Homologous-series relations

Spreading velocities v are on the order of 15-30 cm/sec on water [39], and v for a homologous series tends to vary linearly with the equilibrium film pressure, it", although in the case of alcohols a minimum seemed to be required for v to be appreciable. Also, as illustrated in Fig. IV-3, substrate water is entrained to some depth (0.5 mm in the case of oleic acid), a compensating counterflow being present at greater depths [40]. Related to this is the observation that v tends to vary inversely with substrate viscosity [41-43]. An analysis of the stress-strain situation led to the equation... 

Homologous series (Section 2 9) Group of structurally related substances in which successive members differ by a CH2 group... 

The ability of C to catenate (i.e. to form bonds to itself in compounds) is nowhere better illustrated than in the compounds it forms with H. Hydrocarbons occur in great variety in petroleum deposits and elsewhere, and form various homologous series in which the C atoms are linked into chains, branched chains and rings. The study of these compounds and their derivatives forms the subject of organic chemistry and is fully discussed in the many textbooks and treatises on that subject. The matter is further considered on p. 374 in relation to the much smaller ability of other Group 14 elements to form such catenated compounds. Methane, CH4, is the archetype of tetrahedral coordination in molecular compounds some of its properties are listed in Table 8.4 where they are compared with those of the... 

Various relations have been proposed linking the various power law exponents for a homologous series under specified conditions [ 10,62] such as ... 

The kinetics of reactions of bifunctional compounds are especially significant in relation to polymer reactions. The esterification rate constants shown in the third column (B) of Table V for the homologous series of dibasic acids do not differ greatly from those for the monobasic acids. These differences vanish as the length of chain separating the carboxyl groups increases. 

Higuchi applied this method to 2-naphthol as molecule A and used the resulting ratio for several compounds and complexes to treat mass transport data for com-plexation using a particular model. In general, ad hoc methods may be useful, particularly when dealing with a homologous series or a series of related compounds. 

The above relationship can be related to the change of partition free energies of members of homologous series due to the addition of a given structural increment or to any physical-chemical property that affects the retention. 

It is well known that such quantities as the standard free energy, enthalpy and entropy display a remarkable tendency to be additive functions of independent contributions of part-structures of the molecule. This property, on which the mathematical simplicity of many extrathermodynamic relationships is largely based, is well illustrated, for example, by the enthalpies of formation at 298°K of several homologous series of gaseous hydrocarbons Y(CH2)mH, which are expressed by the relation (28) (Stull et al., 1969). In... 

A universal system for qualitative identification was devised by Kovats some years ago. Based on the linear relation between log t R and the number of carbon atoms for a homologous series, Kovats selected //-alkanes as standards for the following reasons ... 

Since members of a homologous series have incremental boiling point differences and if the amount of any homolog in the moving gas phase is related to vapor pressure at the temperature of the experiment, plots of log k vs. carbon number should also be a straight line. (The enthalpy of vaporization increases monotonically with carbon number.) This in fact is observed in gas-liquid equilibrium separation systems. It is the basis of retention index systems pioneered by Kovats for qualitative identification. 

There is a linear relationship between the free energies of activation for one homologous series of reactions and those of another. The Hemmett relationship are equivalent to the existence of linear relationship between the free energies for different series. The rate constant of a reaction is related with the free energy of activation by the equation... 

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