Order and stoichiometry

Molecularity must be integral, but order need not be there is no necessary connection between molecularity and order, except for an elementary reaction the numbers describing molecularity, order, and stoichiometry of an elementary reaction are all the... 

The composition variation described in the previous chapter has a considerable impact upon the electronic properties of the solid. However, it is often difficult to alter the composition of a phase to order, and stoichiometry ranges arc frequently too narrow to allow desired electronic properties to be achieved. Traditionally, the problem has been circumvented by using selective doping by aliovalent impurities, that is, impurities with a different nominal valence to those present in the parent material. However, it is important to remember that all the effects described in the previous chapter still apply to the materials below. The division into two chapters is a matter of convenience only. 

For rate expressions similar or equivalent to those given by Equation (7-3), reaction orders cannot be defined. That is, for rate laws where the denominator is a polynomial function of the species concentrations, reaction orders are described only for limiting values of the reactant and/or product concenha-tions. Reactions of this type are nonelementary in that there is no direct coite-Spondence between reaction order and stoichiometry. 

A fortuitous example in which order and stoichiometry are identical is the decomposition of N2 O5,... 

When order and stoichiometry of type II reactions do not agree, the analysis is somewhat different. Suppose the stoichiometry maybe represented as ... 

In Sec. 2-8 it was shown that for an elementary process the ratio of rate constants in the forward and reverse directions is equal to the equilibrium constant. When order and stoichiometry do not agree this is not necessarily true. To explain with a simple example, suppose the reversible, overall reaction... 

Use the stationary-state hypothesis to derive an expression for the overall rate of decomposition. Do order and stoichiometry agree in this case ... 

It is important to remember that the order of the reaction is determined experimentally. Although this problem focuses on the mathematical detail of the definition of reaction order, we must keep in mind that reaction order and stoichiometry are not directly related. 

The first possibility envisages essentially the same mechanism as for the second-order process, but with Bt2 replacing solvent in the rate-determining conversion to an ion pair. The second mechanism pictures Bt2 attack on a reversibly formed ion-pair intermediate. The third mechanism postulates collide of a ternary complex tiiat is structurally similar to the initial charge-transfer complex but has 2 1 bromine alkene stoichiometry. There are very striking similarities between the second-order and third-order processes in terms of magnitude of p values and product distribution. In feet, there is a quantitative correlation between the rates of the two processes over a broad series of alkenes, which can be expressed as... 

Cement formation requires a continuous structure to be formed in situ from a large number of nuclei. Moreover, this structure must be maintained despite changes in the character of the bonds. These criteria are, obviously, more easily satisfied by a flexible random structure than by one which is highly-ordered and rigid. Crystallinity implies well-satisfied and rigidly-directed chemical bonds, exact stoichiometry and a highly ordered structure. So unless crystal growth is very slow a continuous molecular structure cannot be formed. 

It is apparent from the last example cited in previous section that there is not necessarily a connection between the kinetic order and the overall stoichiometry of the reaction. This may be understood more clearly if it is appreciated that any chemical reaction must go through a series of reaction steps. The addition of these elementary steps must give rise to the overall reaction. The reaction kinetics, however, reflects the slowest step or steps in the sequence. An overall reaction is taken as for an example ... 

In this work we attempt to measure kinetics data in a time short compared with the response time of the catalyst stoichiometry. An alternative is to measure kinetics in a true steady state, i.e., to increase the line-out time at each reactor condition until hysteresis is eliminated. The resulting apparent reaction orders and activation energies would be appropriate for an industrial mathematical model of reactor behavior. 

Both theories yield laws for elementary reactions in which order, molecularity, and stoichiometry are the same (Section 6.1.2). 

The quantity and quality of experimental information determined by the new techniques call for the use of comprehensive data treatment and evaluation methods. In earlier literature, quite often kinetic studies were simplified by using pseudo-first-order conditions, the steady-state approach or initial rate methods. In some cases, these simplifications were fully justified but sometimes the approximations led to distorted results. Autoxidation reactions are particularly vulnerable to this problem because of strong kinetic coupling between the individual steps and feed-back reactions. It was demonstrated in many cases, that these reactions are very sensitive to the conditions applied and their kinetic profiles and stoichiometries may be significantly altered by changing the pH, the absolute concentrations and concentration ratios of the reactants, and also by the presence of trace amounts of impurities which may act either as catalysts and/or inhibitors. 

The vapor phase decomposition of phosphine is irreversible first order and is in accord with the stoichiometry,... 

The allylic radicals that are formed are too stable to initiate polymerization, and the kinetic chain also terminates when the transfer occurs. The allylic radicals undergo termination by reaction with each other or, more likely, with propagating radicals [Litt and Eirich, I960], Reaction 3-155 is equivalent to termination by an inhibitor, which is the monomer itself in this case. In this polymerization the propagation and termination reactions will have the same general kinetic expression with first-order dependencies on initiator and monomer concentrations, since the same reactants and stoichiometry are involved. The degree of polymerization is simply the ratio of the rate constants for propagation and termination and is independent of the initiator concentration. 

This set of relations between reaction orders and stoichiometric coefficients defines what we call an elementary reaction, one whose kinetics are consistent with stoichiometry. We later wiU consider another restriction on an elementary reaction that is frequently used by chemists, namely, that the reaction as written also describes the mechanism by which the process occurs. We will describe complex reactions as a sequence of elementary steps by which we will mean that the molecular collisions among reactant molecules cause chemical transformations to occur in a single step at the molecular level. 

Some laboratories do not have access to mass spectrometric analysis, but the number is fewer as the cost for this type of instrumentation is decreasing. It is suggested that these laboratories utilize amino acid analysis due to reduced cost and rapid turnaround. Peptide composition and stoichiometry can be determined, the technique is highly reproducible, and can be used to monitor cycle-to-cycle coupling efficiency. However, not all amino acids are recovered quantitatively. Cys and Trp are totally destroyed and must be quantitated using distinctly different hydrolysis procedures. Ser and Thr can be partially destroyed. Some laboratories perform amino acid analysis in addition to mass spectrometric analysis in order to assure peptide composition, stoichiometry, and quantity (see also Sections 7.3, 7.3.1 and 7.3.2). 

Two major theories of the covalent bond are described in this book the main features of valence bond theory are treated in terms of the VSEPR theory of molecular shapes, and MO theory which is based on the symmetry properties of the contributing atomic orbitals. The latter theory is applied qualitatively with MO diagrams being constructed and used to interpret bond orders and bond angles. The problems associated with bond angles are best treated by using the highest symmetry possible for a molecule of a particular stoichiometry. 

The order of a reaction cannot in general be predicted from the chemical equation a rate law is an empirical law. That is, a rate law is an experimentally determined characteristic of the reaction and cannot in general be written down from the stoichiometry of the chemical equation for the reaction. For instance, both the decomposition of N205 and that of N02 have a stoichiometric coefficient of 2 for the reactant, but one reaction is first order and the other is second order. The decomposition of ammonia also has a stoichiometric coefficient of 2 for the reactant, but its rate law is zero order. 

Since we believe that the relationships in Scheme 1 are useful for the design of catalysts (75), we place stress in this chapter on these relationships at atomic/ molecular levels of heteropoly compounds. In our opinion, sufficient care must be taken on the structure and stoichiometry in order to design catalysts taking advantage of the molecular nature of heteropoly compounds. 

For our present purposes, we use the term reaction mechanism to mean a set of simple or elementary chemical reactions which, when combined, are sufficient to explain (i) the products and stoichiometry of the overall chemical reaction, (ii) any intermediates observed during the progress of the reaction and (iii) the kinetics of the process. Each of these elementary steps, at least in solution, is invariably unimolecular or bimolecular and, in isolation, will necessarilybe kinetically first or second order. In contrast, the kinetic order of each reaction component (i.e. the exponent of each concentration term in the rate equation) in the observed chemical reaction does not necessarily coincide with its stoichiometric coefficient in the overall balanced chemical equation. 

At first glance, the structures and stoichiometries of polynuclear carbonyls and their derivatives are of baffling complexity. As we shall see in the next section, some very simple electron book-keeping devices help to bring some order from the apparent chaos. 

The following set of exercises includes each type of stoichiometry problem. They are presented in random order and not grouped by type. 

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