Conversion-concentration relationship

Conversion-concentration relationships Variable-density reactions Reactors Batch reactor... 

Optimum Operating Line. The relationships between the conversion and the average molecular weight can be plotted as a function of initiator concentration while varying the jacket temperature to optimize the conversion. The relationships are shown in... 

Therefore, livingness is validated by analyzing the linear conversion-time, conversion-molecular weight and conversion-iniferter concentration relationships. However, such an interpretation appears to be too simple to describe the whole process of iniferter-based radical polymerization, which is far more complex than expected. 

Figure 3 shows the conversion-time relationship for varying aluminum to titanium ratios. It can be seen that the rate decreases nonuniformly with increasing aluminum-titanium ratio. The small change in rate resulting from a 10-fold change in aluminum-titanium ratio indicates a low order of dependence of the rate upon the Al HsbCl concentration. This low order of rate dependence upon the alkyl aluminum concentration suggests that the main course of the process is insensitive to excess alkyl, but that some side effects exist. 

The performance of the coked catalyst is quantified by the initial conversion, a, and the sensitivity to coke, h, viz., the intercept and slope of the conversion - coke relationship, at least for coke levels less than . The effect of reaction mixtures on a and b dq)ends upon the nature of the feed and the species added. When the additive is less-rapidly coking, then values of a and h for the feed itself change with additive concentration. When the species added is more-rapidly coking, then a and b for the feed itself are independent of the additive concentration, i.e. independent of A- But since only a more-rapidly coking species would be an additive for a typical accelerated-coking test, it can be concluded that the presence of the added species does not influence the activity, at least upto coke levels equal to... 

P11-9a a spherical particle is dissolving in a liquid. The rate of dissolution is first-order in the solvent concentration, C, Assuming that the solvent is in excess, show that the following conversion time relationships hold. 

A linear relation was found between initiator concentration and conversion at lower conversions up to 1 h and in the temperature range between —78° and —30°C (Fig. 8). The plots did not go through the origin which indicated deactivation of initiator possibly by reaction with impurities. The DP increased with increasing initiator concentration at relatively low conversions. Similar relationships were found at —30°C but... 

The reactions used in analytical chemistry never result in complete conversion of reactants to products. Instead, they proceed to a state of chemical equilibrium in which the ratio of concentrations of reactants and products is constant. Equilibrium-constant expressions are algebraic equations that describe the concentration relationships existing among reactants and products at equilibrium. Among other things, equilibrium-constant expressions permit calculation of the error in an analysis resulting from the quantity of unreacted analyte that remains when equilibrium has been reached. 

Overview. In Chapter 2, we showed that if we had the rate of reaction as a function of conversion, = /(X), we could calculate reactor volumes necessary to achieve a specified conversion for flow systems and the time to achieve a given conversion in a batch system. Unfortunately, one is seldom, if ever, given = yiX) directly from raw data. Not to fear, in this chapter we will show how to obtain the rate of reaction as a function of conversion. This relationship between reaction rate and conversion will be obtained in two steps. In Step 1, Part 1 of this chapter, we define the rate law, which relates the rate of reaction to the concentrations of the reacting species and to temperature. In Step 2, Part 2 of this chapter, we define concentrations for fiow and batch systems and develop a stoichiometric table so that one can write concentrations as a function of conversion. Combining Steps 1 and 2, we see that one can then write the rate as a function conversion and use the techniques in Chapter 2 to design reaction systems. 

Further simulations, which are not shown here, were performed in which the impurity was assumed to be a lithium salt of an interfering anion present in aqueous solution. The impurity caused an increase in the slope of the potential-concentration relationship below 10 4 mol/L of dye. Conversely, a cationic impurity will cause the slope to decrease at dye concentrations below 10 5 mol/L when a chloride salt of the impurity is included in the calculations. The reason for the discrepancy between experimental and calculated... 

When the superfluid component flows through a capillary connecting two reservoirs, the concentration of the superfluid component in the source reservoir decreases, and that in the receiving reservoir increases. When both reservoirs are thermally isolated, the temperature of the source reservoir increases and that of the receiving reservoir decreases. This behavior is consistent with the postulated relationship between superfluid component concentration and temperature. The converse effect, which maybe thought of as the osmotic pressure of the superfluid component, also exists. If a reservoir of helium II held at constant temperature is coimected by a fine capillary to another reservoir held at a higher temperature, the helium II flows from the cooler reservoir to the warmer one. A popular demonstration of this effect is the fountain experiment (55). 

Levenspiel considers the cases where the relationship between concentration and conversion of reacting specie is not obvious, but depends on a number of factors. 

This case includes most liquid reactions and also those gas reactions that operate at both constant temperature and pressure with no change in the number of moles during reaction. The relationship between concentration C and fractional conversion is as follows ... 

Artifact removal and/or linearization. A common form of artifact removal is baseline correction of a spectrum or chromatogram. Common linearizations are the conversion of spectral transmittance into spectral absorbance and the multiplicative scatter correction for diffuse reflectance spectra. We must be very careful when attempting to remove artifacts. If we do not remove them correctly, we can actually introduce other artifacts that are worse than the ones we are trying to remove. But, for every artifact that we can correctly remove from the data, we make available additional degrees-of-freedom that the model can use to fit the relationship between the concentrations and the absorbances. This translates into greater precision and robustness of the calibration. Thus, if we can do it properly, it is always better to remove an artifact than to rely on the calibration to fit it. Similar reasoning applies to data linearization. 

Terminal model reactivity ratios may be estimated from the initial monomer feed composition and the dyad concentrations in low conversion polymers using the following relationships (eqs. 45, 46). 

Effects of Initiator Parameters. Initiator types can best be characterized by the frequency factor (k ) and the activation energy (E ), and the effect of these parameters on the molecular weight-conversion relationship is shown in Figures 7 and 8. The curves shown are the result of choosing the jacket temperature-inlet initiator concentration combination which maximizes the reactor conversion for each initiator type investigated. 

Figure 7. Tubular plug-flow addition polymer reactor effect of the frequency factor (ka) of the initiator on the molecular weight-conversion relationship at constant activation energy (Ea). Each point along the curves represents an optimum initiator feed concentration-reactor jacket temperature combination and their values are all different, (Ea = 32.921 Kcal/mol In ka = 35,000 In sec ...

As seen in the figures, the quantity of initiator required to yield a given conversion varies directly with the frequency factor for an initiator with a specified activation energy and inversely with the activation energy for an initiator of specified frequency factor. The relationships do not show a linear proportionality between the reactor conversion and square root of the inlet initiator concentration. 

The conversion is carried out using the equilibrium relationship between the gas- and liquid-phase concentrations. Usual practice is to assume Henry s law. Thus, the gas-phase concentration that is equivalent to u is Kh ai, where Kh is... 

GL 4] [R 5] [P 5] The rate of the fluorination of y0-keto esters is usually correlated with the enol concentration or the rate of enol formation as this species is actually fluorinated [15, 16]. For the fluorination of ethyl 2-chloroacetoacetate in a micro reactor, much higher yields were found as expected from such relationships and as compared with conventional batch processing which has only low conversion. Obviously, the fluorinated metal surface of the micro channel promotes the enol formation. 

Table VIII demonstrates the inverse relationship of conversion to S02 concentration in the feed that is a consequence of applying flow reversal to S02 oxidation using a single reactor. As the S02 concentration in the table moves from 0.8 to over 8 vol%, the conversion drops from 96-97% down to 85%. At the same time, the maximum bed temperature changes from 450 to 610°C. For an equilibrium-limited, exothermic reaction, this behavior is explained by variation of the equilibrium conversion with temperature.

When setting the conditions in chemical reactors, equilibrium conversion will be a major consideration for reversible reactions. The equilibrium constant Ka is only a function of temperature, and Equation 6.19 provides the quantitative relationship. However, pressure change and change in concentration can be used to shift the equilibrium by changing the activities in the equilibrium constant, as will be seen later. 

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