Extent of reaction, determination

To verify the method a 1.00-mL aliquot of a standard solution of 40.0-ppm glucose was added to 1.00 ml of the combined reagents, requiring 34.6 s to produce the same extent of reaction. Determine the calculated concentration of glucose in the standard and the percent error for the analysis. 

As an example of the quantitative testing of Eq. (5.47), consider the polymerization of diethylene glycol (BB) with adipic acid (AA) in the presence of 1,2,3-propane tricarboxylic acid (A3). The critical value of the branching coefficient is 0.50 for this system by Eq. (5.46). For an experiment in which r = 0.800 and p = 0.375, p = 0.953 by Eq. (5.47). The critical extent of reaction, determined by titration, in the polymerizing mixture at the point where bubbles fail to rise through it was found experimentally to be 0.9907. Calculating back from Eq. (5.45), the experimental value of p, is consistent with the value =0.578. 

Previous thermal analysis studies had indicated that while Sb203 did not react directly with DBDPO, there was some evidence that the reaction of a polymer substrate with the Sb203 generated a species which was very reactive (23), and that this product was antimony metal (Sb°). Therefore, simple mixtures of DBDPO with powdered antimony, bismuth and zinc metals (mole ratio of bromine to metal of 3 1) were pyrolyzed and the extent of reaction determined by CGC. 

In this equation, is the extent of reaction (determined from Equation 9.1-3) n, and H,- are respectively the molar flow rate and specific enthalpy of a process species in an inlet or outlet stream and the summations are taken over all species in all of their inlet and outlet stales. Once calculated, AH is substituted in the open-system energy balance, which is solved for Q or whichever other variable is unknown. 

It must be noted that the extents of reaction determined by calorimetric measurements are kinetically defined. The reaction is considered to be finished when its rate falls below the limit of detection, that is when the rate of heat production has decreased by 2-3 decades with respect to the maximum rate. Below we will show that the reaction may go on for quite a long time at a very low and continuously decreasing rate. 

The concept of extent of reaction Determination of the Individual rates In e complex reaction Selectivity and yield Definitions Analytical solutions... 

Having found the values for k, AH and , a simulated calorimetric signal can be constructed for the reaction over any time interval and the extent of reaction determined. The reaction half life (ti ) can be found from Equation (7) ... 

Usually the experimental error in the measurement of time is negligible relative to the error in concentration, and the choice of plotting form may be determined by this factor. Another consideration is the extent of reaction that has been followed... 

A second way to achieve constancy of a reactant is to make use of a buffer system. If the reaction medium is water and B is either the hydronium ion or the hydroxide ion, use of a pH buffer can hold Cb reasonably constant, provided the buffer capacity is high enough to cope with acids or bases generated in the reaction. The constancy of the pH required depends upon the sensitivity of the analytical method, the extent of reaction followed, and the accuracy desired in the rate constant determination. 

Knowledge of the mechanism enables one to obtain more insight into the various factors which determine the extent of reaction along both pathways. In this chapter special attention will be given to the kinetics and mechanism of the hydrolysis of simple enamines.f... 

As pointed out above, accumulatory pressure and weight loss measurements usually refer to the total reaction. When there are several volatile products, it is necessary to identify all components and investigate progressive changes in gas composition. Quantitative determinations of the amounts of each product (EGA) should, ideally, be combined with measurements of the total extent of reaction, although Gam [143] has recommended caution in the interpretation of results from simultaneous measurements. 

Hulbert [77] points out that, in general, attempts to include an allowance for the influence of particle size variations in the reactant mixtures on kinetic analyses using the above equations have been unsatisfactory because some of the parameters are not readily defined. Kapur [42], working with powders of known crystal size distribution, indicated that the overall extent of reaction can be estimated by a summation of the individual contributions from each size fraction and thus the best kinetic fit determined. 

The design equations for a CSTR do not require that the reacting mixture has constant physical properties or that operating conditions such as temperature and pressure be the same for the inlet and outlet environments. It is required, however, that these variables be known. Pressure in a CSTR is usually determined or controlled independently of the extent of reaction. Temperatures can also be set arbitrarily in small, laboratory equipment because of excellent heat transfer at the small scale. It is sometimes possible to predetermine the temperature in industrial-scale reactors for example, if the heat of reaction is small or if the contents are boiling. This chapter considers the case where both Pout and Tout are known. Density and Q ut wiU not be known if they depend on composition. A steady-state material balance gives... 

In the reaction of lactic acid to form pyruvic acid over the iron phosphate catalysts, formation of a new compound was observed. As the extent of reaction increased, the amount of pyruvic acid increased to a maximum and then decreased, while that of the new compound increased steadily. It was therefore concluded that the new compound is formed from pyruvic acid in parallel with acetic acid and CO2. According to gas-mass analyses, the molecular weight was determined as 112. However, there are many compounds with molecular weigth of 112. After the NMR analyses and X-ray diffraction analyses for the single crystal, the new compound was determined to be citraconic anhydride, i.e., mono-methyl maleic anhydride. 

Boc-protected a,a-diatyl-L-prohnol (6) was placed in a sand bath under a weak vacuum somce (approx. 15 imuHg) and heated to 210°C. Ten minutes after the formation of bubbles had ceased. The reaction was cooled to room temperature and H-NMR was used to determine the extent of reaction. If the Boc group was still detectable by H-NMR, then the reaction was reheated to 210°C for an additional twenty minutes and allowed to cool and the extent of reaction was reevaluated by H-NMR. This procedtrre was repeated rmtil the Boc group cotrld not be detected by H-NMR. 

Fig. 2. Relaxation modulus G(t) of a set of polydimethylsiloxane samples with increasing extent of crosslinking plotted against time of crosslinking. The linear PDMS chains (Mn 10 000, polydis-persity index 2) were endlinked with a four-functional silane crosslinker catalyzed by a platinum compound. Samples with different extent of reaction were prepared by poisoning the reaction at different times. The actual extent of reaction was not determined. Two of the samples are clearly before the gel point (LST) and two beyond. The third sample is very close to the gel point. Data of Chambon and Winter [5] evaluated by Baumgartel and Winter [8]...

Several assumptions were made in order to analyze kinetic data in terms of this expression (2). First it was assumed that k 2 m kj, k2 k 3, and kj/k j k /k ( - If). Second it was assumed that the rate constants were independent of the extent of reaction i.e., that all six functional groups were equally reactive and that the reaction was not diffusion controlled. The concentration of polymer hydroxyl functionality was determined experimentally using infrared spectroscopy as described elsewhere (7). A major unknown is the instantaneous concentration of methanol. Fits to the kinetic data were made with a variety of assumptions concerning the methanol concentration. The best fit was achieved by assuming that the concentration of methanol was initally constant but decreased at a rate proportional to the concentration of residual polymer hydroxy groups towards the end of the reaction. As... 

The variable / depends on the particular species chosen as a reference substance. In general, the initial mole numbers of the reactants do not constitute simple stoichiometric ratios, and the number of moles of product that may be formed is limited by the amount of one of the reactants present in the system. If the extent of reaction is not limited by thermodynamic equilibrium constraints, this limiting reagent is the one that determines the maximum possible value of the extent of reaction ( max). We should refer our fractional conversions to this stoichiometrically limiting reactant if / is to lie between zero and unity. Consequently, the treatment used in subsequent chapters will define fractional conversions in terms of the limiting reactant. 

From the stoichiometry of the reaction it fs possible to determine the mole numbers of the various species in terms of the extent of reaction and their initial mole numbers. 

In this case one obtains an expression for that cannot be manipulated to yield a simple algebraic form. However, if the concentration of one species is known as a function of time, the concentrations of all other species may be determined from the definition of the extent of reaction per unit volume that is,... 

From a knowledge of the reaction stoichiometry and measurements of the total pressure as a function of time, it is possible to determine the extent of reaction and the partial pressures or concentrations of the various reactant and product species at the time at which the measurement is made. Illustration 3.3 indicates how pressure measurements can be used to determine a reaction rate function. 

What is the order of the reaction and the reaction rate constant The reverse reaction may be neglected. The volume of the solution as determined by the height of the meniscus in the capillary may be assumed to be a measure of the fraction conversion (i.e., the volume change is proportional to the extent of reaction). 

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