Stoichiometrically balanced reaction

An extension of isomerism from molecules to ensembles of molecules (EM) leads to new perspectives in chemistry. The left and right hand sides of a stoichiometrically balanced reaction equation are isomeric EM. Any chemical reaction may be regarded as an isomerization, i.e. the conversion of an EM into an isomeric EM. Let A = A1(... A be a finite collection of atoms with the empirical formula A. Any EM that contains each atom of A exactly once is an EM (A). The family of all isomeric EM (A), the FIEM(A) contains the complete chemistry ofA = At,... A . The FIEM(A) is closed and finite. It has well-defined limitations and invariancies. Accordingly, the logical structure of the chemistry of an FIEM(A) is much easier to elucidate than the logical structure of chemistry without the above restrictions [9],... 

The chemistry for a stoichiometrically balanced reaction suggests that m = 1 and n = 2 in Eq. (2.86). For real systems, values are often close to these values but not identical. In the epoxy-amine reaction the alcohol, which may be present initially in small concentrations but is also a product of the reaction, catalyzes further reaction, resulting in autocatalysis. Since there are four unknowns ki, k2, m, and n) nonlinear regression analysis must be employed, although ki can be evaluated independently as the extrapolated reaction rate at a = 0. Autocatalytic kinetics are usually evaluated by the derivative form of the autocatalytic rate equation [Eq. (2.86)] with data coUected by isothermal method 1 measurements. Activation energy E and preexponential factor A are measured from the Arrhenius equation... 

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.

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. 

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. ... 

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. 

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. 

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. 

The equation for a chemical reaction speaks in terms of molecules or of moles. It contains the basis for stoichiometric calculations. However, in the laboratory a chemist measures amounts in such units as grams and milliliters. The first step in any quantitative calculation, then, is to convert the measured amounts to moles. In mole units, the balanced reaction connects quantities of reactants and products. Finally, the result is expressed in the desired units (which may not necessarily be the same as the original units). 

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

P2.Q1.07. STOICHIOMETRIC BALANCE IN TERMS OF AMOUNTS CONVERTED BY SUCCESSIVE REACTIONS. 

The decomposition reactions of RDX and HMX are stoichiometrically balanced-when it is assumed that CO, rather than COj, is formed as a combustion product ... 

The synthesis of polyamides follows a different route from that of polyesters. Although several different polymerization reactions are possible, polyamides are usually produced either by direct amidation of a diacid with a diamine or the self-amidation of an amino acid. The polymerization of amino acids is not as useful because of a greater tendency toward cycliza-tion (Sec. 2-5b). Ring-opening polymerization of lactams is also employed to synthesize polyamides (Chap. 7). Poly(hexamethylene adipamde) [IUPAC poly(iminohexanedioylimi-nohexane-l,6-diyl) or poly(iminoadipoyliminohexane-l,6-diyl)], also referred to as nylon 6/6, is synthesized from hexamethylene diamine and adipic acid [Zimmerman, 1988 Zimmerman and Kohan, 2001]. A stoichiometric balance of amine and carboxyl groups is readily obtained by the preliminary formation of a 1 1 ammonium salt (XU ) in aqueous solution at a concentration of 50%. The salt is often referred to as a nylon salt. Stoichiometric... 

In general, concentrations of the products are divided by the concentrations of the reactants. In the case of gas-phase reactions, partial pressures cire used instead of molar concentrations. Multiple product or reactant concentrations are multiplied. Each concentration is raised to an exponent equal to its stoichiometric coefficient in the balanced reaction equation. (See Chapters 8 and 9 for details on balanced equations and stoichiometry.)... 

The mechanistic models are more representative of the resin curing kinetics because they are based on stoichiometric balances of reactants involved in the elementary reactions. As a consequence, they are much more complex than the phenomenological models, but they can better represent the kinetics of cure. The physical and mechanical behaviors of the cured resins are determined by the chemical reactions that occur dining cure. The understanding of the mechanism and kinetics of cure is one of the most important steps in evaluating the... 

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