Structure effects linear correlations

Linear anodic potential sweep, 30 256-257 Linear correlations, structure effects, 29 160-161... 

This approach did not seem to be as satisfactory for those sulfamates having heteroatom substituents (hetero-sulfamates). Spillane suggested that the various electronic effects of the hetero-atoms probably introduce an additional variable that is apparently absent, or constant, for the carbosulfamates. Because molecular connectivity correlates structure with molecular volume and electronic effects, Spillane included molecular connectivity, (computed for the entire molecule, RNHSOO to the four variables, x, y, z, and V, and applied the statistical technique of linear-discrimination analysis to 33 heterosulfamates (10 sweet, 23 not sweet). A correlation of >80% was obtained for the x, z, x subset 5 of the 33... 

The analysis of the magnetic and structural data reported by Ryabova revealed a linear correlation between the Fe-S bond distance and the effective magnetic moment [106]. 

Assuming that a linear approximation can be made for the correlation between the sectoral employment level and the sectoral production level, the quantitative impacts on employment are calculated using job coefficients. Of course, the constant input-output coefficients are a strong assumption and could be criticised (Zhang and Folmer, 1998). However, structural effects could be analysed in a ceteris-paribus analysis with the chosen approach. 

In the case of Type B linear correlations of two presumably related processes, the main problem is to find a suitable partner to a heterogeneous catalytic reaction the requirements include a good knowledge of its mechanism, easy measurement of structure effects, and the possibility of using the same reactants in both series. It already has been mentioned that this task may be more easily fulfilled with heterogeneous acid-base reactions but may be impossible with reactions on metals or some oxides. 

Linear correlations of structure effects on rate and equilibria may be obtained for a single reaction proceeding on different catalysts. In this way. 

Studies of structure effects on rate have helped substantially to bring researchers to the present deep understanding (72,13) of the mechanism of elimination reactions. Beside stereochemical evidence, successful linear correlations have yielded the desired information. The published series of reactants and correlations are summarized in Table II. The fit of straight lines to experimental data is usually good or very good, and only a few points deviate significantly. Details of the correlations may be found in the original literature here we will concentrate on the values of the slopes. 

Some information about structure effects on the rate of dehydrogenation of alcohols to aldehydes and ketones on metals is found in the older literature 129-132) from which it follows that secondary alcohols react more easily than the primary alcohols 129) and that the reactivity decreases with the length of the carbon chain 131). Some series can be correlated by the Taft equation using a constants (Ref. 131, series 103, Cu-Cr203 catalyst, 350°C, four points, slope 18 Ref 132, series 104, Cu catalyst, four points, slope 22). Linear relationships have been used in a systematic way by... 

Kinetic Acidities in the Condensed Phase. For very weak acids, it is not always possible to establish proton-transfer equilibria in solution because the carbanions are too basic to be stable in the solvent system or the rate of establishing the equilibrium is too slow. In these cases, workers have turned to kinetic methods that rely on the assumption of a Brpnsted correlation between the rate of proton transfer and the acidity of the hydrocarbon. In other words, log k for isotope exchange is linearly related to the pK of the hydrocarbon (Eq. 13). The a value takes into account the fact that factors that stabilize a carbanion generally are only partially realized at the transition state for proton transfer (there is only partial charge development at that point) so the rate is less sensitive to structural effects than the pAT. As a result, a values are expected to be between zero and one. Once the correlation in Eq. 13 is established for species of known pK, the relationship can be used with kinetic data to extrapolate to values for species of unknown pAT. 

Structural Effects and Solvent. The effect of solvent on the equilibrium of Reaction 4 can be first discussed in terms of effects on the susceptibility to substituent effects. The values of pK2, characterizing this equilibrium, are a satisfactorily linear function of the Hammett constants correlation coefficient r (Table VI). The values of reaction constant p are practically independent of the ethanol concentration (Table VI), as was already indicated by the almost constant value of the difference (A) between pK2(H20) and p 2 (mixed solvent) for a given composition of the mixed solvent (Table I). The same situation is indicated for DMSO mixtures (Table II) by the small variations in A for any given solvent composition. In this case, the number of accessible p 2 values was too small to allow a meaningful determination of reaction constants p. The structural dependence for various water-ethanol mixtures is thus represented by a set of parallel lines. The shifts between these lines are given by the differences between the pK2H values (p 2 of Reaction 4 for the unsubstituted benzaldehyde) in the different solvent mixtures. 

Effects of structure on reactivity have been studied several times. The sulphides are more stable than the thiols [248,250], In both series of thiols and of sulphides, the reactivity increases with the inductive effect of the alkyl group [248,251,252], in accordance with other elimination reactions. A linear relation between the logarithm of the rate coefficient and the enthalpy change on carbonium ion formation from the corresponding alkanes has been observed [248]. As Fig. 9 shows, linear correlation of the same rate data by means of the Taft equation is also possible. 

Temperature control is important in conductivity measurements, since the conductivity of milk increases by about 0.0001 ohm 1cm 1 per degree Celsius rise in temperature (Gerber 1927 Muller 1931 Pinkerton and Peters 1958). Increased dissociation of the electrolytes and decreasing viscosity of the medium with increasing temperature are undoubtedly responsible for this effect. An investigation (Sudheendra-nath and Rao 1970) of the viscosity and electrical conductivity of skim milk from cows and buffaloes failed to reveal a simple relationship. The authors attributed the lack of linear correlations to variations in casein structure and its hydration. 

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