New parametric model to correlate the gibbs excess function and other thermodynamic properties of multicomponent systems. application to binary systems

A new empirical mathematical model for the Gibbs excess function, g ^E = ψ(p,T,x), is presented for a multicomponent system. Dependence on the composition is achieved through the so-called active fraction, zi, which, in turn, is related to the molar fraction x_i of the components of a solution and a parameter k_ij, the determination of which is also indicated. The efficacy of the model in relation to its extension of application is discussed, considering various cases and three possible ways to calculate the parameter k_ij. This produces different versions of the model for data correlation the advantages of which are discussed. The model proposed for the Gibbs excess function adopts the following generic expression, g^E(P,T,x) = z(x)[1 - z(x)]σ-0gi(P,T)z_i where g _i(P,T) = g_i1 + g_i2P² + g _i3PT + g_i4T + g_i5T², which can be applied to a general case of vapor-liquid equilibrium with variation of the three main variables x_i, p, and T, or by considering the experimental values for two important situations, isobaric and isothermal, which are also studied here. Other mixing properties are obtained via mathematical derivation, and a simultaneous correlation is carried out on several of them. The model has been applied to various binary systems for which experimental data are available in the literature and over a wide range of p and T. The results obtained can be considered acceptable.