Stoichiometric balances

Figure 3-2. Two reaction equations showing two completely different uses for the (+) symbol a) giving a fully balanced single reaction, b) combining two parallel reactions into a single equation that is not stoichiometrically balanced.

The diacid-diamine amidation described in reaction 2 in Table 5.4 has been widely studied in the melt, in solution, and in the solid state. When equal amounts of two functional groups are present, both the rate laws and the molecular weight distributions are given by the treatment of the preceding sections. The stoichiometric balance between reactive groups is readily obtained by precipitating the 1 1 ammonium salt from ethanol ... 

Calculate the value of p at which the reaction should be stopped to obtain this polymer, assuming perfect stoichiometric balance and neglecting end group effects on. ... 

Using the case of f = 3 and p = 0.3 as an example, p, = 0.877 when r = 1 in contrast to, say, 0.886 when r = 0.98. This illustrates that failure to maintain stoichiometric balance continues to have a limiting effect on polymerization in this case also. 

For a fixed extent of reaction, the presence of multifunctional monomers in an equimolar mixture of reactive groups increases the degree of polymerization. Conversely, for the same mixture a lesser extent of reaction is needed to reach a specified with multifunctional reactants than without them. Remember that this entire approach is developed for the case of stoichiometric balance. If the numbers of functional groups are unequal, this effect works in opposition to the multifunctional groups. 

Liquid crystal polyesters are made by a different route. Because they are phenoHc esters, they cannot be made by direct ester exchange between a diphenol and a lower dialkyl ester due to unfavorable reactivities. The usual method is the so-called reverse ester exchange or acidolysis reaction (96) where the phenoHc hydroxyl groups are acylated with a lower aHphatic acid anhydride, eg, acetic or propionic anhydride, and the acetate or propionate ester is heated with an aromatic dicarboxyHc acid, sometimes in the presence of a catalyst. The phenoHc polyester forms readily as the volatile lower acid distills from the reaction mixture. Many Hquid crystal polymers are derived formally from hydroxyacids (97,98) and thein acetates readily undergo self-condensation in the melt, stoichiometric balance being automatically obtained. 

With as httie as 0.5% hydrolysis of the sulfone monomer, the polymerization stoichiometric balance is sufficientiy upset to prevent high molecular weight polymer from being achieved. The dependence of maximum attainable PSF molecular weight on water content during polymerization can be inferred from Figure 1. 

Represents EDC necessary for a stoichiometric balance, including that converted to by-products, but no recycled EDC. 

Stoichiometric Balances The amounts of aU participants in a group of reactions can be expressed in terms of a number of key components equal to the number of independent stoichiometric relations. The independent rate equations will then involve only those key components and will be, in principle, integrable. 

These equations will have to he solved numerically for A, B, and C as functions of time then D and E can he found hy algehra. Alternatively, five differential equations can he written and solved directly for the five participants as functions of time, thus avoiding the use of stoichiometric balances, although these are really involved in the formulation of the differential equations. 

One molecule (or mole) of propane reacts with five molecules (or moles) of oxygen to produce three molecules (or moles) or carbon dioxide and four molecules (or moles) of water. These numbers are called stoichiometric coefficients (v.) of the reaction and are shown below each reactant and product in the equation. In a stoichiometrically balanced equation, the total number of atoms of each constituent element in the reactants must be the same as that in the products. Thus, there are three atoms of C, eight atoms of H, and ten atoms of O on either side of the equation. This indicates that the compositions expressed in gram-atoms of elements remain unaltered during a chemical reaction. This is a consequence of the principle of conservation of mass applied to an isolated reactive system. It is also true that the combined mass of reactants is always equal to the combined mass of products in a chemical reaction, but the same is not generally valid for the total number of moles. To achieve equality on a molar basis, the sum of the stoichiometric coefficients for the reactants must equal the sum of v. for the products. Definitions of certain terms bearing relevance to reactive systems will follow next. 

Steam Utilization. Less steam is used in the RMProcess than is required for conventional shift conversion even though in other methanation processes as little as one-half of the total syngas is processed through shift conversion in order to achieve a near-stoichiometric balance of hydrogen and carbon monoxide for methanation. 

As long as concentrations are used no correction is needed for stoichiometric reactions. With non-stoichiometric balance, corrections must be carried out. 

Ionic solids with surface layers containing the ionic species in near proper stoichiometric balance and most... 

The diamine and diacid monomers used to make type AABB nylons are typically rather difficult to handle in their pure form. Diamines are liquids or semisolids at room temperature, while the diacids are crystalline solids. These monomers become much more manageable when they are combined to form nylon salts, as shown in Fig. 23.7 a). Nylon salts are solids that can be easily handled and ensure a stoichiometric balance between the diacid and diamine, which is necessary to produce high molecular weight polymers. In the case of nylon 66, the precursor salt is made by boiling adipic acid and hexamethylene diamine in methanol, from which the nylon salt precipitates. 

When comparing results from one small scale method to the other it is observed that an increase in C02 in mg/g are not stoichiometrically balanced by a decrease in CO mg/g. Carbon takes... 

Three-way catalysts are able to reduce NO as well as oxidize CO and hydrocarbons when the exhaust composition is held near the stoichiometrically balanced composition, or "stoichiometric point." This control of exhaust composition is accomplished, after the initial warmup period, through the use of the feedback control system illustrated in Figure 1 (2, 3, 4). ... 

Alternatively, five differential equations can be written and solved simultaneously for the five participants as functions of time, thus avoiding the making of the stoichiometric balances. 

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