News
THERMODYNAMIC MODEL OF BINARY HYDROPHILIC NONELECTROLYTE SOLUTIONS

In binary nonelectrolyte equeous solutions the nonelectrolyte can be called as a hydrophilic if the water-nonelectrolyte interaction is dominated and gives rise to formation of hydrates. In this work the term "hydrophilic system" has been extended over any systems where solute-solvent interaction is general in spite of if solvent is water or not. Such systems show the negative deviation from Raoult's law that is usual for number of byological active substances such as lineral and cyclic sugars, glycerol, алколамины et. cet. These systems differ in the fact that assential deviation from ideal beheviour takes place so activity coefficients and excess thermodynamic functions are used for calculation of their thermodynamic properties. For description of such solutions behaviour there use some equations (empirical and halfempirical) for example Redlich-Kister's, Van Laar's and models such as Robinson's, изодейсмическая but physical mean of equation parameters isn't definite.

Most of the models describe thermodynamic properties of "hydrophilic" solutions within narrow limits of concentration range (in general within range of diluted solution) and their parameters are at variance with each other if they are estimated by different models. All these can be assigned to inderect disadvantages of analogeous models.

Distribution of components in extraction equilibrium often describes without respect to activity coefficients because there is no adequate model for calculating them. It is shown in [ ] that the results of this investigation can be used to adjust the method for describtion of components destribution in extraction equilibrium.

The foundation of the suggested model in this work is well-known hypothesis of ideal solution that was proposed by Долезалик and then was advanced by Prigogine and Defay. According to this hypothesis interactions in system lead to formation of corresponding species and with the solute and the solvent molecules they are compounded the ideal solution. But in this case the problem is to determine stoicheometric composition of each species and their concentration in solution.

If in the solution the solute molecules interact with molecules of the solvent in response to the process:

A + iS -> ASi (1)

where A is a solute molecule, S is a solvent molecule and i is the stoicheometric solvation number, then existance in the system of stoicheometric solvates with the various solvation numbers i (i=0,1,2, ... N) in equilibrium at the same time can be suggested. Concentration of each solvate with the solvation number i is equal ni.

To refuse of consideration of each species the average solvation number can be introduced in according to the equation:

h=sum ini/sum ni(2)

It is clear that the value of this number depends on the system composition. Based on physical analogy between solvation process and adsorbtion of gase molecules on a solid body at constant temperature, that was proposed by Ленгмюр, solvent mole fraction dependence of average solvation number h can be obtained in the form:

h = h1Xs (3)

where h1 is the solvation number when mole fraction of the solvent XS is equal to one.

Thus the solution can be considered as a composition of solvent molecules, solute molecules and particles (solvates) with the solvation number h (h in general isn't whole-number). Such a consideration of the solvation process in the solute has been called as a nonstoicheometric solvation, the number h1 has been called as a nonstoicheometric solvation number and the suggested approache has been called as the nonstoicheometric model of solutions.

In terms of nonstoicheometric nature of solute-solvent interactions in the solution, new equations for activity of components can be dirived by solving of Gibbs-Duhem equation. In the following part of this report all reasoning will be done for two "types" of the solutions. The solute in solutions of the first type, as they will be called below, has the limited solubility in the solvent and the solute in solutions of the second type mixes with the solvent in all proportions.

Thus for solutions of the first type equations are of the form:

(4)

for the solvent activity coefficient and the solute activity coefficient respectively. For solutions of the second type these equations take the form:
(5)

Quantity of the h1 can be estimated easely from the first equation of the group (4). As a basis for this calculation it is proposed to take the results of isopiestic experiment that is based on vapour pressure mesurements over the solution. In case of solution with the limited solubility of the solute, results of isopiestic experiment can be considered as a rather reliable experimental data, because there is only one volatile component (solvent) in the solution. If both components of the solution are volatile, this takes place in case of the solution of the second type, it isn't reasonable to count on calculations of activity of the particular component from data of the isopiestic experiment because the experimental results are the total vapour pressure of two volatile components. Therefore value of h1 can be estimated from the equation:

p=p0sX1+h1s exp(h1X)+p0 X exp(-h1 Xs)(6)

where pS0 and p0 are the vapour pressure over the pure solvent and solute respectively; p is the total vapour pressure over the solution. On the contrary to the first equation of the group (4) the equation (6) isn't lineral with respect to the parameter h1 and it makes a bit more difficult the estimation of the value h1, but this problem can be succesfully overcome with the help of upto date mathematical methods.

Using the definition of molar excess Gibbs energy it is rather easy to obtain equations:

GEm=RTh1(XslnXs+X) (7)

GEm=RTh1XslnXs (8)

where (7) and (8) are for the first and for the second type of solutions respectively, h1 is the value of the solvation number for the particular system that was found like given above.

Molar excess Gibbs energy of the solution cann't be mesured directly, it can only be calculated from the results of some experiment. On the contrary to molar excess entalpy HEm can be mesured by калометрический experiment. Hence in the context of the suggested model it is important to obtain the form of the HEm as a function of system composition.

According to well-known equation of Gibbs-Helmgoltz it is necessary to find, in the framework of this model, the view for the particle derivative of the solvation number with respect to the temperature dh/dT . There are some ways of solving this problem that depend on what distribution function of solvates over the stoicheometric solvation numbers will be taken. One of them is to take Пуасоновское distribution for which мат. ожидание is equal to дисперсия. In this case the particle derivative takes the form:

dh1/dT = DH0ST h1 / RT^2 (9)

where DH0ST is the change in entalpy when one molecule of the solvent has attached to the solvate (it can be called a solvation step) with reference to one mole of the solution in standart state. The addition assumption for deriving (9) is the independence of DH0STon any solvation step.

Based on equation (9) forms for HEm have been derived as functions of the composition of the solution:

HEm = - DH0ST h1(XslnXs+X) (10)

HEm = - DH0ST h1 XslnXs (11)

where (10) and (11) are for the first and for the second type of solutions respectively.

Using the definition of molar excess Gibbs energy and equations (7), (8), (10), (11) the view for molar entropy can be found in form:

SEm = -h1 R(Xs lnXs + X) (DH0ST/RT +1) (12)

SEm = -h1 R(Xs lnXs) (DH0ST/RT +1) (13)

In the context of the suggested model equations for heat capacibility CE m , temperature dependences of excess system functions have been obtained as well.

Nonstoicheometric model for thermodynamic properties of solutions of hydrophilic nonelectrolytes makes posible to calculate their volumetric properties. In order to obtain the dependence of molar excess volume as a function of concentration it is necessary to determine the view of the function dh1/dp. It can be done by anology with the method given above for the function dh/dT and then:

dh1/dp = -DV0ST h1/ RT  (14)

where DV0ST is the change in the volume when one molecule of the solvent has attached to the solvate with reference to one mole of the solution in standart state. Therewith excess volumes for solutions of two types can be obtain as:
VEm=- DV0ST h1(Xs lnXs + X) (15)

VEm=- DV0ST h1(Xs lnXs) (16)

In addition it was considered that changes in DV0ST on any solvation step are equal.

Then with respect to the definition for density the next equation can be written:

ro = MX+MsXs / V0X + V0sXs + VEm (17)

where M and MS are molar mass of the solute and the solvent respectively; VS0 is molar volume of the pure solvent, V0 is either partial molar volume of the solute in case of the first type of solutions or molar volume for the other case.

Values of solvation numbers were estimated by treating experimental data of different athors [ ] on water activities of such substances as lineral and nenlineral sugars, glycerol. Equations (4) describe these data well in the whole cincentration range. Some conclusions can be made from the results of this modeling. 1) Parameters h1 are reasonable and are not big. In some cases values of h1 correlate with the numbers of e-OH groupes. For the sucrose solution in water at 25 0C the value of h1 agrees closely with the hydration number estimated by мет. мол. динамики. 2) Solvation numbers decrease with increasing temperature. The equation (9) has been used to calculate values h1 for different temperatures in some studied systems relating to the value h1 calculated for the standart temperature T=298.15 K. It has been made with the assumption of independence DH0ST from temperature. A comparison these results with the results of direct describtion of experimental data by equations (4) and (5) shows that values of solvation numbers for corresponding temperatures are equal. 3) It is rather likely that with the known value h1 for studied solution it can be distinguished if this solution is of the first or of the second type because for the second type of solutions values h1 are no more then one. 4) Values of the DH0ST and DV0ST are reasonable as well and correlate with the literature's ones. Besides physical mean of activity coefficients in equation (4) and (5) is clear. The distinctive property of thermodynamic studies of solutions of the second type is the dependence of describtion quality on what component will be choosen as a solvent.

It has been established that it is possible to describe thermodynamic properties of ternery solutions with the values of parameters h1 estimated from data on corresponding binary systems.