Russian Journal of Applied Chemistry, 2009, Vol. 82, No. 11, pp. 1924−1927.
Pleiades Publishing, Ltd., 2009.
Original Russian Text
A.N. Marinichev, 2009, published in Zhurnal Prikladnoi Khimii, 2009, Vol. 82, No. 11, pp. 1775−1778.
OF SYSTEMS AND PROCESSES
Calculation of the Limiting Activity Coefﬁ cients of Components
in a Solution from Isothermal Data on the Equilibrium
Compositions of Liquid and Vapor Phases
A. N. Marinichev
St. Peterburg State University, St. Petersburg, Russia
Received April 15, 2009
Abstract—The method of calculating the limiting activity coefficients of components was developed and illustrated
by a number of examples. Isothermal binary data on the compositions of the solution and vapor coexisting phases
were fitted to the Porter, Margules, Van Laar, Wilson, Redlich-Kister, and NRTL interpolation equations. In this
method, nonideality of a vapor phase is directly taken into account and the composition of the azeotrope in the
system, if exists, may be calculated.
The limiting activity coefﬁ cients (LACs) of volatile
components in a solution are the important thermodynamic
characteristics describing the deviation of a dissolved
substance from the Raoult’s law. They are directly
related to the gas chromatographic retention values .
In calculation of LACs, nonideality of a gas phase is
taken into account by introducing virial coefﬁ cients. At
the same time, availability of detailed isothermal data on
the equilibrium compositions of liquid and vapor phases
makes LAC determination considerably simpler.
Processing of data on the liquid-vapor equilibrium
by different interpolation equations characterizing
the concentration dependence of activity coefﬁ cients
is widely used in science and industry. Commonly,
the properties of a nonideal solution are described by
a dimensionless function g
, which is the ratio of the
excess Gibbs energy to the product of the universal gas
constant and temperature (K) , and are characterized
by the relation
= Σ x
are the mole fraction and activity coefﬁ cient
of the ith component in a solution and the summation is
done over the all components of the mixture.
It is easy to show that, if temperature T, pressure P,
and all mole fractions are constant and only the mole
fractions of the ith and the ﬁ rst components vary, then
the following relation holds
The equilibrium distribution of the ith component
between the solution and vapor is described as
is the mole fraction of ith component in vapor
, vapor pressure of a pure ith component at
temperature T, and Φ
characterizes the vapor phase
deviation from ideal behavior. Then, the ﬁ nal formula
for calculating the vapor phase composition can be
We will consider the binary systems under the
isothermal conditions. Then, the given relations transform