Stoichiometric coefficients, convention

Because v represents the stoichiometric coefficient of a given species, the value of AH clearly depends on the way the stoichiometric equation is written for the reaction. It is conventional to express the above equation in a simplified form as... 

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,... 

This example shows that the method discussed can deal with the difficulties frequently met in real situations. One of the products (D) was difficult to measure and another one (F) not accurately analyzed. So the balance could not close and conventional methods of determining stoichiometry via balancing could fail. The standard error in determination of species (C) was in the range of 6-14 % of the measured value in the first period of the experiment . Despite these difficulties, two simple reactions were found with stoichiometry that can adequately represent the reactions. The final representation of the chemical system is not unique but the final stoichiometric coefficients are within 10 % of the original ones. This indicates that the proposed methodology can yield reasonable approximations. 

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. 

The generalized stoichiometric coefficients are defined as positive quantities for the products of the reaction and as negative quantities for the reactants. The coefficients of species that are neither produced nor consumed by the indicated reaction are taken to be zero. Equation 1.1.2 has been written in inverted form with the zero first to emphasize the use of this sign convention, even though this inversion is rarely used in practice. 

This second form is preferred, provided that one keeps the proper sign convention for the stoichiometric coefficients in mind. 

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. 

B. LAW OF MASS ACTION. Using the conventional notation, we will define an overall reaction rate 31 as the rate of change of moles of any component per volume due to chemical reaction divided by that component s stoichiometric coefficient... 

This displays the convention, tacitly assumed later, that the positive direction of a step corresponds to the advancement from left to right of the stated chemical equation. The matrix of stoichiometric coefficients for these reactions is shown in Table II. The diagonalization of the matrix in Table II gives the matrix in Table III, from which the steady-state mechanism is S + 2s2 + 2s3 + 2s4. In Horiuti s terminology the stoichiometric numbers are 1 for Sj and 2 for s2, s3, and s4. 

Note that reactions 2.14, 2.15, and 2.23 involve fractional stoichiometric coefficients on the left-hand sides. This is because we wanted to define conventional enthalpies of formation (etc.) of one mole of each of the respective products. However, if we are not concerned about the conventional thermodynamic quantities of formation, we can get rid of fractional coefficients by multiplying throughout by the appropriate factor. For example, reaction 2.14 could be doubled, whereupon AG° becomes 2AG, AH° = 2AH , and AS° = 2ASf, and the right-hand sides of Eqs. 2.21 and 2.22 must be squared so that the new equilibrium constant K = K2 = 1.23 x 1083 bar-3. Thus, whenever we give a numerical value for an equilibrium constant or an associated thermodynamic quantity, we must make clear how we chose to define the equilibrium. The concentrations we calculate from an equilibrium constant will, of course, be the same, no matter how it was defined. Sometimes, as in Eq. 2.22, the units given for K will imply the definition, but in certain cases such as reaction 2.23 K is dimensionless. 

In (3.93), the A are chemical species and the vt are the corresponding stoichiometric coefficients of the balanced reaction, with the convention... 

For the most oxygenated sample, the carboxidation reaction may be presented by (7.19), having huge stoichiometric coefficients compared to conventional chemical reactions ... 

In this equation v, and p, stand, respectively, for the stoichiometric coefficient and the thermodynamic potential of component i taking part in the reaction. The convention is that v, is positive for a product and negative for a reactant. The reaction will proceed to the right if Xvji, is negative and to the left if this sum is positive. It is therefore convenient to define the chemical affinity A as... 

Reaction Rate The time dependent evolution of the concentrations of reactant ca or product c taking the stoichiometric coefficients into account, is a measure for the reaction rate or its velocity, cf. Equation (3). The convention requires a negative sign for reactants, indicating consumption, and a positive sign for the products, indicating formation ... 

Calculate the algebraic sum of the stoichiometric numbers for the reaction Asdiscussed in Example 4.4, stoichiometric numbers for the components in a given reaction are numerically equal to the stoichiometric coefficients, but with the convention that the reactants get minus signs. In the present case, the stoichiometric numbers for H20, H2, and 02 are, respectively, —1, +1, and +V2-Their sum is + V2 ... 

The overall reaction of the electrolysis cell (Eq. 7) provides the required stoichiometric coefficients for the products and reactant used in Eq. 8. The sign convention is positive for products and negative for reactants with analogous definitions for AB, AC and AD. Data for the constants A, B, C and D are thermodynamic properties and are reproduced in Table 1 from,19... 

Where, for the ith species, AG is the Gibbs free energy of formation, a,- is the activity, and Zj is the stoichiometric coefficient in the balanced reaction statement (by convention, z,- is negative for reactants and positive for products). The absolute temperature is T R is the gas constant, and P is the absolute pressure. The standard Gibbs free energy of formation, AGf, can be obtained from standard tables, from values of the standard enthalpy AH( and entropy AS of formation for each species via... 

The stoichiometric coefficients, n, are used as pure numbers (molar convention) to obtain AGf in kJ mol. The same convention is used for AG, below. 

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