Conversion equations

AUC is the area under the curve or the integral of the plasma levels from zero to infinite time. Conversely, equation 1 may be used to calculate input rates of dmg that would produce steady-state plasma levels that correspond to the occurrence of minor or major side effects of the dmg. 

When the flow pattern is known, conversion in a known network and flow pattern is evaluated from appropriate material and energy balances. For first-order irreversible isothermal reactions, the conversion equation can be obtained from the R sfer function by replacing. s with the specific rate k. Thus, if G(.s) = C/Cq = 1/(1 -i- t.s), then C/Cq = 1/(1 -i-kt). Complete knowledge of a network enables incorporation of energy balances into the solution, whereas the RTD approach cannot do that. 

Each group of molecules reacts independently of any other group, that is, as a batch reaclor. Batch conversion equations for power law rate equations are ... 

For zero conversion, /jv = /ip = 1 since only monomers are present initially. At high conversion, Equation (13.18) approaches Equation (13.4). The poly-dispersity for the complete conversion case is... 

For variable density systems it is more convenient to work in terms of the fraction conversion (equation 8.2.9), but for constant density systems either equation 8.2.9 or equation 8.2.10 is appropriate. 

This equation may be solved numerically by trial and error, recognizing that fB1 must lie between 0 and 0.875. The appropriate value of fB1 is 0.6285. Equation F may now be used to determine that fB2 = 0.8038. With a knowledge of these conversions, equation C, D, or E may be used to determine the required reactor volume. Thus... 

Conversion in a known network and flow pattern is evaluated from appropriate material and energy balances. For first order irreversible isothermal reactions, the conversion equation can be obtained from the transfer function if that is known by replacing the parameter s by the... 

A reaction for which the batch conversion equation is [Pg.588]

This equation relates the hold-up to the flowrates of the phases and column diameter through the characteristic velocity, u0. It therefore gives a method of calculating the holdup for a given set of flowrates if u0 is known. Conversely, equation 13.33 may be used to calculate uq from experimental hold-up measurements made at different flowrates. Thus, if hold-up data are plotted with L d + (J/( 1 — j))L c as the ordinate against j( 1 — j) as the abscissa, a linear plot is obtained which passes through the origin and which has a slope equal to fir, Wl. 

As these conversion equations show, in addition to the molecular weight of a measured gaseous pollutant, the temperature and pressure at the time of the measurement must be known. Because this information is often not given in the literature, no attempt has been made in this report to convert to a common unit. 

To evaluate how best to distribute the side entry feed and how to calculate the corresponding conversion equation is a rather complex problem. For this type of contacting in general see Westerterp et al. (1984). 

Chapter 6 develops the conversion equation. Thus for first-order reactions in one tank... 

Table 16.2 Conversion Equations for Macrofluids and Microfluids with 8 = 0 in Ideal Reactors...

In this treatment we develop the conversion equations for spherical particles in which steps 1, 2, and 3, in turn, are rate-controlling. We then extend the analysis to nonspherical particles and to situations where the combined effect of these three resistances must be considered. 

The oxidation of thioacylamidines (220) (R = alkyl, aryl) and thioacylguanidines (220) (R = NR 2) affords a wide range of 3,5-disubstituted 1,2,4-thiadiazoles (221). A wide variety of oxidizing agents have been used for this conversion (Equation (34)) <82AHC(32)285). 

We have used a different approach for determining the conversion of hydrocarbon. Our approach, which requires measuring the consumption of only one hydrocarbon plus the oxygen, has a distinct advantage where reactants have large differences in reactivity. At low conversions Equation 1 applies,... 

Value at 630 nm determined from the spectral shape reported in [162] and the 2PA absorption coefficient at 595 nm reported in [163]. Calculated from the value of Im y reported in the cited paper, using a conversion equation consistent with other papers by the same authors. 

Recently, Henderson has investigated the effect of Lewis base additives such as HMPA in enantioselective deprotonation of ketones mediated by chiral magnesium amide bases. In almost all reactions investigated, the additive HMPA could be replaced by DMPU without any undue effect on either selectivity or conversion (equation 69) ... 

Malkin s autocatalytic model is an extension of the first-order reaction to account for the rapid rise in reaction rate with conversion. Equation 1.3 does not obey any mechanistic model because it was derived by an empirical approach of fitting the calorimetric data to the rate equation such that the deviations between the experimental data and the predicted data are minimized. The model, however, both gives a good fit to the experimental data and yields a single pre-exponential factor (also called the front factor [64]), k, activation energy, U, and autocatalytic term, b. The value of the front factor k allows a comparison of the efficiency of various initiators in the initial polymerization of caprolactam [62]. On the other hand, the value of the autocatalytic term, b, describes the intensity of the self-acceleration effect during chain growth [62]. 

When the catalyst (enzyme) acts on a racemic mixture, Equation 4 also applies in the limit of low conversion (with the extent of conversion) (Equation 4a) ... 

Also, a dimensionless time ( = t/r, where r is the average residence time, will be introduced. The chemical conversion equation —da/dt — fcja" now becomes... 

A controls the overall rate of conversion, equation 3.81 could be used directly as the rate equation for design purposes. If, however, external mass transfer were important the partial pressures in equation 3.81 would be values at the interface and an equation (such as equation 3.66) for each component would be required to express interfacial partial pressures in terms of bulk partial pressures. If internal diffusion were also important, the overall rate equation would be multiplied by an effectiveness factor either estimated experimentally, or alternatively obtained by theoretical considerations similar to those discussed earlier. 

Despite this large favorable energy change, the prismane rearranges by way of intermediate structures (Equation 11.40) with the activation enthalpies indicated. Hence the activation enthalpy for the direct conversion (Equation 11.39) must be greater than 33 kcal mole-1. This barrier is remarkably high for a... 

In a similar fashion, cycloaddition reaction of 2-vinylpyrrolidines with carbodiimides in the presence of Pd(OAc)2 and l,5-bis(diphenylphosphino)pentane affords the seven-membered ring cyclic arylguanidines in acceptable yields and conversions (Equation 16) <2004T73>. 

In the example shown in Figure 7.5, a 25% molar excess of B has been added (M = 1.25). The function of this excess is to increase the reaction rate when CA becomes small. It is often called the kinetic excess, because it increases the reaction rate at high conversion (Equation 7.7). 

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