Stoichiometric coefficients for reaction

Relative Rates of Reaction. The relative rates of reaction of the various species involved in a reaction can be obtained from the ratio of stoichiometric coefficients. For Reaction (2-2),... 

The term stoichiometric coefficients for reaction j, and since the stoichiometric coefficients for products are positive while those of the reactants are negative, there is a fair degree of cancelling inherent in f7 i= ii However, AU j = AH j only when the number of kilogram-moles of products formed by the reaction equals the number of kilogram-moles of reactants used up in doing so, i.e. when the reaction exhibits neither a... 

The system is composed of C total species and nig total elements. In (7.4.17) Vy is the vector of stoichiometric coefficients for reaction j and A is the (nig x C) matrix of coefficients, with the number of atoms of element fc on one molecule of species i. With values for the stoichiometric coefficients, we can form expressions for the species mole fractions in terms of an extent for each of the (R reactions. 

Here N is the number of moles of species i initially present, N is the total number of moles initially present, and Oy = E, v y is the algebraic smn of stoichiometric coefficients for reaction j. 

The reaction rate may be defined as the rate of change of concentration of a reactant or product divided by its stoichiometric coefficient. For reaction (2.1)... 

The stoichiometric coefficients for the zinc half-reaction are multiplied by 3 so that both half-reactions involve 6 electrons. 

The quantities Vj and are the stoichiometric coefficients for the fuel cell reaction, and andare the fugacities of fuel and oxygen in their respective streams. 

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. 

Stoichiometric coefficients for cell growth for the production of SCP from hexadecane is given by the following reaction ... 

To keep the units straight, we need to use the molar convention for this calculation and to use the stoichiometric coefficients in reaction E as pure numbers. To find an expression for AGr, we substitute F q. 4 for each substance into Eq. 3a. For example, for the general reaction E,... 

A note on good practice The chemical equations for elementary reaction steps are written without the state symbols. They differ from the overall chemical equation, which summarizes bulk behavior, because they show how individual atoms and molecules take part in the reaction,. We do not use stoichiometric coefficients for elementary reactions. Instead, to emphasize that we are depicting individual molecules, we write the formula as many times as required. 

Solution We begin with the stoichiometric coefficients for each component for each reaction ... 

Reverse Reaction Rates. Suppose that the kinetic equilibrium constant is known both in terms of its numerical value and the exponents in Equation (7.28). If the solution is ideal and the reaction is elementary, then the exponents in the reaction rate—i.e., the exponents in Equation (1.14)—should be the stoichiometric coefficients for the reaction, and Ei mettc should be the ratio of... 

Figure 15-5 also shows that each species has its own rate, but the individual rates are linked by the stoichiometric coefficients. The reaction generates one molecule of N2 O4 for every two molecules of NO2 that are destroyed. That is, the 1 2 stoichiometry of this reaction results in a 1 2 relationship between the rate of disappearance of NO2 and the rate of appearance of N2 O4. The ratio of rates for different species is always equal to the ratio of their stoichiometric coefficients. 

Remember that the number of electrons transferred is not explicitly stated in a net redox equation. This means that any overall redox reaction must be broken down into its balanced half-reactions to determine n, the ratio between the number of electrons transferred and the stoichiometric coefficients for the chemical reagents. 

The coefficients of any balanced redox equation describe the stoichiometric ratios between chemical species, just as for other balanced chemical equations. Additionally, in redox reactions we can relate moles of chemical change to moles of electrons. Because electrons always cancel in a balanced redox equation, however, we need to look at half-reactions to determine the stoichiometric coefficients for the electrons. A balanced half-reaction provides the stoichiometric coefficients needed to compute the number of moles of electrons transferred for every mole of reagent. 

Figure A-2. Normalized stoichiometric coefficients for the two reactions associated with the singular vectors.

Vj is the stoichiometric coefficient for species i in the reaction. By convention, the value of v is positive for the products and negative for the reactants. The stoichiometric coefficients relate the simplest ratio of the number of moles of reactant and product species, involved in the reaction. 

Here va and va are the stoichiometric coefficients for the reaction. The formulation is easily extended to treat a set of coupled chemical reactions. Reactive MPC dynamics again consists of free streaming and collisions, which take place at discrete times x. We partition the system into cells in order to carry out the reactive multiparticle collisions. The partition of the multicomponent system into collision cells is shown schematically in Fig. 7. In each cell, independently of the other cells, reactive and nonreactive collisions occur at times x. The nonreactive collisions can be carried out as described earlier for multi-component systems. The reactive collisions occur by birth-death stochastic rules. Such rules can be constructed to conserve mass, momentum, and energy. This is especially useful for coupling reactions to fluid flow. The reactive collision model can also be applied to far-from-equilibrium situations, where certain species are held fixed by constraints. In this case conservation laws... 

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