Equations, stoichiometric

If the composition of the waste stream is known, then the theoretical oxygen demand can be calculated from the appropriate stoichiometric equations. As a first level of approximation, we can assume that this theoretical oxygen demand would be equal to the COD. Then, experience with domestic sewage indicates that the average ratio of COD to BOD will be on the order 1.5 to 2. The following example will help to clarify these relationships. 

In reaction kinetics it is conventional to define reaction rates in the context of chemical reactions with a well defined stoichiometric equation... 

The fiinctional dependence of tire reaction rate on concentrations may be arbitrarily complicated and include species not appearing in the stoichiometric equation, for example, catalysts, inliibitors, etc. Sometimes, however, it takes a particularly simple fonn, for example, under certain conditions for elementary reactions and for other relatively simple reactions ... 

This is the situation exploited by the so-called isolation method to detennine the order of the reaction with respect to each species (see chapter B2.1). It should be stressed that the rate coefficient k in (A3,4,10) depends upon the definition of the in the stoichiometric equation. It is a conventionally defined quantity to within multiplication of the stoichiometric equation by an arbitrary factor (similar to reaction enthalpy). 

Exploiting the stoichiometric equation one can eliminate Cp. Integration yields the simple relaxation of the... 

Combining the two conservation equations gives the following stoichiometric equation between C10H20N2S4 and NaOH... 

As discussed earlier, the simultaneous analysis of samples containing two analytes requires the isolation of two precipitates. As shown in Example 8.2, conservation of mass can be used to write separate stoichiometric equations for each precipitate. These equations can then be solved simultaneously for both analytes. 

Combining all four equations gives a final stoichiometric equation of Moles HCl = moles N + moles NaOH Making appropriate substitutions for the moles of HCl, N, and NaOH gives... 

Chemistry. The stoichiometric equations pertinent to the vapor-phase hydration of ethylene over a catalyst support impregnated with phosphoric acid have been summari2ed (84). 

The exponents (p, q,. . . ) are empirical, but they are identical with the stoichiometric coefficients (v, Vi, V, . . . ) when the stoichiometric equation truly represents the mechanism of reaction. The first group of exponents identifies the oi der of the reaction, the stoichiometric coefficients the molecularity. 

Designate 6 as the increase in the total mol per mol decrease of substance A according to the stoichiometric equation Eq. (7-5) ... 

Single Reaction For the stoichiometric equation, Eq. (7-5), the relations between the conversions of the several participants are... 

Some reactions apparently represented by single stoichiometric equations are in reahty the result of several reactions, often involving short-hved intermediates. After a set of such elementary reactions is postulated by experience, intuition, and exercise of judgment, a rate equation is deduced and checked against experimental rate data. Several examples are given under Mechanisms of Some Complex Reactions, following. 

The free radical eventually disappears by some reaction, called termination. The stoichiometric equations are... 

If the magnitude of the stoichiometric coefficient of a reactant exceeds the order of the reaction with respect to that species, there are one or more intermediates and reactions after the ratedetermining step. Before applying this rule, the stoichiometric equation must be formulated for the reaction such that all coefficients are integers. 

Assume that the rate equations for each elementary step can be written by inspection of the stoichiometric equation ... 

It is assumed that for each initiation there are many propagation cycles before termination. The main reaction is therefore given by the addition of the propagation steps alone, which gives the correct stoichiometric equation. A small amount of ethane, C2Hg, is expected due to the termination reaction. 

We therefore conclude that for a complex reaction the rate equation cannot be inferred from the stoichiometric equation, but must be determined experimentally. Because we do not know a priori whether a reaction of interest is elementary or complex, we are required to establish the form of all rate equations experimentally. Note that a rate equation is a differential equation. 

Equation (2-4) is the stoichiometric equation for an elementary first-order reaction, and Eq. (2-5) is the corresponding differential rate equation. 

This argument can be extended to consecutive reactions having a rate-determining step. - P The composition of the transition state of the rds is given by the rate equation. This composition includes reactants prior to the rds, but nothing following the rds. Thus, the rate equation may not correspond to the stoichiometric equation. We will consider several examples. In Scheme IV a fast acid-base equilibrium precedes the slow rds. 

A catalyst is a substance whose concentration appears in the rate equation to a higher power than it does in the stoichiometric equation. 

The net stoichiometric equation for the oxidation of glucose, using the glycerol phosphate shuttle, is... 

Stoichiometry in Reactive Systems. The use of molar units is preferred in chemical process calculations since the stoichiometry of a chemical reaction is always interpreted in terms of the number of molecules or number of moles. A stoichiometric equation is a balanced representation that indicates the relative proportions in which the reactants and products partake in a given reaction. For example, the following stoichiometric equation represents the combustion of propane in oxygen ... 

Choose a basis of 100 lb of ethane (limiting reactant). The stoichiometric equation is... 

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... 

The two basic principles permit the algebraic manipulation of chemical reactions (represented by their stoichiometric equations and associated enthalpy changes) in order to achieve desired thermochemical results. 

In practice, this ratio is even lower than what is shown hy the stoichiometric equation because part of the methane is oxidized to carhon dioxide and water. When resids are partially oxidized hy oxygen and steam at 1400-1450°C and 55-60 atmospheres, the gas consists of equal parts of hydrogen and carhon monoxide. Table 4-2 compares products from steam reforming natural gas with products from partial oxidation of heavy fuel oil. 

In the stationary phase, assuming that the total cell mass in the reactor is constant and that only L-phenylalanine and acetate are produced, the following stoichiometric equations are used ... 

From the literature the following stoichiometric equation for E. coli growing aerobic on glucose is well known. 

Hint Consider the number of moles of phenylalanine and acetic add formed and the stoichiometric equations 8.1 and 8.2. 

A completely different method of synthesis of azo compounds from diazonium salts involving radical intermediates was found by Citterio et al. (1980, 1982 c), Cit-terio and Minisci (1982), and Fontana et al. (1988). It is a new general synthesis of arylazoalkanes based on the addition of an alkyl radical to an arenediazonium ion followed by reduction of the intermediate azo radical cation adduct by a metal salt (Scheme 12-80). The preferred source for the alkyl radical R in this reaction is an alkyl iodide, which gives rise to alkyl radicals cleanly in the presence of an arenediazonium salt and a Ti3+ or Fe2+ salt as in Scheme 12-81. The overall stoichiometric equation is therefore as given in Scheme 12-82. The yields vary between 36% and 79% (with respect to alkyl iodide). 

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