Iranian Journal of Science & Technology, Transaction B, Vol. 25, No. B2 Printed in Islamic Republic of Iran, 2001 to Shiraz University MODIFICATION OF THE VAN LAAR ACTIVITY Yr COEFFICIENT MODEL G. R. VAKILI-NEZHAAD*1, H. MODARRESS *2AND G. A. MANSOORI3 IChemical Engineering Department, Faculty of Engineering, University of Kashan, Kaspan, 1 R. of Iran 2 Chemical Engineering Department, Amirlcabir (polytcclmic) University of Technology, Tehran, I. R. of Iran 3 Chemical Engineering Department, University of illinois, 810 S. Clinton Street, Chicago, USA Abstract - Based on statistical and mechanical arguments, the original van Laar activity coefficient model has been improved by reasonable assumptions. This modification has been done by replacing the van der Waals equation of state with the Redlich-Kwong equation of state in the formulation of van Laar with consistent mixing rules for the energy and volume parameters of this equation of state (a",ix, bmix). Other equations of state, such as the Soave modification of the Redlich-Kwong equation of state, Peng-Robinson and Mohsen-Nia, Modarress and Mansoori equations of state, have been introduced in the formulation of van Laar for the activity coefficients of the components present in the binary liquid mixtures, and their effects on the accuracy of the resultant activity coefficient models have been examined. The results of these revised models have been compared with the experimental data and it was found that the Redlich-Kwong equation of state with the van der Waals mixing rules for the volume and energy parameters of this equation, is the best choice among these equations of state. In addition, it can improve the original van Laar activity coefficient model and, therefore a better agreement with the experimental data is obtained. Keywords -statistical mechanics, phase equilibria, activity coefficients models, non-ideal solutions 1. INTRODUCTION There are two ways for the estimation of fugacities of the species in liquid mixtures: (i) For the mixtures involving onfy hydrocarbons and dissolved gases, simple equations of state such as the Peng -Robinson equation of state [1] may be used for the estimation of species fugacities. (ii) However, for liquid mixtures containing alcohols or electrolytes, in which one or more of the components cannot presently be described by an equation of state in the liquid phase, another procedure for estimating species fugacitieS must be used. The most common starting point can be written as follows: (1) where r I is the activity coefficient and J/ is the fugacity of the species (i) in the pure state. It is evident from the above equation that in case (ii) for the purpose of studying the behavior of the liquid mixture, one must have the activity coefficient of the species present in the liquid mixtures. Many efforts have been made to present the various activity coefficient models, such as Margules, van Laar, UNIQUAC, etc. In this work, the van Laar model is improved to increase its accuracy in activity coefficient calculations for liquid mixtures. 'Received by the editors November I, 1998 and in final revised form Octohec 4, 1999 'Corresponding author 282 G. R. Va/cJIl-ne:/uuzd / et Q/. In the van Laai' theory leading to its activity coefficient mo