Additivity Rule of the Partial Molal Volume. 1. Its Validity for a Series of Normal Alkane Liquids

Abstract

Y. Yoshimura, J. Osugi, and M. Nakahara: Additivity Rule of the Partial Molal Volume etc. 25 In Fig. 5 the critical p ( T ) curves of the N,-binaries are compiled; the data are taken from the present work or from the literature. Full lines and circles are experimental results, the dashed lines are curves calculated from the Redlich-Kwong equation of state by Deiters [26, 271. Calculations The critical p ( T ) curves and some characteristic p ( x ) isotherms were calculated for both systems from a one-fluid approach using the Redlich-Kwong equation of state (Deiters and Schneider [26]; Deiters [27]; here details concerning the combining rules used and the definition of the parameters a,, , az2, , 19 and ( are also given). The adjustable parameters 19 and [ as well as the critical curve or isothermal phase equilibria were solved numerically by a computer program developed by Deiters [28]. Calculations were carried out on reproducing the critical curves interpolated from experiments as well as possible. The parameters 19 and [ were calculated using one experimental point on the critical curve. The Redlich-Kwong parameters were obtained from critical and p . V,, T data of the pure components. Some of the results are shown in Figs. 6 -8. The values for the parameters used in the calculations are given in the legends. The isothermal p(x) sections of the system N, + pentane have been calculated with the same values of the parameters as those used for correlating the critical curve. In the case of N, + pentane the fit of the parameters from experimental results was realized using a p , Vm, T data point of pure pentane additionally. This procedure has the consequence that the coordinates of the critical point of' pentane d o not equal those determined experimentally. Some difficulties for the calculation of isothermal p ( x ) sections of the system N, + ethane result from the high reduced densities of the mixtures which are outside the range of the validity of the equation of state used; such isothermal p ( x ) plots are not shown. For details see [23]. Equations of State / High Pressure / Liquids / Solutions / ThermodynamicsA critical test of the additivity rule of the partial molal or molal volume (t) at constant temperature and pressure, expressed by = an + / 3 where n is the carbon number, has been made for a wide range of n-alkanes at a variety of temperatures and pressures. In the pure liquid state the additivity rule is obeyed approximately well by the higher n-alkanes but broken by the lower ones having the boiling point close to the temperature of interest, and in solution at infinite dilution it is obeyed much more accurately by both high and low n-alkanes. These facts indicate that the

Additivity of the partial molar volumes of organic compounds

“…The same expression has been derived by Yoshirnura i t al. (8,9) on the basis of the virial theorem for classical fluids. However, the experimental verification of this term is difficult.…”

“…[7]) to 16.3 for CA, and from 38.6 (eq. [9]) to 38.7 for CE. It is noted that the covolume of 11.61 cm3/mol proposed by Edward et al (3)(4)(5) has no theoretical background in spite of that the arbitrariness of the value of covolume appeared in the literature was discussed by them.…”

“…The intercepts for CA and CE are (1.5 * 2.3) cm3/mol and (3.3 k 0.3) cm3/mol, respectively (eqs. [7] and [9]). These values may be compared with the reported values of K~R T / c~~ mol-' = 2.64 (14), 2.62 (15), and 2.67 (16) for CC14 at 25OC and 1 atm.…”

“…1 is that the strictly linear relationship between V 0 and n holds for each series of compounds and that, if we eliminate the data for smallmembered ring compounds (vide infra), the slopes of the plots for NA and CA, and PEGDE and CE are virtually the same (eqs. [61- [9]). The above findings means that all the repeating units, irrespective of their positions, contribute equally to VO.…”

“…Their ideas are of great significance for high pressure kineticists since they have not been taken into account for the activation volume (AV*) and reaction volume (AV). They further developed the additivity rule of the partial molar volume (9,10). Based on the virial theorem, they have derived the following equation:…”