Heat and Mass Transfer in Continua, 2d ed., Krieger, Huntington, N.Y., 1981), for example. These references also present the equations in other useful coordinate systems besides the cartesian system. The coordinate systems are fixed in inertial reference frames. The two most used equations, for mass and momentum, are presented here. 

Herbst et al. [International J. Mineral Proce.ssing, 22, 273-296 (1988)] describe the software modules in an optimum controller for a grinding circuit. The process model can be an empirical model as some authors have used. A phenomenological model can give more accurate predictions, and can be extrapolated, for example from pilot-to full-scale apphcation, if scale-up rules are known. Normally the model is a variant of the popiilation balance equations given in the previous section. 

A second order reaction is performed adiabatically in a CESTR. Use die data in Example 6-11 to plot bodi conversions for die mass and heat balance equations. The second order rate constant k is... 

As you found in Example 4.10, the balanced equation for the reaction between Mn04 and Fe2+ in acidic solution is... 

The order of a reaction must be determined experimentally it cannot be deduced from die coefficients in the balanced equation. This must be true because there is only one reaction order, but there are many different ways in which the equation for the reaction can be balanced. For example, although we wrote... 

Example 12.4 illustrates a principle that you will find very useful in solving equilibrium problems throughout this (and later) chapters. As a system approaches equilibrium, changes in partial pressures of reactants and products—like changes in molar amounts—are related to one another through the coefficients of the balanced equation. 

Express the equilibrium partial pressures of all species in terms of a single unknown, x. To do this, apply the principle mentioned earlier The changes in partial pressures of reactants and products are related through tite coefficients of the balanced equation. To keep track of these values, make an equilibrium table, like the one illustrated in Example 12.4. 

Sometimes we need to construct a balanced chemical equation from the description of a reaction. For example, methane, CH4, is the principal ingredient of natural gas (Fig. H.3). It burns in oxygen to form carbon dioxide and water, both formed initially as gases. To write the balanced equation for the reaction, we first write the skeletal equation ... 

Distinguish homogeneous and heterogeneous equilibria and write equilibrium constants for both types of reaction from a balanced equation (Example 9.1 and Self-Tests 9.2 and 9.5). 

Balancing the chemical equation for a redox reaction by inspection can be a real challenge, especially for one taking place in aqueous solution, when water may participate and we must include HzO and either H+ or OH. In such cases, it is easier to simplify the equation by separating it into its reduction and oxidation half-reactions, balance the half-reactions separately, and then add them together to obtain the balanced equation for the overall reaction. When adding the equations for half-reactions, we match the number of electrons released by oxidation with the number used in reduction, because electrons are neither created nor destroyed in chemical reactions. The procedure is outlined in Toolbox 12.1 and illustrated in Examples 12.1 and 12.2. 

Although a catalyst does not appear in the balanced equation for a reaction, the concentration of a homogeneous catalyst does appear in the rate law. For example, the reaction between the triiodide ion and the azide ion is very slow unless a catalyst such as carbon disulfide is present ... 

This mass balance equation shows that material that is initially at radial position rin will move to radial position r for some downstream location, >0. A worked example of radial velocities and curved streamlines is given in Chapter 13, Example 13.10. 

Solution The initial liquid-phase concentration of oxygen is 0.219mol/m as in Example 11.1. The final oxygen concentration will be 1.05 mol/m. The phase balances. Equations (11.11) and (11.12), govern the dynamic response. The flow and reaction terms are dropped from the liquid phase balance to give... 

All changes are related by stoichiometry. Each ratio of changes in amount equals the ratio of stoichiometric coefficients in the balanced equation. In the example above, the changes in amounts for H2 and N2 are in the ratio 3 1, the same as the ratio for the coefficients of H2 and N2 in the balanced equation. 

Each side of this balanced equation has a net charge of +2. Remember, however, that the net ionic equation does not show all of the species present in solution, in this example. Cl ions balance out the positive charges of ond H3 O. All solutions... 

C05-0138. In an explosion, a compound that is a solid or a liquid decomposes very rapidly, producing large volumes of gas. The force of the explosion results from the rapid expansion of the hot gases. For example, TNT (trinitrotoluene) explodes according to the following balanced equation ... 

C14-0083. Although the ATP-ADP reaction is the principal energy shuttle in metabolic pathways, many other examples of coupled reactions exist. For example, the glutamic acid-glutamine reaction discussed in the text can couple with the acetyl phosphate reaction shown in Example 14-10. Write the balanced equation for the coupled reaction operating in the direction of overall spontaneity and calculate A G ° for the overall process. 

Acrylonitrile Is produced from propene, ammonia, and oxygen by the following balanced equation (see Example 14-5) 2 C3 Hg + 2 NH3 + 3 O2 2 CH2 CHCN -1- 6 H2 O Relate the rates of reaction of starting materials and products. 

For example, experimental studies show that the rate law for the reaction of O3 with NO2 to give N2 O5 and O2 is first order in each reactant 2 NO2 + O3 N2 O5 + O2 Experimental rate = [N02 ][03 ] Notice that for this reaction, the order of reaction with respect to NO2 is 1, whereas the stoichiometric coefficient is 2. This shows that the order of a reaction for a particular species cannot be predicted by looking at the overall balanced equation. We describe additional examples in Section 15-1. 

The balanced half-reactions appear in Example. Balance the overall equation by combining the half-reactions in such a way that electrons cancel. 

The component mass balance, when coupled with the heat balance equation and temperature dependence of the kinetic rate coefficient, via the Arrhenius relation, provide the dynamic model for the system. Batch reactor simulation examples are provided by BATCHD, COMPREAC, BATCOM, CASTOR, HYDROL and RELUY. 

Thus Y1 is obtained not as the result of the numerical integration of a differential equation, but as the solution of an algebraic equation, which now requires an iterative procedure to determine the equilibrium value, Xj. The solution of algebraic balance equations in combination with an equilibrium relation has again resulted in an implicit algebraic loop. Simplification of such problems, however, is always possible, when Xj is simply related to Yi, as for example... 

The combination of the two mass balance equations, together with an explicit form of equilibrium relationship gives a system that is very easily solvable by direct numerical integration, as demonstrated in the simulation example BSTILL. 

A similar finite-differenced equivalent for the energy balance equation (including axial dispersion effects) may be derived. The simulation example DISRET involves the axial dispersion of both mass and energy and is based on the work of Ramirez (1976). A related model without reaction is used in the simulation example FILTWASH. 

Solution of the required column height is achieved by integrating the two component balance equations and the heat balance equation, down the column from the known conditions Xi , yout and TLin, until the condition that either Y is greater than or X is greater than Xqui is achieved. In this solution approach, variations in the overall mass transfer capacity coefficient both with respect to temperature and to concentration, if known, can also be included in the model as required. The solution procedure is illustrated by the simulation example AMMON AB. 

Although the Lewis cell was introduced over 50 years ago, and has several drawbacks, it is still used widely to study liquid-liquid interfacial kinetics, due to its simplicity and the adaptable nature of the experimental setup. For example, it was used recently to study the hydrolysis kinetics of -butyl acetate in the presence of a phase transfer catalyst [21]. Modeling of the system involved solving mass balance equations for coupled mass transfer and reactions for all of the species involved. Further recent applications of modified Lewis cells have focused on stripping-extraction kinetics [22-24], uncatalyzed hydrolysis [25,26], and partitioning kinetics [27]. 

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