1070-4272/04/7704-0670 C 2004 MAIK [Nauka/Interperiodica]
Russian Journal of Applied Chemistry, Vol. 77, No. 4, 2004, pp. 670!672. Translated from Zhurnal Prikladnoi Khimii, Vol. 77, No. 4, 2004,
Original Russian Text Copyright + 2004 by G. Mikhailov, V. Mikhailov, Reva, Ryabchuk.
Predicting the Normal Temperature Depression in Boiling
of Complex Aqueous Solutions of Nonvolatile Substances
G. M. Mikhailov, V. G. Mikhailov, L. S. Reva, and G. V. Ryabchuk
Volgograd State Technical University, Volgograd, Russia
Received June 26, 2003; in final form, December 2003
Abstract-An equation for predicting the normal temperature depression in boiling of complex aqueous
solutions of nonvolatile substances is considered. The constants of the equation are tabulated. The equation
is compared with experimental data for a binary solution of caustic soda and sodium chloride.
In the theory and practice of calculations of evap-
oration installations, the difference in the boiling
temperatures of a solution of nonvolatile substances
and a pure solvent is commonly referred to as the tem-
perature depression in boiling of solutions. This is
because it is a measure of the extent to which the driv-
ing force of the heat transfer (i.e., the difference be-
tween the temperature of the heating vapor and the
boiling point) in boiling of a solution is lower than
that in boiling of a pure solvent, all other conditions
being the same. The temperature depression in boil-
ing of solutions at an arbitrary pressure is expressed
in terms of the normal temperature depression, i.e.,
the temperature depression at normal pressure [1, 2].
To predict the normal temperature depression for
simple aqueous solutions of separate nonvolatile sub-
stances, the following equation has been suggested 
= ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ ,
Az + Bz
ÄÄÄÄÄÄÄÄÄÄÄ 3 1
where z = x/(1 3 x) is the relative mass concentra-
tion of the solute: x, its mass concentration (kg kg
and A, B, and C, tabulated coefficients dependent on
the nature of the solute.
However, the importance of Eq. (1) is diminished
by the fact that, commonly, complex solutions, i.e.,
solutions of two or more nonvolatile substances, are
used for evaporation in the engineering practice.
We suggest that the normal temperature depression
of complex solutions can be predicted using the equa-
ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ 3 1
= ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ ,
Here i and j are the ordinal numbers of solutes,
n, the number of different types of solutes; and z
the ratio of the concentration of a given solute to that
of water in the complex solution.
In a particular case of simple solutions, i.e., at
n = 1, Eq. (2) transforms into Eq. (1), whose adequacy
as applied to simple solutions was convincingly de-
monstrated in .
It is possible to verify the applicability of Eq. (2)
for the example of a solution of two substances, name-
ly, caustic soda and sodium chloride.
According to the data of , A
= 1.5828, and C
= 31.0365 at x > 0.5,
= 1.6272, B
= 0.009015 at x > 0.5, i.e., z
= 0.47309, B
= 1.02646, and C
30.7679 at z
Table 1 lists the values of the normal temperature
depressions in boiling of a binary solution of caustic
soda and sodium chloride, calculated using Eq. (2), and
compares them with the experimental values from .
It can be seen that the maximum deviation of
the calculated values from those obtained exper-