Extent of conversion

The extent of conversion is a measure of fractional conversion of reactants achieved in a specified time. Let and be the initial number of moles of A and B, respectively, present in the reaction vessel of volume V. Let nJ and Hg be the number of moles of A and B, respectively, present in the vessel after some time t. The extent of conversion or fractional conversion of A is defined as the number moles of A converted in a specified time per moles of A present at the time of start-up. Thus, 

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Throughout this section we have used mostly p and u to describe the distribution of molecular weights. It should be remembered that these quantities are defined in terms of various concentrations and therefore change as the reactions proceed. Accordingly, the results presented here are most simply applied at the start of the polymerization reaction when the initial concentrations of monomer and initiator can be used to evaluate p or u. The termination constants are known to decrease with the extent of conversion of monomer to polymer, and this effect also complicates the picture at high conversions. Note, also, that chain transfer has been excluded from consideration in this section, as elsewhere in the chapter. We shall consider chain transfer reactions in the next section. 

The lifetime of polystyrene radicals at 50 C was measuredt by the rotating sector method as a function of the extent of conversion to polymer. The following results were obtained ... 

The operating conditions in the gasifier (temperature and pressure) and the reaction kinetics (residence time, concentration of the constituents, and rate constants) determine the extent of conversion or approach to equiUbrium. 

Quantitative Analysis of Selectivity. One of the principal synthetic values of enzymes stems from their unique enantioselectivity, ie, abihty to discriminate between enantiomers of a racemic pair. Detailed quantitative analysis of kinetic resolutions of enantiomers relating the extent of conversion of racemic substrate (c), enantiomeric excess (ee), and the enantiomeric ratio (E) has been described in an excellent series of articles (7,15,16). 

Theoretical plots of ee (substrate) and eep (product) as a function of c are shown in Figure 2a and b. It can be seen that the ee increases with the extent of conversion. Consequently the enantiomeric purity of the substrate can be increased by sacrificing the yield and carrying out the reaction to higher degrees of conversion. Conversely, if high purity product is required the conversion should be terminated at early stages. 

The law of mass action, the laws of kinetics, and the laws of distillation all operate simultaneously in a process of this type. Esterification can occur only when the concentrations of the acid and alcohol are in excess of equiUbrium values otherwise, hydrolysis must occur. The equations governing the rate of the reaction and the variation of the rate constant (as a function of such variables as temperature, catalyst strength, and proportion of reactants) describe the kinetics of the Hquid-phase reaction. The usual distillation laws must be modified, since most esterifications are somewhat exothermic and reaction is occurring on each plate. Since these kinetic considerations are superimposed on distillation operations, each plate must be treated separately by successive calculations after the extent of conversion has been deterrnined (see Distillation). 

Fig. 2.6. Dependence of enanhomeric excess on relative rate of reaction and extent of conversion with a chiral reagent in kinetic resolution. [Reproduced from J. Am. Chem. Soc. 103 6237 (1981) by permission of the American Chemical Society.]...

These expressions relate the terms X, (-i ), Vr, and u. Therefore, tlie fourtli term can be determined if the remaining terms are known. When designing, the size of the reactor needed for a given duty or the extent of conversion in a reactor of given size can be directly obtained. 

Strongly basic anion exchangers (polystyrene quaternary ammonium resins). These resins (Duolite A113, Amberlite 400, etc.) are usually supplied in the chloride form. For conversion into the hydroxide form, treatment with 1M sodium hydroxide is employed, the volume used depending upon the extent of conversion desired two bed volumes are satisfactory for most purposes. The rinsing of the resin free from alkali should be done with de-ionised water free from carbon dioxide to avoid converting the resin into the carbonate form about 2 litres of such water will suffice for 100 g of resin. An increase in volume of about 20 per cent occurs in the conversion of the resin from the chloride to the hydroxide form. 

Steam-Moderated Process. The basic idea behind this approach is to limit the extent of conversion of the methanation reaction, Reaction 1, by adding steam to the feed gases. This process simultaneously provides for (46) elimination of the CO shift, Reaction 2, to get a 3 1 H2 CO ratio from the make-up gas ratio of about 1.5 1 and avoidance of carbon laydown by operation under conditions in which carbon is not a thermodynamically stable phase (see Chemistry and Thermodynamics section above). 

The molecular weight of a polymer will be reduced if either die extent of conversion or the average functionality is decreased. At 95% conversion of difunctional monomers, for example, Xn is only 20.25 The molecular weight is also related to a stoichiometric imbalance, r, which is normally defined to be less than 1.0 ... 

As mentioned previously, the use of multifunctional monomers results in branching. The introduction of branching and the formation of networks are typically accomplished using trifunctional monomers, and the average functionality of the polymerization process will exceed 2.0. As the average functionality increases, the extent of conversion for network formation decreases. In... 

It is important to note that and C2 are quantitative descriptors of the gel effect which depend only on the monomer, temperature and reaction medium. The full description of given by equation (11), requires g and g2 which are functions of the rate of initiation and extent of conversion. The kinetic parameters used in these calculations and their sources are given in Table 1. All data are in units of litres, moles and second. Figure 5 shows the temperature dependencies of and C2 and Table 2 lists these and other parameters determined by fitting the model to the data in Figures 1-4. 

The enantioselectivity of biocatalytic reactions is normally expressed as the enantiomeric ratio or the E value [la], a biochemical constant intrinsic to each enzyme that, contrary to enantiomeric excess, is independent of the extent of conversion. In an enzymatic resolution of a racemic substrate, the E value can be considered equal to the ratio of the rates of reaction for the two enantiomers, when the conversion is close to zero. More precisely, the value is defined as the ratio between the specificity constants (k st/Ku) for tho two enantiomers and can be obtained by determination of the k<-at and Km of a given enzyme for the two individual enantiomers. 

However, considering practical limitations, that is, the availability of optically pure enantiomers, E values are more commonly determined on racemates by evaluating the enantiomeric excess values as a function of the extent of conversion in batch reactions. For irreversible reactions, the E value can be calculated from Equation 1 (when the enantiomeric excess ofthe product is known) or from Equation 2 (when the enantiomeric excess ofthe substrate is knovm) [la]. For reversible reactions, which may be the case in enzymatic resolution carried out in organic solvents (especially at extents of conversion higher than 40%), Equations 3 or 4, in which the reaction equilibrium constant has been introduced, should be used [lb]. 

In an ideal DKR, where the substrate stays racemic throughout the reaction process, the optical purity depends only on the enantiomeric ratio (E) (ee =(E— 1)/ (E +1)), and is independent of the extent of conversion. The enantiomeric excess of the product formed under racemizing conditions is equal to the initial enantiomeric... 

OS 52[ [R 4b[ [P 38] To achieve comparable extents of conversion, 24 h operation was needed for batch synthesis, whereas micro-reactor operation needs only about 20 min [8],... 

Once the mole fraction of acetic acid has been obtained, calculation of the conversion is then trivial, and we have defined the extent of conversion at a given time t, X(t), as ... 

Fig. 5.5.5 1 D CSI datasets showing the extent of conversion during a batch reaction. The form of the feature identified as peak B is associated with a single chemical shift i.e., it is of constant form at all positions across the bed, and therefore shows that the extent of conversion is uniform throughout the bed. The low intensity horizontal streaking" effect observed in these datasets and that shown in Figure 5.5.6 are artifacts arising from the automatic phase correction applied to the data ...

Studies of this reaction have recently been extended to acquisition of a 3(4)D CSI dataset, shown in Figure 5.5.12 the grey scale indicates the extent of conversion. As expected from the 1(2)D CSI and volume selective imaging studies discussed earlier, conversion is seen to be heterogeneous within transverse sections through the bed at any position along the direction of superficial flow. 

Chain-growth polymerizations are diffusion controlled in bulk polymerizations. This is expected to occur rapidly, even prior to network development in step-growth mechanisms. Traditionally, rate constants are expressed in terms of viscosity. In dilute solutions, viscosity is proportional to molecular weight to a power that lies between 0.6 and 0.8 (22). Melt viscosity is more complex (23) Below a critical value for the number of atoms per chain, viscosity correlates to the 1.75 power. Above this critical value, the power is nearly 3 4 for a number of thermoplastics at low shear rates. In thermosets, as the extent of conversion reaches gellation, the viscosity asymptotically increases. However, if network formation is restricted to tightly crosslinked, localized regions, viscosity may not be appreciably affected. In the current study, an exponential function of degree of polymerization was selected as a first estimate of the rate dependency on viscosity. 

Another expression which has been used relates the extent of conversion of the total input energy (both electrical and optical) to chemical energy ... 

At low temperatures, the nonenzymatic reaction is reduced to a larger extent than the enzymatic reaction. The mass transfer rate is reduced to a smaller extent. Mass transfer limitation is required for high enantiomeric excess and determines the conversion rate. Therefore, the volumetric productivity decreases at lower temperatures. The equilibrium constant is considerably higher at low temperatures, resulting in a higher extent of conversion or a lower HCN requirement. Both the volumetric productivity and the required enzyme concentration increase by increasing the reaction temperature and aqueous-phase volume while meeting the required conversion and enantiomeric excess [44]. The influence of the reaction medium (solvent and water activity) is much more difficult to rationalize and predict [45],... 

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