The parachor

Dv — density of the vapor in equilibrium with the liquid under the conditions of measurement. 

Mumford and Phillips33 were the first to evaluate the influence of chain branching on the molecular parachor of hydrocarbons. They calculated values for the atomic parachors, which formed the basis for the specific parachor vs. molecular weight diagram of Leendertse and Waterman34 (Fig. 56). In this diagram curves are drawn 

57 and 58. Diagrams representing specific refraction vs. and specific parachor vs. — based on A.P.I. data of w-alkanes and -alky -cyclohexanes at 20° and 7O°03.  

The specific refraction vs. —- and the specific parachor vs. -diagrams of Weber 

For non-branched saturated hydrocarbon mixtures the average number of rings per molecule can be read directly from one of these diagrams. 

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Values of Rj, probably close to the required accuracy, can be estimated from the parachor, P the parachor can be calculated from a group-contribution method given by Reid et al. The... 

The Parachor is a parameter used to determine the interfacial tension. It can be estimated by a simple method proposed by Quayle in 1953 ... 

Group contributions for estimating the parachor by Quayle s method (1953). 

The surface tension is calculated starting from the parachor and the densities of the phases in equilibrium by the Sugden method (1924) J... 

S. Sugden, The Parachor and Valeny, Roudedge Sons, London, 1930. 

TABLE 2-402 Atomic Group Contributions for Calculation of the Parachor [P]... 

Values for hydrocarbons other than alkynes and alkadienes can be predicted by the method of Suzuki et al. The best model includes the descriptors T, P, the parachor, the molecular surface area (which can be approximated by the van der Waals area), and the zero-order connectivity index. Excluding alkynes and alkadienes, a studv for 58 alkanes, aromatics, and cycloalkanes showed an average deviation from experimental values of about 30 K. 

Tyn-Calus This correlation requires data in the form of molar volumes and parachors = ViCp (a property which, over moderate temperature ranges, is nearly constant), measured at the same temperature (not necessarily the temperature of interest). The parachors for the components may also be evaluated at different temperatures from each other. Quale has compiled values of fj for many chemicals. Group contribution methods are available for estimation purposes (Reid et al.). The following suggestions were made by Reid et al. The correlation is constrained to cases in which fig < 30 cP. If the solute is water or if the solute is an organic acid and the solvent is not water or a short-chain alcohol, dimerization of the solute A should be assumed for purposes of estimating its volume and parachor. For example, the appropriate values for water as solute at 25°C are = 37.4 cmVmol and yn = 105.2 cm g Vs mol. Finally, if the solute is nonpolar, the solvent volume and parachor should be multiplied by 8 Ig. 

The physical properties associated with the parachor, vi2., the liquid surface tension and the density at various temperatures, for benzofuroxan and 5-methylbenzofuroxan are given by Hammick et al. The parachor values were reevaluated by Boyer et al ... 

Values of the parachor are given in the literature [240]. Then the example gives ... 

The vapour density can be neglected when it is small compared with the liquid density. The parachor can be calculated using the group contributions given in Table 8.7. The method is illustrated in Example 8.13. 

Briggs GG (1981) Theoretical and experimental relationships between soil adsorption, octanol-water partition coefficients, water solubilities, bioconcentration factors, and the parachor. J Agric Food Chem 29 1050-1059... 

Provided, therefore, the additive contributions for different structural components can be quantified, the partition coefficient can be readily computed, A long established and convenient means for such quantification is already available in the form of the parachor, which is equivalent to the molar volume of a substance when its surface tension is unity. Parachor is primarily an additive property and there are extensive tabulations of parachor equivalents for various structural elements, such as that by Quayle (30). Parachor (H) can be related to partition coefficient (P) using the relationship of McGowan (3I) -... 

Constitution XV for sucrose has up to the present satisfied all demands made upon it. Like its precursors, I and II (page 6), it was not incompatible with physical properties of sucrose such as the magnetic rotation, or the parachor, although the latter claim has been denied. Von Lippmann lists a great many early determinations of the physical properties of the sugar more recent measurements include the heat of combustion, the molecular weight in liquid ammonia, and various optical and electrical constants. ... 

Sugden J.G.S. cxxv. 1177, 1924 cxxvii. 1525, 1868, 1925) has compared the molecular volumes of substances under conditions such that they possess identical surface tensions and has shown that they are determined by the molecular constitutions of the substances. In obtaining the parachor P Sugden makes use of the approximate relationship between free surface energy and density noted by Macleod Trans. Farad. Soc. xix. 38, 1923) a = c(pi- p y... 

It has been shown 8) that VT, the molar volume calculated from Traube s rule 4), VM, the molar volume of Exner 3), and the parachor,5) P all give significant correlation with the equation... 

For pure liquids, an empirical estimation method for surface tension is that of McLeod and Sudgen, based on the parachor (P), which be calculated from the chemical groups of the molecule [13]. 

In this equation, (P) is the parachor and the p values are the liquid- and vapour- molar densities in mol/cm3. Then a is obtained in mJ/m2. For the case of mixtures in the presence of vapour phase, the surface tension of a mixture is calculated in terms of the liquid and vapour composition, as ... 

The results of calculations as illustrated in Example 11-21 should be within 10 percent of laboratory measured values. Better accuracy will be obtained if the heptanes plus fraction is divided into several fractions and the parachor for each fraction obtained from Figure 11-18 according to the molecular weight of the fraction. This is the manner in which the data of Figure 11-18 were obtained. The deviation of the heavier fractions from the line on Figure 11-18 is attributed to the collection of asphaltenes in the heaviest fraction of the liquid.15 The correlation line obviously does not give good values of parachors for this fraction. 

Fowler, R.H. A Tentative Statistical Theory of Macleod s Equation for Surface Tension and the Parachor, Proc., Royal Soc. of London, Series A (1937) 229-246. 

The parachor does not have a readily apparent physicochemical meaning it is useful as a parameter for estimating a range of other properties, especially those related to liquid-liquid interactions. 

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