# Behavior of the Thermodynamic Properties of Binary Mixtures near the Critical Azeotrope

## Abstract

**:**

## 1. Introduction

_{i}, of the two components, with i=1 and i=2. These field variables are related by the Gibbs-Duhem equation, furthermore, it is useful to consider the difference between the two chemical potentials [4] such as:

_{1}− μ

_{2}

_{1}, μ

_{2}and T such that:

## 1. Thermodynamic properties of binary mixtures

_{T,x}is the compressibility of the binary mixtures. For the purpose of implementing our idea, we demand that x =ζ along the critical line [2]. Consequently, K

_{T,}

_{ζ}behaves in the same way as the compressibility of a pure fluid, which we denote by:

_{T,}

_{ζ}→∞ on the critical azeotrope of the binary mixtures, this result follows from the basic notion that, at the critical point of pure fluids, the compressibility diverges strongly [7]. Therefore, it comes out that the V-x critical curve possesses an inflection point approaching a vertical tangent, as will be shown in the next section in figure 1. A similar observation is readily seen if one looks at the enthalpy and entropy functions of the binary mixtures. We can take the enthalpy as H, or the entropy S, along the critical locus. From the basic thermodynamic relation, we have:

## 2. Investigation of the critical line

_{c}(x) = T

_{c}

^{(1)}(1 - x)+ T

_{c}

^{(2)}x + (T

_{1}x + T

_{2}x

^{2}+ T

_{3}x

^{3}+ T

_{4}x

^{4})(1 − x)

_{j}are to be determined by fitting Eq. (15) and Eq. (16) to experimental data obtained by Raja et al. [12]. The values obtained for the coefficients in Eq. (15) and Eq. (16) are presented in Table 1, together with the critical densities as well as the critical temperatures of the pure fluids, namely, acetone and n-pentane.

Equation (16) for ${\mathsf{\rho}}_{c}$(m^{3}/mol): ${\mathsf{\rho}}_{c}$^{(1)}=311.0, ${\mathsf{\rho}}_{c}$^{(2)}=213.0, ${\mathsf{\rho}}_{1}$=38.14, ${\mathsf{\rho}}_{2}$=-15.60 |

Equation (17) for T_{c}(K): T_{c}^{(1)}=469.80, T_{c}^{(2)}=507.60, T_{1}=-69.309, T_{2}=87.175, T_{3}=-204.59, T_{4}=128.68 |

**Figure 1.**Representation of the critical temperature as a function of the concentration. The curve represents the values calculated from Eq. (16). The squares represent the experimental data obtained by Raja et al. [12].

## 3 Conclusion

#### Acknowledgments:

**ANDRU**) for the financial support under grant No CU 39718.

**Figure 2.**Representation of the critical density as a function of the concentration. The curve represents the values calculated from Eq. (15). The squares represent the experimental data obtained by Raja et al. [12].

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Abbaci, A. Behavior of the Thermodynamic Properties of Binary Mixtures near the Critical Azeotrope. *Entropy* **2003**, *5*, 348-356.
https://doi.org/10.3390/e5040348

**AMA Style**

Abbaci A. Behavior of the Thermodynamic Properties of Binary Mixtures near the Critical Azeotrope. *Entropy*. 2003; 5(4):348-356.
https://doi.org/10.3390/e5040348

**Chicago/Turabian Style**

Abbaci, Azzedine. 2003. "Behavior of the Thermodynamic Properties of Binary Mixtures near the Critical Azeotrope" *Entropy* 5, no. 4: 348-356.
https://doi.org/10.3390/e5040348