V
V
S
Prediction of thermodynamics of solutions of 13 homologous series of solutes in apolane via the Solubility-Parameter-
Based Method
M. Zare Baniasadi a, M. Mousavi a, A. Nasehzadeh b*
a Department of Chemistry, Shahid Bahonar University, Kerman 76175, Iran
b School of Chemical Engineering and Analytical Science, the University of Manchester, Manchester, UK, M60 1 QD
"maryam Zare" <[email protected]>
Introduction
While many attempts have been made in the measurement or prediction of L87 [1, 2, 3
, 4, 5, 6,7 and 8], no attempt has been made in measuring or predicting comprehensive thermodynamic properties of solution of different solutes in apolane. The processes gas‹
liquid (solution) and liquid‹liquid (solution) can be related through the standard Gibbs free energy of vaporization of the pure liquid solute to the ideal gas at 1 atm [9]:
Since the free energy is a state function, then for any solution process the following equation can be deduced:
∆G O (gas → liquid ) + ∆G O = ∆G O (liquid → Liquid )
S V S
Similar equations may be set up in terms of enthalpy, entropy etc.
There are two main methods of obtaining OGso values. 1) Henry's law constants
∆G o (gas → liquid ) = RT ln K X .
S H
may be used for solution of gaseous solutes in a solvent (apolane).
If the solute vapor pressure (or fugacity) is known,
∆G O (liquid → liquid ) can be deduced.
∆G O = −RT ln p and then
2) The solubility of sparingly soluble solutes may be measured and then based on the mole fraction scale, ∆G O (liquid → liquid ) = −RT ln
X
, and combination with OGvo
will now yield corresponding values of OGso(g‹l).
Corresponding OHso values are again obtained by two methods. First, variation of
i
combination
with OHvo will give OHso(l‹l). Second, calorimetric determination of OHso(l‹l) may b e carried out and values of OHso(g‹l) obtained by again using OHvo values.The preci sion of the OGs0(gas‹liq) prediction of the criterion was tested on an independent experimental data set, obtaining a correlation coefficient of 0.99. In our two previous works [8,11] we have extended the solubility-parameter-based-model to predict logL16 (gas–hexadecane partition coefficient) for 550 solutes and thermodynamics properties of solutions of 13 homologous series of solutes in n-hexadecane .
This work is a continuation of our previous work [8,11] and we predict thermodynamic properties[Free energy(OGs0), Excess free energy(GE), Enthalpy(OHi0), Exchange enthalpy(HE), Entropy(OSi0)] of 13 homologous series of solutes in Apolane. The values of parameters which were obtained by a best fit non-linear regression analysis are calculated. These constant characteristics values of different sets of homologous were applied to predict the values of OGs0(gas‹liq) of desired compound. The consistency of our results with the literatures is of interest, and there is a good agreement between our predicted results and those obtained by the others, experimentally.
Keywords: Apolane; Solubility parameter; Hildebrand–Scatchard; Activity coefficient;
Free energy; Excess free energy; Exchange enthalpy; Combinatorial entropy
Theory and Method
This model is based on the concept of cohesive energy density or solubility parameter (6) after its introduction by Hildebrand and Scatchard [10].
(3)
where OHv, R and T are the molar volume, molar heat of vaporization, gas constant and the absolute temperature, respectively. It has been shown [8] that the solubility- parameter-based-model enables the calculation of properties as accurate as the available experimental data.
We start by assuming an infinitely diluted solution of solute (i) in apolane so that the Henry's law activity coefficient is unity. The free energy of solution of gaseous solute (i) is then calculated.
s
i
i P
S
s
∆G 0 (g → l) = −RT ln L87 =
RT106 V P
RT log γ ∞ − RT log
P
∗V
= RT log γ
∞ − RT log
g
Vs
+ RT i
i
In the above equations xi, (cm3 mol−1), pi* (Pa), pi (pa), Ci (mol l−1), R(=8.314 J mol−1 K
−1) and T (K) are the solubility of solute (i) in terms of mole fraction, molar volume (cm3 mol−1) of the solvent (apolane), vapor pressure of pure solute (i) at temperature T, vapor pressure of the solute (i) above the solution, the concentration or the solubility of solute (i) in solution, gas constant and temperature, respectively.
Results
The predicted values of free energy of solution of different compounds in Apolane , ∆G O (l → l) , are presented in the following figure.
Figure 1. Correlation between experimental and calculated values of bG o (liq‹liq) at 298.15 K.
This Fig. Illustrates that the predicted values are in good agreement with the observed values.
References
1. M.H. Abraham, P.L. Grellier and R.A. McGill. J. Chem. Soc. Perkin Trans. II
0
10000 20000 30000 -OG(exp)
40000 40000
30000 20000 10000 0
y = 1.0166x - 338.79 R2 = 0.9902 -O G (c a l d )
∗
s i
0
5. D. Weckwerth, P.W. carr, M.F. Vita and A. Nasehzadeh. Anal. Chem. 70 (1998), p. 3712.
6. F. Mutelet and M. Rogalski. J. Chromatogr. A923 (2001), p. 153.
7. J.D. Weckwerth, M.F. Vitha and P.W. Carr. Fluid Phase Equilib.
8. A. Nasehzadeh, E. Jamalizadeh and G.A. Mansoori. J. Mol. Struct. (Theochem) 623 (2003), p. 135.
9. M.H. Abraham. J. Chem. Soc. Faraday Trans.1 80 (1984), p. 153.
10. J.H. Hildebrand and R.L. Scott, The Solubility of Nonelectrolytes. Reinhold, New York (1950), p. 119.
11. A. Nasehzadeh, E. Jamalizadeh and G.A. Mansoori. J. Mol. Struct. (Theochem) 629 (2003), p. 117.
