1070-4272/02/7511-1770$27.00C2002 MAIK [Nauka/Interperiodica]
Russian Journal of Applied Chemistry, Vol. 75, No. 11, 2002, pp. 1770!1773. Translated from Zhurnal Prikladnoi Khimii, Vol. 75, No. 11,
2002, pp. 1806 !1809.
Original Russian Text Copyright + 2002 by Sladkov.
OF SYSTEMS AND PROCESSES
Calculating Density of Molecular Liquids
Using Agrawal!Thodos Equation
I. B. Sladkov
St. Petersburg State Polytechnic University, St. Petersburg, Russia
Received November 1, 2001
Abstract-The correlation between the parameters of the Agrawal!Thodos equation and the fundamental
constants of a substance are established. A modified equation is proposed, in which the minimum set of easily
measurable properties of the substance is used as input data.
The majority of molecular compounds under
normal conditions exist in the liquid state. The most
important characteristic of such compounds is liquid
density. Data on the density are necessary for theoreti-
cal calculations and for process development and con-
trol, including calculation of heat exchangers, distilla-
tion columns, and all the equipment for fluid control.
A number of correlations allowing prediction of
the density of molecular liquids on the saturation line
in the entire range of existence of the liquid phase
have been reported. These include the Mathias ,
Goldhammer , Spencer!Danner , Campbell!
Thodos , and Eselev!Krupskii equations . To
these correlations also belongs the Agrawal!Thodos
equation  derived from the following prerequisites.
Based on experimental data on the density of liquid
Ar, Ne, H
, CO, and CH
, Agrawal and
Thodos found that the temperature dependence of
density, if plotted in the coordinates ln(1 ! T
! 1), is the simplest (linear) dependence over
the entire region of existence of the liquid phase.
is the reduced density; T
reduced temperature; and H
, critical density
and temperature, respectively. As a result, the tem-
perature dependence of the liquid density is described
by the following equation:
H = H
[1 + =(1 ! T /T
Agrawal and Thodos found that, for the above sub-
stances, the temperature dependence of the liquid
density can be described with sufficient accuracy by
Eq. (1) with properly chosen individual constants =
and >. The errors averaged over the whole tempera-
ture range (T
) were from 0.4 (for Ne) to 1.3%
The Agrawal!Thodos equation is advantageous
over analogous equations, because it allows the tem-
perature dependence of the liquid density to be ob-
tained in a simple and compact form; it does not re-
quire data on the vapor density (unlike Mathias!
Goldhammer equations), critical pressure (unlike
Spencer!Danner equation), or saturated vapor pressure
(unlike Eselev!Krupskii equation); as compared to
the Campbell!Thodos equation, it contains consider-
ably smaller number of fitting parameters.
All the above shows that the Agrawal!Thodos
equation is, without doubt, promising and efficient for
predicting the density of molecular liquids. At the
same time, the authors’ proposal to use the experi-
mental temperature dependence of the liquid density
for determining = and > limits practical application of
Eq. (1) to a small number of thoroughly studied sub-
stances. This equation has practical value and can be
applied solely in the case when = and > can be deter-
mined from calculation rather than from experimental
data on the liquid density.
The goals of this work were (a) to establish a
correlation between the parameters = and > and the
fundamental constants of a substance and, as a result,
to derive equations for calculating the above param-
eters without data on liquid density, (b) to propose a
modification of the Agrawal!Thodos equation allow-
ing prediction of the liquid density from the minimum
amount of easily accessible data, and (c) to study
potentials of this modified equation on substances
belonging to different classes of chemical compounds.
Solving this problem would make the Agrawal!
Thodos equation more versatile and applicable to
poorly studied substances.
Let us consider the main relationships underlying