INTRODUCTION CONCLUSION JNC 2014 - 18èmes Journées Nationales de Chimie, 21-23 Décembre 2014 Institut Supérieur de Technologies Médicales de Tunis. Laboratoire de Biophysique et Technologies Médicales. CORRELATION BETWEEN THE REDUCED REDLICH-KISTER FUNCTIONS AND THE LIMITING EXCESS PARTIAL MOLAR PROPERTIES OF N,N-DIMETHYLACETAMIDE + 2-ETHOXYETHANOL BINARY MIXTURES H. Salhia*, Z. Trabelsia, M. Hichrib, D. Dasc, N.O. Alzamild, N. Ouerfellia,d  a) Université de Tunis El Manar, Laboratoire Biophysique et de Technologies Médicales LR13ES04, Institut Supérieur des Technologies Médicales de Tunis, 9 Avenue Dr. Zouhaier Essafi 1006 Tunis, Tunisie b) Université de Tunis El Manar, Faculté des Sciences de Tunis, LR01SE10, Laboratoire de Thermodynamique Appliquée, Département de Chimie, 2092 Tunis, Tunisie c) Department of Chemistry, Dinhata College, North Bengal University, Dinhata-736135, Cooch-Behar, West Bengal, India; d) University of Dammam, Department of Chemistry, College of Science, P.O. Box 1982, Dammam 31441, Saudi Arabia *Corresponding Author: e-mail: hanenbayna@yahoo.fr INTRODUCTION Excess molar volumes, viscosity deviations and isentropic compressibility changes in N,N-dimethylacetamide + 2-Ethoxyethanol binary mixtures at (298.15, 308.15 and 318.15) K. were calculated from experimental density, viscosity and sound velocity data presented in previous work. Here these experimental values were used to test the applicability of the correlative reduced Redlich-Kister equation and the Herráez equation as well as their corresponding relative functions. These relative functions are important to reduced the effect of temperature and, consequently, to reveal the effects of different types of interactions. Limiting excess partial molar volume was deduced from different methods, activation parameters and partial molar Gibbs energy of activation of viscous flow against compositions were investigated. The results of these observations have been interpreted in terms of structural effects of the solvents. The correlating equation recently proposed by Belda, has also been applied to the present system in order to assess the validity of this equation. Key words: Binary liquid mixture • Arrhenius activation energy • Reduced Redlich-Kister equation • Interaction • 2-Ethoxyethanol. Three Methods of calculation of the excess partial molar volumes at infinite dilution A/ Direct thermodynamic Method (derivation) when we proceed to operations of limits of Eq. 1 at infinite dilution (x1 → 0+ or x1 → 1-), we can easily obtain the values of the excess partial molar volume at infinite dilution of the component ‘i’ in the other one. The fit of the molar volume V(x1) against the molar fraction (x1) gives directly the partial molar volume V of the component ‘i’ by the following equation (Eq. 1): (2) (1) B/ The reduced Redlich-Kister equations Qy,T(x1): Exemple Y = Molar volume = V Redlich-Kister expression for a molar excess property This ratio is so called the experimental reduced R-K excess properties QY,exp,T(x1) which is expressed by the following equation (3) (4) The variation of Q V,exp,T = VE/x1(1 – x1) with composition was used in every case to test the quality of the data; this function is extremely sensitive to experimental errors, particularly in the dilute ranges Its values at infinite dilution represent the values of the partial excess molar volume at infinite dilution, which can be also calculated from the adjustable parameters using the Eqs. (*) and (**): For the Redlich–Kister expression in Eqs. (*) and (**), Vi is the molar volume of pure component ‘i’. Molar volume of the mixture (V) and Partial molar volumes of DMA (V1) and EOE (V2) for DMA (2) + EOE (2) mixtures against the mole fraction x1 in DMA at the temperatures 298.15, 308.15 and 318.15 K are reported in Table1. The values of calculated by using Eqs. (*) and (**) are listed in Table 2. It can also readily be shown that, for many properties, such as enthalpies, heat capacities, volumes, compressibilities and expansibilities, this quantity (QY,T(x1)) is directly related to the apparent molar quantities of both components: This function is equivalent to an apparent molar quantity over whole mole fraction range, and its extrapolation to x1 = 0 and x1 = 1 (parameters sum QY,T(x1=0) and QY,T(x1=1) of Eqs. (*) and (**) will give the two excess partial molar quantities (where i = 1 or 2). These two limiting parameters are of fundamental importance since they are by definition measures of the solute-solvent interactions of both components: C/ Equation of Belda: In recent work, Belda propose a new empirical correlation equation for four properties (density, viscosity, surface tension, and refractive index) (Eq ****) which introduces a correcting Factor to linearity as an homographic function acting upon the molar fraction of one component of the binary mixture (x1). where YB(x1) is the mixture property, m1 and m2 are the two introduced empirical adjustable parameters. Belda coefficients mi for (Eq****) and corresponding errors of molar volume (V) for DMA (1) + EOE (2) mixtures at the temperatures 298.15, 308.15 and 318.15 K are given in Table 5. Figure 1 : Experimental relative reduced Redlich-Kister excess properties Qrel,V,T(x1) for the ratio = QV,T(x1)/V of excess molar volume for DMA (1) + EOE (2) mixtures against mole fraction x1 in DMA at the temperatures, (●): 298.15 K; (○): 308.15 K; (▲): 318.15 K. Figure 1 : Experimental reduced Redlich-Kister excess properties QV,T(x1) = VE / x1(1 – x1) of excess molar volume for DMA (1) + EOE (2) mixtures against mole fraction x1 in DMA at the temperatures, (●): 298.15 K; (○): 308.15 K; (▲): 318.15 K. Comparison of calculated values-with three methods-of the limiting excess partial molar volume (10-6 m3·mol-1) at infinite dilution relative to DMA (1) and of EOE (2) in their binary mixture at the temperatures 298.15, 308.15 and 318.15 K are given in Table 2. In fact, when we proceed to some operations of limits and derivations on the Belda equation, we can easily obtain the values of partial excess property at infinite dilution of the component “i” in the other one through the equations (*****) and (******) Arrhenius behavior CONCLUSION Reduced R-K excess functions have been calculated for N,N-DMA + EOE binary mixture at three different temperatures (298.15, 308.15 and 318.15) K from their experimental density, viscosity and isentropic compressibility's values reported earlier. In fact, the reduced Redlich-Kister function is a real thermodynamic quantity equivalent to an apparent molar quantity over the whole mole fraction range. Also, at the two limits of infinite dilution, this function gives the two excess standard thermodynamic quantities of the corresponding pure components, which depend only on solute-solvent interactions. In addition, the introduced relative reduced Redlich-Kister equation reduce the temperature effect and can be also be good tools, like the reduced Redlich-Kister function, for interpreting different types of interactions. In the present work, Arrhenius parameters of viscosity for DMA+EOE mixtures are investigated at (298.15, 308.15 and 318.15) K. In addition, the use of Belda parameters is introduced here and will allow us to give physical significance of the recent proposed empirical Belda equation in the present system. We have also calculated the Grunberg-Nissan parameter that is an interaction parameter proportional to the interchange energy of the pure components DMA and EOE of the present binary system. It is found that the temperature dependence of viscosity can be fitted with an Arrhenius type-equation as The composition at x1 = 0.25 = 1/4 where there is a structure change and gives two distinct structures. Fig. 3 suggests that it is an indication of the formation of a cluster (1DMA:3EOE) that may occur at very high dilution of DMA in EOE where R, Ea and As are, respectively, the gas constant, the Arrhenius activation energy and the pre-exponential (entropic) factor of the Arrhenius equation for the mixture. The following Equation can be rewritten in the logarithmic form: Figure 3: Correlation between The reduced Redlich-Kister functions relative to the Arrhenius activation energy QEa / kJ·mol-1 of viscosity and the logarithm of the Arrhenius entropic factor QlnAs for N,N-Dimethylacetamide (1) + 2-ethoxyethanol (2) mixtures in the temperature range (298.15 to 318.15 K).