Solution reactions, stoichiometry

The overall reaction stoichiometry having been established by conventional methods, the first task of chemical kinetics is essentially the qualitative one of establishing the kinetic scheme in other words, the overall reaction is to be decomposed into its elementary reactions. This is not a trivial problem, nor is there a general solution to it. Much of Chapter 3 deals with this issue. At this point it is sufficient to note that evidence of the presence of an intermediate is often critical to an efficient solution. Modem analytical techniques have greatly assisted in the detection of reactive intermediates. A nice example is provided by a study of the pyridine-catalyzed hydrolysis of acetic anhydride. Other kinetic evidence supported the existence of an intermediate, presumably the acetylpyridinium ion, in this reaction, but it had not been detected directly. Fersht and Jencks observed (on a time scale of tenths of a second) the rise and then fall in absorbance of a solution of acetic anhydride upon treatment with pyridine. This requires that the overall reaction be composed of at least two steps, and the accepted kinetic scheme is as follows. 

There are, however, two disadvantages associated with use of the phenyldimethylsilyl group. Based on the reaction stoichiometry, for each equivalent of substrate, one silyl group is unused, and after work-up this appears as a relatively involatile by-product. Secondly, after synthetic use of such vinylsilanes involving desilylation, a similar problem of by-product formation arises. One solution to these problems lies in the use of the tri-methylsilyl group (Chapter 8), since the by-product, hexamethyldisiloxane, is volatile and normally disappears on work-up. 

Step 3 Write the chemical equation for the neutralization reaction and use the reaction stoichiometry to find the amount of H. O ions (or OH ions if the analyte is a strong base) that remains in the analyte solution after all the added titrant reacts. Each mole of H30+ ions reacts with 1 mol OH ions therefore, subtract the number of moles of H30+ or OH ions that have reacted from the initial number of moles. 

We can predict the pH at any point in the titration of a polyprotic acid with a strong base by using the reaction stoichiometry to recognize what stage we have reached in the titration. We then identify the principal solute species at that point and the principal proton transfer equilibrium that determines the pH. 

Solution This is a variable-velocity problem with u changing because of the reaction stoichiometry and the pressure drop. The flux marching equations for the various components are... 

Densification is also influenced by the presence of supporting electrolyte. As shown in the last line of Table II, the relative densification in acidified cupric sulfate is less than that in binary cupric sulfate solution. In the case of the supported redox reaction, that is, in the presence of KOH or NaOH, the migration effect makes the density difference larger than that expected from overall reaction stoichiometry. 

For mechanisms that are more complex than the above, the task of showing that the net effect of the elementary reactions is the stoichiometric equation may be a difficult problem in algebra whose solution will not contribute to an understanding of the reaction mechanism. Even though it may be a fruitless task to find the exact linear combination of elementary reactions that gives quantitative agreement with the observed product distribution, it is nonetheless imperative that the mechanism qualitatively imply the reaction stoichiometry. Let us now consider a number of examples that illustrate the techniques used in deriving an overall rate expression from a set of mechanistic equations. 

Schmid and Heinola [J. Am. Chem. Soc., 90 (131), 1968] have studied the liquid phase reactions of 1-phenylpropyne (A) and 2,4-di-nitrobenzenesulfenyl chloride (B) in chloroform solution at 51° C. The primary products of the reaction are l-phenyl-t/ams-l-chloro-2-(2, 4 di-nitrophenylthio) propene (C) and 1-phenyl-tnms-2-chloro-l-(2, 4-dinitrophenylthio) propene (D). The reaction stoichiometry may be... 

Inukai and Kojima (9) have studied the aluminum chloride catalyzed diene condensation of butadiene and methyl acrylate in benzene solution. The stoichiometry for this Diels-Alder reaction is... 

An autocatalytic reaction is to be carried out in aqueous solution in two identical continuous stirred tank reactors operating in series. The reaction stoichiometry is... 

On the contrary, the oxidation of fluorene in a basic solution is not limited by the deprotonation of hydrocarbon [284]. This is in agreement with the oxidation of fluorene and 9,9-dideuterofluorene at the same rate in DMSO and 1,1-dimethylethanol solution. The stoichiometry of fluorene oxidation is close to unity (except oxidation in HMPA) and the main product of the reaction is fluorenone. The stoichiometry and the initial rate of the reaction depends on the solvent (conditions 300 K, [fluorene] = 0.1 mol L 1, [Me3COK] = 0.2mol L 1,p02 = 97kPa). 

Reaction stoichiometry can then be used to solve for the molarity of the acid solution. See the Stoichiometry chapter for a discussion of solution stoichiometry. 

A standard cell potential depends only on the identities of the reactants and products in their standard states. As you will see in the next Sample Problem, you do not need to consider the amounts of reactants or products present, or the reaction stoichiometry, when calculating a standard cell potential. Since you have just completed a similar Sample Problem, only a brief solution using the subtraction method is given here. Check that you can solve this problem by adding a reduction potential and an oxidation potential. 

This example illustrates the qualitative nature of information that can be gleaned from macroscopic uptake studies. Consideration of adsorption isotherms alone cannot provide mechanistic information about sorption reactions because such isotherms can be fit equally well with a variety of surface complexation models assuming different reaction stoichiometries. More quantitative, molecular-scale information about such reactions is needed if we are to develop a fundamental understanding of molecular processes at environmental interfaces. Over the past 20 years in situ XAFS spectroscopy studies have provided quantitative information on the products of sorption reactions at metal oxide-aqueous solution interfaces (e.g., [39,40,129-138]. One... 

This is an equation in the total concentration of chemicals. One solution of eqn (11.5) which satisfies the boundary conditions is that the sum of the concentrations a + b should be equal to a constant everywhere and at all times. This constant is determined by the reaction stoichiometry and gives the sensible relationship... 

Solution The stoichiometry of Reaction 6-19 tells us that H and OH are produced in a 1 1 molar ratio. Their concentrations must be equal. Calling each concentration x, we can write... 

Stoichiometry (28) is followed under neutral or in alkaline aqueous conditions and (29) in concentrated mineral acids. In acid solution reaction (28) is powerfully inhibited and in the absence of general acids or bases the rate of hydrolysis is a function of pH. At pH >5.0 the reaction is first-order in OH but below this value there is a region where the rate of hydrolysis is largely independent of pH followed by a region where the rate falls as [H30+] increases. The kinetic data at various temperatures both with pure water and buffer solutions, the solvent isotope effect and the rate increase of the 4-chloro derivative ( 2-fold) are compatible with the interpretation of the hydrolysis in terms of two mechanisms. These are a dominant bimolecular reaction between hydroxide ion and acyl cyanide at pH >5.0 and a dominant water reaction at lower pH, the latter susceptible to general base catalysis and inhibition by acids. The data at pH <5.0 can be rationalised by a carbonyl addition intermediate and are compatible with a two-step, but not one-step, cyclic mechanism for hydration. Benzoyl cyanide is more reactive towards water than benzoyl fluoride, but less reactive than benzoyl chloride and anhydride, an unexpected result since HCN has a smaller dissociation constant than HF or RC02H. There are no grounds, however, to suspect that an ionisation mechanism is involved. 

Introduction and Orientation, Matter and Energy, Elements and Atoms, Compounds, The Nomenclature of Compounds, Moles and Molar Masses, Determination of Chemical Formulas, Mixtures and Solutions, Chemical Equations, Aqueous Solutions and Precipitation, Acids and Bases, Redox Reactions, Reaction Stoichiometry, Limiting Reactants... 

STRATEGY First, we find the volume of titrant needed to reach the stoichiometric point. At this point, pH = 7. After the stoichiometric point, the amount of acid added exceeds the amount of base in the analyte, and we expect a pH of less than 7. We use the reaction stoichiometry to determine how much of the acid added remains after neutralization. Then we use the total volume of solution to find the molar concentration of H30+ and convert it to pH. To implement the calculation, work through the steps in Example 11.5. 

We can predict the pH at any point in the titration of a polyprotic acid with a strong base (see Toolbox 11.1). First, we have to consider the reaction stoichiometry to recognize what stage we have reached in the titration. Next we have to identify the principal solute species at that point and the proton transfer equilibrium that determines the pH. We then carry out the calculation appropriate for the solution, referring to the previous worked examples if necessary. In this section, we see how to describe the solution at various stages of the titration our conclusions are summarized in Tables 11.3 and 11.4. 

The isolation and identification of hexaborane(lO) and decaborane(14) from the reaction of diborane(6) with lithium octahydropentaborate(—1) was reported by Geanangel and Shore 16>. Decaborane(14) was obtained in 25 to 30 per cent yields by refluxing 1,2-dimethoxyethane solutions of the reaction products 16,178) while hexaborane(lO) was conveniently isolated in 25 to 35 per cent yields when the reaction was conducted in dimethyl ether and the products were distilled from the reaction mixture at low temperature 176-179). The reaction was initially thought to involve the unsymmetrical cleavage of diborane(6) by the octahydro-pentaborate(—1) ion because the reaction stoichiometry appeared to be 1 B2H0 to 1 BsHi and both LiBEU and Bell 10 were found among the reaction products 16>. 

Pressure measurement devices such as a manometer are used without disturbing the system being monitored. Another type of reacting system that can be monitored involves one of the products being quantitatively removed by a solid or liquid reagent that does not affect the reaction. An example is the removal of an acid formed by reactions in the gas phase using hydroxide solutions. From the reaction stoichiometry and measurements of the total pressure as a function of time, it is possible to determine the extent of the reaction and the partial pressure or concentrations of the reactant and product species at the time of measurement. 

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