Parachor

Surface Tension The surface tension of a liquid is defined as the force per unit length exerted in the plane of the liquid s surface [1,2]. Some authors use the symbol cr, others use y to represent the surface tension. The surface tension is expressed in dyncm-1. For most organic liquids, a is between 25 and 40 dyncm-1 at ambient temperatures. The surface tension of water is 72 dyncm-1 at 25°C. For polyhydroxy compounds, the surface tension ranges up to 65 dyncm-1. 

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. 

Multiparametric correlations between x and physicochemical and molecular properties are known. Needham et al. [2] reported the following model for alkanes (C2-C9)  

Stanton and Jurs [3] developed a model for a more diverse set of compounds, including hydrocarbons, halogenated hydrocarbons, alkanols, ethers, ketones, and esters. The model has been evaluated with 31 compounds, using, among others, charge partial surface area (CPSA) descriptors  

In 1923, McLeod assumed n = 6/5 in Equation (339), and by combining with Equation (337) and eliminating (Tc - T), he found an expression to relate the surface tension to the density  

It should be noted that Eotvos, Ramsay-Shields and Sugden s parachor equations are empirical in nature and their theoretical foundations are rather obscure. There have been several attempts to associate these equations with strict thermodynamical terms, but none have been successful. 

However, for a gas bubble in a liquid environment where the two radii of curvature are also the same but negative for the liquid, the resultant AP is negative for the liquid the vapor pressure inside the gas bubble is lower than for the flat liquid surface and it is easier for the liquid molecules to evaporate in the bubble, causing vapor condensation within the gas bubble. 

conversely, if we consider a spherical liquid drop in air, having a radius of r, the vapor pressure of a drop, Pcv P that is Pv is higher than that of the same liquid with a flat surface, Pv (the superscript c indicates a curved surface). If d mol of liquid evaporates from the drop and condenses onto the bulk flat liquid under isothermal and reversible conditions, the free-energy change of this process can be written by differentiating Equation (155) as 

Since Pf, Pv, dG is negative and the process is spontaneous. This free-energy change can also be calculated from the surface free-energy change of the droplet, which results from the surface area decrease due to the loss of dn mol of the liquid having a molar mass of Mw. This evaporation process produces a volume decrease of -d (JVfw/pi.) in the liquid drop. As a result of this volume decrease, a spherical shell from the drop surface whose volume is = Ajzfdr is lost from the total drop volume. Then we can write 

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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... 

However, there are other molecular properties, such as molar volume, molar refi action [3], diamagnetic susceptibility [4], and parachor [5], that can be obtained to sufficient accuracy fi om contributions, p , of its N atoms (Eq. (5)). 

Parachor is the name (199) of a temperature-independent parameter to be used in calculating physical properties. Parachor is a function of Hquid density, vapor density, and surface tension, and can be estimated from stmctural information. Critical constants for about 100 organic substances have been correlated to a set of equations involving parachors and molar refraction (200). 

Diffiusion Coefficient. The method of Reference 237 has been recommended for many low pressure binary gases (238). Other methods use solvent and solute parachors to calculate diffusion coefficients of dissolved organic gases in Hquid solvents (239,240). Molar volume and viscosity are also required and may be estimated by the methods previously discussed. Caution should be exercised because errors are multiphcative by these methods. 

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

The temperature-independent parachor [P] may be calculated by the additive scheme proposed by Quale.The atomic group contributions for this method, with contributions for silicon, boron, and aluminum from Myers,are shown in Table 2-402. At low pressures, where Pi. pc, the vapor density term may be neglected. Errors using Eq. (2-168) are normally less than 5 to 10 percent. 

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 ... 

Liquid surface tension is calculated using the Sugden Parachor method [242]. Neglecting vapor density, surface tension for the liquid mixture is ... 

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

G = superficial mass vapor velocity based on the cross-sectional area of the column, Ib/hr-sq ft M = molecular weight, Ib/lb mole N = dimensionless number P = pressure, consistent units [P] = Sugden parachor sg = specific gravity T = temperature, °F U = superficial velocity, ft/hr... 

A small number of physical properties appears to provide more definite information these are molecular refraction, parachor, and (in a more limited way) ultraviolet absorption6. 

On the basis of these values one can conclude that, with increasing bond orders, the force constants rise, suggesting that the S—O bond of sulphoxides should have more semipolar character than that of sulphones. Furthermore, molecular diffraction measurements and Parachors for sulphoxides also suggest that the S—O bond in sulphoxides should have a semipolar single-bond representation while the S—O bond in sulphones is described by double bonds or better as the resonance hybride shown in Scheme 1. 

If reliable values of the liquid and vapour density are available, the surface tension can be estimated from the Sugden parachor which can be estimated by a group contribution method, Sugden (1924). 

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