2.1 Thermodynamic model

The correlation of the iso-p {VLE + h<sup>E</sup> } data for each one of the two systems selected is carried out using a parametric equation already used by us [8], which is applied to the excess Gibbs function of a binary system:

$$\mathbf{g}^{\to}(p,T,\mathbf{x}) = \mathbf{z}\_1(\mathbf{1} - \mathbf{z}\_1) \sum\_{\mathbf{i}=0}^{2} \mathbf{g}\_{\mathbf{i}}(p,T)\mathbf{z}\_1^{\mathbf{i}}\mathbf{z}\_1 = \frac{\boldsymbol{\varkappa}\_1}{\boldsymbol{\varkappa}\_1 + \boldsymbol{k}\_{\operatorname{\mathbb{g}}}^{2 \cdot \mathbf{1}}\mathbf{z}\_2} \tag{1}$$

and as described in [8]:

$$\mathbf{g}\_{i}(p,T) = \mathbf{g}\_{i1} + \mathbf{g}\_{i2}p^{2} + \mathbf{g}\_{i3}pT + \mathbf{g}\_{i4}/T + \mathbf{g}\_{i5}T^{2} \tag{2}$$

where k<sup>g</sup> <sup>2</sup>–<sup>1</sup> is a fitting parameter. In this study, several forms of Eq. (2) are tested, by adapting it according to the availability of experimental data. Thus, different "sub-models" are defined by neglecting terms in Eq. (2) which give rise to the following four cases:

$$\begin{aligned} \mathbf{M1} &\rightarrow \{ \mathbf{g}\_{i2}, \mathbf{g}\_{i3}, \mathbf{g}\_{i4}, \mathbf{g}\_{i5} \} = \mathbf{0}; \mathbf{M2} &\rightarrow \{ \mathbf{g}\_{i2}, \mathbf{g}\_{i3}, \mathbf{g}\_{i5} \} = \mathbf{0};\\ \mathbf{M3} &\rightarrow \{ \mathbf{g}\_{i2}, \mathbf{g}\_{i5} \} = \mathbf{0}; \mathbf{M4} &\rightarrow \mathbf{g}\_{i2} = \mathbf{0} \end{aligned} \tag{3}$$

From Eq. (1), the expression that characterizes the activity coefficients is

$$\begin{aligned} RT \ln \chi\_{\mathbf{i}} &= \mathbf{z}\_{1} (\mathbf{1} - \mathbf{z}\_{1}) \left( \mathbf{g}\_{0} + \mathbf{g}\_{1} \mathbf{z}\_{1} + \mathbf{g}\_{2} \mathbf{z}\_{1}^{2} \right) + (\mathbf{1} - \mathbf{i} - \mathbf{x}\_{1}) \\ &\quad \left[ \mathbf{g}\_{0} + 2 \left( \mathbf{g}\_{1} - \mathbf{g}\_{0} \right) \mathbf{z}\_{1} + 3 \left( \mathbf{g}\_{2} - \mathbf{g}\_{1} \right) \mathbf{z}\_{1}^{2} - 4 \mathbf{g}\_{2} \mathbf{z}\_{1}^{3} \right] \mathbf{k}\_{\mathbf{g}}^{2 \cdot 1} \left( \mathbf{z}\_{1} / \mathbf{x}\_{1} \right)^{2} \end{aligned} \tag{4}$$

Likewise, the excess enthalpies h<sup>E</sup> are calculated considering.

$$h^{\mathcal{E}} = \mathbf{g}^{\mathcal{E}} - T \left( \partial \mathbf{g}^{\mathcal{E}} / \partial T \right)\_{\mathbf{x}, \mathbf{p}'} ; h^{\mathcal{E}} = \mathbf{z}\_1 (\mathbf{1} - \mathbf{z}\_1) \left( h\_0 + h\_1 \mathbf{z}\_1 + h\_2 \mathbf{z}\_1^2 \right) \tag{5}$$

Eqs. (1) and (5) assume that the different sub-models established by Eq. (3) impose certain behavior hypothesis in the mixture. Thus, sub-model M1 implies that g <sup>E</sup> = h<sup>E</sup> . For the remaining assumptions, g <sup>E</sup> 6¼ <sup>h</sup><sup>E</sup> , allowing different functions to express the h<sup>E</sup> s.
