Balancing Chemical Reactions

Our first major task of this chapter is to learn to balance equations for chemical reactions. Balancing simple equations will be covered in this chapter equations for more complicated oxidation-reduction reactions will be considered in Chapter 16. 

Equations for Chemical Reactions Balancing a Chemical Equation Types of Reactions Functional Groups and Reactions of Organic Compounds ... 

Consider the chemical reaction balanced in two different ways ... 

The chemical reaction (I) caimot come to equilibrium directly it can come to equilibrium only if the two electrodes are coimected so that electrons can flow. One can use this feature to detennine the affinity (or the AG) of reaction (I) by detennining the affinity of reaction (II) which balances it. 

Conservation laws at a microscopic level of molecular interactions play an important role. In particular, energy as a conserved variable plays a central role in statistical mechanics. Another important concept for equilibrium systems is the law of detailed balance. Molecular motion can be viewed as a sequence of collisions, each of which is akin to a reaction. Most often it is the momentum, energy and angrilar momentum of each of the constituents that is changed during a collision if the molecular structure is altered, one has a chemical reaction. The law of detailed balance implies that, in equilibrium, the number of each reaction in the forward direction is the same as that in the reverse direction i.e. each microscopic reaction is in equilibrium. This is a consequence of the time reversal syimnetry of mechanics. 

The differential material balances contain a large number of physical parameters describing the structure of the porous medium, the physical properties of the gaseous mixture diffusing through it, the kinetics of the chemical reaction and the composition and pressure of the reactant mixture outside the pellet. In such circumstances it Is always valuable to assemble the physical parameters into a smaller number of Independent dimensionless groups, and this Is best done by writing the balance equations themselves in dimensionless form. The relevant equations are (11.20), (11.21), (11.22), (11.23), (11.16) and the expression (11.27) for the effectiveness factor. 

A balanced chemical reaction indicates the quantitative relationships between the moles of reactants and products. These stoichiometric relationships provide the basis for many analytical calculations. Consider, for example, the problem of determining the amount of oxalic acid, H2C2O4, in rhubarb. One method for this analysis uses the following reaction in which we oxidize oxalic acid to CO2. 

The balanced chemical reaction provides the stoichiometric relationship between the moles of Fe used and the moles of oxalic acid in the sample being analyzed— specifically, one mole of oxalic acid reacts with two moles of Fe. As shown in Example 2.6, the balanced chemical reaction can be used to determine the amount of oxalic acid in a sample, provided that information about the number of moles of Fe is known. 

Stoichiometric relationships and calculations are important in many quantitative analyses. The stoichiometry between the reactants and products of a chemical reaction is given by the coefficients of a balanced chemical reaction. When it is inconvenient to balance reactions, conservation principles can be used to establish the stoichiometric relationships. 

Gravimetric methods based on precipitation or volatilization reactions require that the analyte, or some other species in the sample, participate in a chemical reaction producing a change in physical state. For example, in direct precipitation gravimetry, a soluble analyte is converted to an insoluble form that precipitates from solution. In some situations, however, the analyte is already present in a form that may be readily separated from its liquid, gas, or solid matrix. When such a separation is possible, the analyte s mass can be directly determined with an appropriate balance. In this section the application of particulate gravimetry is briefly considered. 

A 38.63-mg sample of potassium ozonide, KO3, was heated to 70 °C for 1 h, undergoing a weight loss of 7.10 mg. Write a balanced chemical reaction describing this decomposition reaction. A 29.6-mg sample of impure KO3 experiences a 4.86-mg weight loss when treated under similar condition. What is the %w/w KO3 in the sample ... 

Thermochemistry. From an overall heat and mass balance point of view, the main chemical reactions of the blast furnace include oxidation of carbon in the zone in front of the tuyeres (raceway) to give CO plus heat. 

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 ... 

Equation 235 is the basic expression of material balance for a closed system in which r chemical reactions occur. It asserts that ia such a system... 

The general criterion of chemical reaction equiUbria is the same as that for phase equiUbria, namely that the total Gibbs energy of a closed system be a minimum at constant, uniform T and P (eq. 212). If the T and P of a siagle-phase, chemically reactive system are constant, then the quantities capable of change are the mole numbers, n. The iadependentiy variable quantities are just the r reaction coordinates, and thus the equiUbrium state is characterized by the rnecessary derivative conditions (and subject to the material balance constraints of equation 235) where j = 1,11,.. ., r ... 

The flow of hydrothermal solutions iato the oceans from hydrothermal vents, ie, springs coming from the sea floor ia areas of active volcanism, and the chemical reactions occurring there by high temperature alteration of basalts ate of significance ia the mass balance of and. Eurthermore,... 

Representation of Atmospheric Chemistry Through Chemical Mechanisms. A complete description of atmospheric chemistry within an air quaUty model would require tracking the kinetics of many hundreds of compounds through thousands of chemical reactions. Fortunately, in modeling the dynamics of reactive compounds such as peroxyacetyl nitrate [2278-22-0] (PAN), C2H2NO, O, and NO2, it is not necessary to foUow every compound. Instead, a compact representation of the atmospheric chemistry is used. Chemical mechanisms represent a compromise between an exhaustive description of the chemistry and computational tractabiUty. The level of chemical detail is balanced against computational time, which increases as the number of species and reactions increases. Instead of the hundreds of species present in the atmosphere, chemical mechanisms include on the order of 50 species and 100 reactions. 

The concentration dependence of iron corrosion in potassium chloride [7447-40-7] sodium chloride [7647-14-5] and lithium chloride [7447-44-8] solutions is shown in Figure 5 (21). In all three cases there is a maximum in corrosion rate. For NaCl this maximum is at approximately 0.5 Ai (about 3 wt %). Oxygen solubiUty decreases with increasing salt concentration, thus the lower corrosion rate at higher salt concentrations. The initial iacrease in the iron corrosion rate is related to the action of the chloride ion in concert with oxygen. The corrosion rate of iron reaches a maximum at ca 70°C. As for salt concentration, the increased rate of chemical reaction achieved with increased temperature is balanced by a decrease in oxygen solubiUty. 

Since the system is closed and without chemical reaction, material balances require that... 

Packed Red Reactors The commonest vessels are cylindrical. They will have gradients of composition and temperature in the radial and axial directions. The partial differential equations of the material and energy balances are summarized in Table 7-10. Example 4 of Modeling of Chemical Reactions in Sec. 23 is an apphcation of such equations. 

Those based on strictly empirical descriptions Mathematical models based on physical and chemical laws (e.g., mass and energy balances, thermodynamics, chemical reaction kinefics) are frequently employed in optimization apphcations. These models are conceptually attractive because a gener model for any system size can be developed before the system is constructed. On the other hand, an empirical model can be devised that simply correlates input-output data without any physiochemical analysis of the process. For... 

The yield in a chemical reaction determines the quantities of materials in the material balance. Assumed yields are used to obtain approximate exploratoiy estimates. In this case, possible ranges should be given. Firmer estimates require yields based on laboratoiy or, preferably, pilot-plant work. 

For fast irreversible chemical reactions, therefore, the principles of rigorous absorber design can be applied by first estabhshing the effects of the chemical reaction on /cl and then employing the appropriate material-balance and rate equations in Eq. (14-71) to perform the integration to compute the required height of packing. 

An industrial chemical reacdor is a complex device in which heat transfer, mass transfer, diffusion, and friction may occur along with chemical reaction, and it must be safe and controllable. In large vessels, questions of mixing of reactants, flow distribution, residence time distribution, and efficient utilization of the surface of porous catalysts also arise. A particular process can be dominated by one of these factors or by several of them for example, a reactor may on occasion be predominantly a heat exchanger or a mass-transfer device. A successful commercial unit is an economic balance of all these factors. 

To isolate a system for study, the system is separated from the surroundings by a boundary or envelope that may either be real (e.g., a reactor vessel) or imaginary. Mass crossing the boundaiy and entering the system is part of the mass-in term. The equation may be used for any compound whose quantity does not change by chemical reaction or for any chemical element, regardless of whether it has participated in a chemical reaction. Furthermore, it may be written for one piece of equipment, several pieces of equipment, or around an entire process (i.e., a total material balance). 

If chemical reactions occur only over the catalyst and none on the walls or in the homogeneous fluid stream in the recycle loop, then conservation laws require that the two balances should be equal. 

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