Reactions with unknown stoichiometry

If we study the kinetics of a reaction between A and B and do not know the stoichiometry, it should be clear from our previous discussion that very little real progress can be made in analysing the data. Suppose for the sake of argument that we are unable to analyse our reaction mixture for the reactant B but are able to follow the disappearance of A. Even in the case of the simplest possible type of rate expression, namely the one under discussion 

However, there are two situations in which the previous calculations can be fruitfully undertaken without requiring a knowledge of the concentration of B. These are when the order with respect to B is zero or when the disappearance of A can be studied in the presence of a considerable excess of B. If the preliminary examination of the data suggests that the order of the reaction with respect to B is zero, then the validity of the rate expression 

It must be stressed that this conclusion is only valid under the concentration conditions employed, that is, when the reaction is followed in the presence of a large excess of B. It is quite possible that a more complicated expression for the rate is necessary when the reactant concentrations are close to stoichiometric equivalence. 

Of course, both these attempts to formulate a simple expression for the rate of the reaction may fail. This should not cause any concern since, with access to such a limited amount of data, many of the features of the reaction cannot but remain obscure. In such a case, further experimental work must be carried out particularly with a view to determining the concentration of B. 

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The elemental sulfur that is formed by destmction of the [2Fe-2S] cluster can further react with the DNIC, resulting in oxidation of the thiolate ligands to disulfide and formation of the Roussin s black salt in the reaction of unknown stoichiometry, which can be formally formulated as follows [Eq. (3)]. 

When the kinetics are unknown, still-useful information can be obtained by finding equilibrium compositions at fixed temperature or adiabatically, or at some specified approach to the adiabatic temperature, say within 25°C (45°F) of it. Such calculations require only an input of the components of the feed and produc ts and their thermodynamic properties, not their stoichiometric relations, and are based on Gibbs energy minimization. Computer programs appear, for instance, in Smith and Missen Chemical Reaction Equilibrium Analysis Theory and Algorithms, Wiley, 1982), but the problem often is laborious enough to warrant use of one of the several available commercial services and their data banks. Several simpler cases with specified stoichiometries are solved by Walas Phase Equilibiia in Chemical Engineering, Butterworths, 1985). 

Primary and secondary aUcyltetrasulfanes may be prepared from ketones via hydrazones by reaction with H2S (equations 70 and 71). The mechanism and stoichiometry of equation (71) are unknown, but MeC02H and 2NH4+ are probably formed as by-products, in which case four equivalents of H2S are needed, resulting in a tetrasulfane. 

When chemists are faced with problems that require them to determine the quantity of a substance by mass, they often use a technique called gravimetric analysis. In this technique, a small sample of the material undergoes a reaction with an excess of another reactant. The chosen reaction is one that almost always provides a yield near 100%. If the mass of the product is carefully measured, you can use stoichiometry calculations to determine how much of the reactant of unknown amount was involved in the reaction. Then by comparing the size of the analysis sample with the size of the original material, you can determine exactly how much of the substance is present. 

The first important contribution to atomic stoichiometry in this century seems to be provided by Brinkley (1946). He has shown the importance of the rank of the atomic matrix and presented a proof of the phase rule of Gibbs (1876). A systematic outline of stoichiometry was presented by Petho (sometimes Petheo) and Schay (Petheo Schay, 1954 Schay, Petho, 1962). They gave a necessary and sufficient condition for the possibility of calculating an unknown reaction heat from known ones based upon the rank of the stoichiometric matrix. They introduced the notion of independence of components and of elementary reactions, the completeness of a complex chemical reaction (see the Exercises and Problems) and gave a method to generate a complete set of independent elementary reactions with as many zeros in the stoichiometric matrix as possible (see Petho, 1964). 

I n volumetric analysis, the volume of a known reagent required for complete reaction with analyte by a known reaction is measured. From this volume and the stoichiometry of the reaction, we calculate how much analyte is in an unknown substance. In this chapter we discuss general principles that apply to any volumetric procedure, and then we illustrate some analyses based on precipitation reactions. Along the way, we introduce the solubility product as a means of understanding precipitation reactions. 

The similarity of reaction rates and yields conld be explained by either interconversion of these species to one another, or conversion of each of them to a more advanced, common reactive intermediate. H-NMR analysis of a mixture of TBAF with either siletane 13, silanol 32, disiloxane 202, or fluorosilane 203 shows only two species that are formed almost immediately. One is identified as the disiloxane of the corresponding silanol, and the other species an unknown compound 204 (or 205) containing both silicon and fluorine as determined by Si- and F-NMR (Scheme 7.51). Moreover, the ratio of204 (205) to disiloxane increased with TBAF stoichiometry under typical conditions for cross-coupling the ratio is heavily in favor (>10 1) of204 (205). 

Solution Stoichiometry Quantitative studies of reactions in solution require that we know the concentration of the solution, which is usually represented by the molarity unit. These studies include gravimetric analysis, which involves the measurement of mass, and titrations in which the unknown concentration of a solution is determined by reaction with a solution of known concentration. 

In order to effectively utilize the stoichiometry of the reaction involved in a titration, both the titrant and the substance titrated need to be measured exactly. The reason is that one is the known quantity, and the other is the unknown quantity in the stoichiometry calculation. The buret is an accurate (if carefully calibrated) and relatively high-precision device because it is long and narrow. If a meniscus is read in a narrow graduated tube, it can be read with higher precision (more significant figures) than in a wider tube. Thus a buret provides the required precise measurement of the titrant. 

The concentration of an acid or a base may be determined by titrating a solution of an unknown concentration with a solution of a known concentration. (See the chapter on Reactions and Periodicity and the chapter on Stoichiometry.)... 

Each of these dissociation reactions also specifies a definite equilibrium concentration of each product at a given temperature consequently, the reactions are written as equilibrium reactions. In the calculation of the heat of reaction of low-temperature combustion experiments the products could be specified from the chemical stoichiometry but with dissociation, the specification of the product concentrations becomes much more complex and the s in the flame temperature equation [Eq. (1.11)] are as unknown as the flame temperature itself. In order to solve the equation for the n s and T2, it is apparent that one needs more than mass balance equations. The necessary equations are found in the equilibrium relationships that exist among the product composition in the equilibrium system. 

For hydroxamic acids, it is generally assumed that it is the Af-hydroxyamide/keto form, as opposed to the hydroximic/hydroxyoxime form, that predominates in acid medium, the environment usually required for most precipitates or colors to form . It is in general unknown what is the stoichiometry and structure of most metal hydroxamate complexes in solution. Nevertheless, the reaction of the majority of hydroxamic acids with metal ions can be written schematically as shown in equation 2. 

The first transition metal derivatives of a Zintl ion was prepared by Teixidor et al. in 1983 in reactions between Pt(PPli4)4 and en solutions of the Eg (E = Sn, Pb) [25, 26]. Despite being the first examples in this important class of clusters, the complexes have yet to be isolated and their structures and compositions remain unknown. The authors propose that complexes have a (PPh3)2PtSng stoichiometry and a nido-ty structure. Based on comparisons with NMR parameters from the past 30 years and the stoichiometry of the reactions described by Teixidor et al., we believe that the Rudolph compounds are most likely 22-electron cZos )-Pf E9Pt (PPh3) complexes. Our rationale is given below. 

A major difference with desired reactions is that the stoichiometry is often unknown, that is, the decomposition products are unknown. The reason is that decomposition reactions are often affected by the triggering conditions and thus often run along different reaction paths. This is a major difference compared to a total combustion, for example. The consequence is that the decomposition enthalpy cannot be predicted using standard enthalpies of formation AHjj taken from, for example, tables or estimated by group increment methods, such as Benson groups [3, 4] ... 

In the article of Kaarls and Quinn [34] primary methods are carefully defined as methods for the determination of the amount of substance in pure or simple compound systems, i.e. in samples which do not contain impurities acting as potential interferences. It is explicitly stated that it is a future task of the CCQM to investigate the applicability and robustness of these methods for complex mixtures encountered in practical analytical chemistry. Many other papers (e.g. [36]), however, tend to identify primary methods already as methods of analysis (to be used on complex samples of unknown overall composition). This over-optimistic (and unwarranted) enlargement of the definition implies that all titrimetric methods of analysis would be considered as primary methods putting aside any interference that occurs in complex samples. Considering all possible sources of error that may occur in both the stoichiometry of the reaction and with the determination of the equivalence point of a titration, this cannot be possible. Neither was this the intention of the CCQM. 

Calculating The concentration of thallium(I) ions in solution may be determined by oxidizing to thallium(III) ions with an aqueous solution of potassium permanganate (KMn04) under acidic conditions. Suppose that a 100.00 mL sample of a solution of unknown T1+ concentration is titrated to the endpoint with 28.23 mL of a 0.0560M solution of potassium permanganate. What is the concentration of T1+ ions in the sample You must first balance the redox equation for the reaction to determine its stoichiometry. 

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