Solvent adsorption correlation equations

The measured data also were used (700) in a quantitative representation of the effect of structure on the reactivity and adsorptivity of substrates by means of the Taft-Pavelich equation (22). The adsorption data suffered from a larger scatter than the rate data. No substrate or substituent could be detected that would fail to satisfy completely the correlation equations. In the correlation of the initial reaction rates and relative adsorption coefficients the parameter p was negative, while the parameter S was positive. In correlations of the reaction rates obtained by the hydrogenation of a similar series of substrates on the same catalyst in a number of solvents, the parameters p and had the same sign as in the hydrogenation in solvent-free systems, while in the correlation of the adsorption coefficients the signs of the parameters p and in systems with solvents were opposite to those in solvent-free systems. This clearly indicates that solvents considerably affect the influence of the structure of substrates on their reactivity. 

A similar system, (CH3)2C=CH X, was studied by Endrysova and Kraus (55) in the gas phase in order to eliminate the possible leveling influence of a solvent. The rate data were separated in the contribution of the rate constant and of the adsorption coefficient, but both parameters showed no influence of the X substituents (series 61). A definitive answer to the problem has been published by Kieboom and van Bekum (59), who measured the hydrogenation rate of substituted 2-phenyl-3-methyl-2-butenes and substituted 3,4-dihydro-1,2-dimethylnaphtalenes on palladium in basic, neutral, and acidic media (series 62 and 63). These compounds enabled them to correlate the rate data by means of the Hammett equation and thus eliminate the troublesome steric effects. Using a series of substituents with large differences in polarity, they found relatively small electronic effects on both the rate constant and adsorption coefficient. 

In the discussed series (77) of hydrogenated compounds the reaction rate and relative adsorptivity of substrates in most solvents were affected to a comparable degree by steric and polar influences. Negative values of the parameter p and positive values of the parameter 8, were obtained in most cases in the correlation of the reaction rates by the Taft-Pavelich equation, while correlation of the relative adsorption coefficients gave opposite results. This can be seen as an example of an interesting compensation of the kinetic and adsorption terms. 

It has been found in many papers (91-97) that the solvent may considerably affect also the relative adsorptivity of substrates. The majority of these authors, however, only point out differences in the relative adsorp-tivities of substrates in competitive hydrogenations under various conditions, or attempt to correlate these adsorptivities with the physical properties of solvents. In order to predict the effect of solvents on the selectivity of heterogeneously catalyzed hydrogenations, it is of course very important to obtain more general information on the effect of solvents on the adsorption coefficients of reacting compounds, based on a qualitative basis. Cerveny, Prochazka, and Ruzicka (70) suggested, for correlation of the effect of solvent on the relative adsorptivity of compounds, an equation in the form... 

Equation (6-6) is one of the fundamental relationships of adsorption chromatography. It expresses K" as a function of two adsorbent properties, V and a, and a quantity f X,S) which is determined by the particular sample and solvent involved. F and a are independent of the nature of X and S. f X,S) is equal to the adsorption energy AE on a surface of standard activity (i.e., a = 1.0) it is independent of adsorbent activity (i.e., V and a) but does depend upon adsorbent type. Equation (6-6) immensely simplifies the correlation of /f values for adsorbents of differing activity. Once a series of K" values (different samples and/or solvents) have been measured on one adsorbent, values of /f can be predicted for another adsorbent (of the same type) if the values of and a are known for each adsorbent. Alternatively, once we have tabulated values of f(X,S) for a series of samples and a given solvent or solvents, measurement of two or more A values for these same samples and solvent(s) on a new adsorbent batch permits us to derive values of and a for that adsorbent (see Section 6-3B).t... 

For a given chromatographic system and a series of different substituted phenols, the parameters a and b are constant, since 0 and for each of the substituted phenols (in a vertical configuration) is constant. Equation (1 l-2a) is tested in Fig. 11-4 against the data for one of the solvent systems studied by Bark and Graham. A resonable correlation of R versus (7 is observed. Although the data of Fig. 11-4 show more scatter than those of Fig. 1 l-3(a), in all but two cases the adsorption affinity of the substituted... 

Adsorption of some organic solvent vapours onto HSZ were studied. Binary adsorption equilibriums except azeotropic mixture-HSZ systems could be correlated by Markham-Benton equation for the whole concentration range, and the break times could be estimated well by using the Extended-MTZ-Method. For azeotropic mixture-HSZ systems, the equilibriums and the break times could be correlated and estimated only for a part of the all concentration range. Then, two azeotropic points appeared in the adsorption equilibriums for IPA-TCE -Y-type system. For this binary systems adsorption equilibrium data could be expressed by proposed equation, similar to liquid-vapour azeotropic equilibrium equation. Breakthrough curve could be simulated using the Stop Go method in the whole range for azeotropic mixture systems as well as for zeotropic systems. 

Porter et al. [34] found an equation relating Vjt to the activity coefficient at infinite dilution of the solute, y - This correlation was deduced on the basis of the following simplifying assumptions (a) the column operates under ideal conditions (the equilibrium distribution of the component between the gas and the liquid phase is preserved), the partial pressure of the component obeys Henry s law, the pressure drop along the colunm is zero) (b) the carrier gas and the vapours are ideal (c) the carrier gas is insoluble iu the solvent (d) there are no adsorption effects. 

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