Alkanes linear correlations

For n-alkanes, n-alcohols, 1-chloroalkanes, n-ethers, and chloroethenes, the carbon chain length influences the reactivity, and the clear linear correlations indicate that the attack mechanism of these pollutants by OH or Cl radicals occurs via the same pathway. However, such correlations do not hold true for aromatics, ketones, and aldehydes, for reasons discussed in our previous paper [3]. We also estimated missing values of kci by analogy for ethylbenzene, we take kci = 1.5e-10 cm molecule S, greater than that for m-xylene, but smaller than the 2.0e-10 cm molecule- s-i value for very reactive compoxmds. Also we estimate a similar value for butyraldehyde kci = le-10 cm molecule- s-, only 10% larger than kci of acetaldehyde to remain consistent with the equivalent koH value. 

The PIT dependence profiles generated for the nonionic surfactants in contact with alkanes are given in Figure 6. Their linear correlations allow suitable coefficients to be extracted from these data which may be used in later, derivable interrelationships. It was observed that variations in the water to oil ratio (W0R) affected the recorded PIT (Figure 7). The... 

Thermal cleavage of C—C bonds has been studied in cyclopropanes and cyclophanes, and particularly extensively in highly substituted alkanes. Riichardt and his school discovered a linear correlation between the experimental activation enthalpy for the homolysis of the weakest bond in overcrowded ethanes and the strain in the ground states of these molecules in accordance to MM2 calculations (284). 

This result is similar to that obtained by Widing and Levitt for the normal alkanes and to that observed for alkyl-substituted ethylenes [171] in the latter case, linear correlations were obtained between the IPs and the sum of charges of the unsaturated carbon atoms, whereby any increase of their electron density due to substituent effects leads to a lowering of the molecular ionization potential. 

The linear correlation of enthalpies of formation with the number of carbon atoms is a useful and well-known feature of homologous series of functionalized organic compounds. The slope of the regression line for the gaseous n-alkanes (CH3—(CH2)j —H), —20.6 kJmol-, and the similar values of the slopes for other CH3—(CHi) —Z series is often called the universal methylene increment . In the liquid phase, the increment for the n-alkanes is —25.6 0.1 klmoD. The most accurate determination of the increment... 

The exchange of a considerable number of linear, branched-chain, and cyclic alkanes have been studied (5i). The exchange rate increases with increase in the carbon chain length forn-alkanes (methane to hexane). It is found that there is a linear correlation between the logarithm of the exchange rate and the ionization potential of the alkane (Fig. 5 n-alkanes are plotted as circles). This correlation extends to aromatic compounds (Fig. 5 aromatic compounds are plotted as squares) and is evidence that alkanes and aromatic compounds react by a common mechanism. Indeed, the least reactive aromatic, benzene, is only about... 

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. 

Correlation of Estrada Estrada [22] derived the following simple, linear correlation between (cm3 mol-1) and the e index for alkanes (C5-C9) (eq. 2.3.6) ... 

Gas viscosity generally decreases with increased molecular size. This trend is reversed for liquids, for which the viscosity increases with increasing Nc within homologous series [2]. The latter observation is confirmed for alkanes, alkanethiols, and n-alkyl /3-ethoxypropionates in Tables 6.2.1a-c. Linear correlations between viscosity and Nc have been evaluated, for example, for n-alkyl n-alkoxypropionates [3] and n-alkyl carbonates of methyl and butyl lactates [4,5]. Similarly, correlations... 

Alkenes (R2 < 0.69), amines (R2 < 0.64), carboxylic acids (R2 < 0.001), and sulfonic acids (R2 < 0.20) show a poor correlation with dipole moment. With dipole moment as descriptor, benzene and halide classes have a predictable trend for linear correlations. The correlation coefficients of multicarbon alkanes or combinations of one-carbon and multicarbon halogenated alkanes are smaller than 0.67. They all have the same trend of correlations in that the rate constants decrease as the dipole moment increases. 

The sum of the above energy components and the constant 4RT (0.00382 hartree) must linearly correlate with the number of carbon atoms in the compound for n-alkanes (nc > 4) and for n-alkanols (nc > 3) and again, the slopes must be identical ... 

A further quantitative measure of the solvent solvophobic effecfi has been introdueed by Abraham et al. [282]. It has been shown that the standard molar Gibbs energies of transfer of nonpolar, hydrophobic solutes X (X = argon, alkanes, and alkane-like compounds) from water (W) to other solvents (S) can be linearly correlated through a set of equations such as Eq. (7-12b),... 

Figure 5.14 shows high-pressure isobars for the self-diffusion data of the n-alkanes in a plot of log D against log where is the molecular weight. These are the first data obtained with the titanium autoclave described in Section 1.4.2. Such results are commonly described by the Rouse model or by the reptation model, which both predict a linear correlation in this type of plot at constant pressure and temperature this linear correlation is clearly established in Fig. 5.14. Judging from the chain length of the polymethylenes the Rouse model should apply. This model predicts, that D should be proportional to M while the experiments give a D correlation, which is...

Alkane elimination from mer-RhH(R)Cl(PMe3)3 involves preliminary dissociation of PMes ligand [57]. Thus 1/fcobsd values linearly correlate with the concentration of free PMes added to the system. This observation is consistent with the mechanism involving a five-coordinate intermediate (Scheme 9.25). The reaction... 

Plots of X against 75/(Ff) for solute families of n-alkanes, monosubstituted alkanes, disubstituted alkanes, alk-l-enes, and monosubstituted benzenes in solvents n-C24Hso, n-CsoHea, and n-Cs H74 gave straight lines which in these cases gave an average linear correlation coefficient of 0.984. 

A simple criterion, which has the same nature as Ath of the catalyst, was used to represent the electron donor power during reaction the absolute value of the potential ionization difference. A/ = /r — /p, weighed by the ratio p/ r of carbon in product and reactant molecules respectively. The linear correlations obtained between A/ and Ath show that their slope is related to the electron donor power of the reactant, positive when C-C (alkanes, alkyl-aromatics) or C-H (alcohols) bonds are to be transformed, and negative when C=C bonds are concerned. The intercept depends on the extent of oxidation, and its absolute value increases from mild to total oxidation, respectively. A main difficulty is the actual state of cations at the steady state, but each time accurate experiments allow determining the mean valence state, the calculated Ath fits well the correlations. These lines may be used as a predictive trend, and allow, for example, to precise that more basic catalysts are needed for alkane ODH than for its mild oxidation to oxygenated compound. As a variety of solids have been catalytically experienced in literature, it would be worthwhile to consider far more examples than what is proposed here to refine the relationships observed. Finally, theoretical considerations are proposed to tentatively account for these linear relationships. Optical basicity would be closely related to the free enthalpy, and, as an intensive thermodynamic parameter, it is normal that it could be related to several characteristic properties, including now catalytic properties. 

In another study, McCabe and Jackson considered TPTl as applied to square well chains in order to model the n-alkane series [255]. These authors proposed a linear correlation for the square well strength, e and range parameters, X. In the limit of infinitely long chains, their correlation yields e°°/kB = 266K and X°° = 1.64. Fortunately, for the square well chain Eq. (115) provides analytical results for the asymptotic critical temperature [271]. For the above range parameter, one finds = 5.03, so that the estimated critical temperature for polyethylene is found to be about 1339K. 

In summary, there are three basic approaches to use contact angle data to determine the surface tensions of solid surfaces. These approaches are the Zisman method, the surface tension component methods, and the equation of state. Within these three approaches, there are many variants. It is reasonable to wonder the merit, accuracy, and limitation of some of the methods. The Zisman method is an empirical approach based on the correlation between the cosines of the contact angles on a solid surface versus the surface tensions of the test liquids. With alkanes, linear plots are usually obtained, and the critical solid surface tension (yc) is determined by extrapolating... 

Matthews-Akgerman The free-volume approach of Hildebrand was shown to be valid for binary, dilute liquid paraffin mixtures (as well as self-diffusion), consisting of solutes from Cg to Cig and solvents of Cg and C o- The term they referred to as the diffusion volume was simply correlated with the critical volume, as = 0.308 V. We can infer from Table 5-15 that this is approximately related to the volume at the melting point as = 0.945 V, . Their correlation was vahd for diffusion of linear alkanes at temperatures up to 300°C and pressures up to 3.45 MPa. Matthews et al. and Erkey and Akger-man completea similar studies of diffusion of alkanes, restricted to /1-hexadecane and /i-octane, respectively, as the solvents. 

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