Stoichiometric coefficients for

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. 

The respiratory quotient (RQ) is often used to estimate metabolic stoichiometry. Using quasi-steady-state and by definition of RQ, develop a system of two linear equations with two unknowns by solving a matrix under the following conditions the coefficient of the matrix with yeast growth (y = 4.14), ammonia (yN = 0) and glucose (ys = 4.0), where the evolution of C02 and biosynthesis are very small (o- = 0.095). Calculate the stoichiometric coefficient for RQ =1.0 for the above biological processes ... 

Therefore, the stoichiometric coefficients for the projected equation in production of penicillin G are ... 

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

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... 

We can identify the limiting reactant by dividing each amount in moles by the stoichiometric coefficient for that reactant. To see how this works, rearrange the ratios for H2 and N2 ... 

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. 

Note that the stoichiometric coefficients for reactants are negative and those for products positive. As a consequence, rs and rp are both positive. 

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... 

One of the challenges in kinetic studies is how to define the rate of a reaction. Typically, we have two options we can define the rate in terms of how quickly reactant molecules are depleted from the reaction vessel, or we can monitor the rate at which product molecules are formed during the reaction. Either way, we are attempting to define the rate for the same reaction, so we ought to get the same answer. But, often, the stoichiometric coefficients for the individual reactant and product species are different. For example, for the general reaction shown in Eq. 4.1... 

Be very careful to note the appropriate stoichiometric coefficients for use in your analysis. 

The stoichiometric coefficient for A is a, and for B is b, choosing the convention that for reactants the coefficients are negative (—a, —b) whereas for products the coefficients are positive. 

The stoichiometric coefficient for methanol is +1 because it is a product and — 1 for CO and -2 for H2 because they are reactants. The reaction is not spontaneous under standard conditions of temperature and pressure but at 500 K the equilibrium constant is given by Equation 8.12 ... 

Definitions for the variables and constants appearing in eqns. 1 and 2 are given in the nomenclature section at the end of this paper. The first of these equations represents a mass balance around the reactor, assuming that it operates in a differential manner. The second equation is a species balance written for the catalyst surface. The rate of elementary reaction j is represented by rj, and v j is the stoichiometric coefficient for component i in reaction j. The relationship of rj to the reactant partial pressures and surface species coverages are given by expressions of the form... 

Stoichiometric coefficient for component i in reaction j. Catalyst density [gm/cnu]. 

A The law of combining volumes permits us to use stoichiometric coefficients for volume ratios. 

---