Phase Equilibrium of Binary Mixture for the (propylene oxide + 1-pentanol) System at Several Temperatures

Abstract

Isothermal (vapor + liquid) equilibrium data measurements were undertaken for the binary mixtures of (propylene oxide + 1-pentanol) system at three different temperatures (303.15, 318.15, and 333.15) K. The Peng-Robinson-Stryjek-Vera equation of state (PRSV EOS) was used to correlate the experimental data. The van der Waals one-fluid mixing rule was used for the vapor phase and the Wong-Sandler mixing rule, which incorporates the non-random two liquid (NRTL) model, the universal quasi-chemical (UNIQUAC) model and the Wilson model, was used for the liquid phase. The experimental data were in good agreement with the correlation results.

1. Introduction

Glycol ethers are a group of solvents based on alkyl ethers of ethylene glycol or propylene glycol commonly used in pharmaceuticals, cosmetics and paints. These solvents typically have a higher boiling point, together with the favorable solvent properties of lowermolecular weight ethers and alcohols. Glycol ethers are classified into ethylene glycol ethers and propylene glycol ethers, depending on whether the raw material used in the synthesis is ethylene oxide or propylene oxide [1]. The negligible toxicity of propylene glycol ether supports its use as a safe alternative to toxic ethylene glycol ether [2]. Propylene glycol ethers are based on reacting propylene oxide with varying chain alcohols [1]. The (vapor + liquid) equilibrium information about the mixtures of propylene oxide with alcohols is significant in the design and operation of separation processes. Previously, we measured (vapor + liquid) equilibrium data for (propylene oxide + ethanol) and (propylene oxide + 1-propanol) [3]. In this work, isothermal (vapor + liquid) equilibrium data for the binary mixtures of (propylene oxide + 1-pentanol) system were measured at temperatures between 303.15 and 333.15 K. The experimental data were correlated using the Peng-Robinson-Stryjek-Vera equation of state (PRSV EOS) [4]. The van der Waals one-fluid mixing rule was used for the vapor phase and the Wong-Sandler mixing rule [5], which incorporates the non-random two liquid (NRTL) model [6], the universal quasi-chemical (UNIQUAC) model [7] and the Wilson model [8], was used for the liquid phase.

2. Experimental section

2-1. Materials

Propylene oxide and 1-pentanol were supplied by Sigma Aldrich (St. Louis, MO, USA). All chemicals were used without further purification. The supplier and purity of the chemicals are reported in Table 1.

Table 1. Specifications of the chemicals used for measurements

2-2. Apparatus and procedures

A static (vapor + liquid) equilibrium apparatus was used to measure the isothermal (vapor + liquid) equilibrium of binary mixtures. A schematic diagram of the apparatus is shown in Fig. 1. The details of the experimental apparatus and procedures can be found in previous work [3], so only the most salient information is offered here. The experimental pressure was determined using a pressure transducer (Honeywell, Model STJE) with an accuracy of ± 0.01 kPa, and the experimental temperature was determined using a digital thermometer (Hart Scientific, Model 5618B) with an accuracy of ± 0.008 K. For each experiment, a small amount of liquid-phase sample was extracted and analyzed by gas chromatography.

Fig. 1. Schematic diagram of experimental apparatus.

1. Isothermal water bath

2. Equilibrium cell

3. Temperature indicator

4. Pressure indicator

5. Feed container

6. Cooling bath circulator

7. Trap

8. Vacuum pump

2-3. Sample analysis

The composition of the extracted liquid was determined by a DS 6200 gas chromatograph equipped with a thermal conductivity detector. A 10% Carbowax 20M Chrom W-AW packed column (length, 2.438 m; o.d., 3.175 mm; i.d., 2.159 mm) and a 10% OV101 CHROM W-HP packed column (length, 3.048 m; o.d., 3.175 mm; i.d., 2.159 mm) were used for the (propylene oxide + 1-pentanol) system. For the (propylene oxide + 1-pentanol) system, the oven and detector temperatures were both kept at 373 K, the injector temperature was kept at 423 K and the current of thermal conductivity detector was 60 mA. A cooled syringe was used to inject a liquid sample into gas chromatography. In each analysis, 1.5 µL of sample was analyzed. High purity helium gas (purity ≥ 99.99%) was used as a carrier gas.

3. Results and Discussion

Phase equilibrium data for the (propylene oxide + 1-pentanol) were measured and the experimental uncertainty [9] was estimated to be 0.1 K for the temperature and 0.003 for the mole fraction of propylene oxide. Table 2 lists the experimental (propylene oxide + 1- pentanol) equilibrium data with standard uncertainty u(p) [9] at three different temperatures (303.15, 318.15, and 333.15) K.

Table 2. Experimental (vapor + liquid) equilibrium data for temperature T, pressure p with standard uncertainty u(p), and mole fraction x₁ for the system propylene oxide(1) + 1-pentanol(2)^a

^aStandard uncertainties u are u(T) = 0.10K and u(x₁) = 0.0030

PRSV EOS was used for correlating the experimental data. The PRSV EOS is represented as follows:

\(p=\frac{R T}{V-b}-\frac{a(T)}{V(V+b)+b(V-b)}\)            (1)

\(a(T)=0.45724 \frac{R^{2} T_{\mathrm{c}}^{2}}{p_{\mathrm{c}}} \alpha(T)\)            (2)

\(b=0.07780 \frac{R T_{\mathrm{c}}}{p_{\mathrm{c}}}\)            (3)

\(\alpha(T)=\left[1+\kappa\left(1-T_{t}^{0.5}\right)+\kappa_{1}\left(1-T_{t}\right)\left(0.7-T_{t}\right)\right]^{2}\)            (4)

\(\kappa=0.378893+1.4897153 \omega-0.17131848 \omega^{2}+0.0196554 \omega^{3}\)            (5)

where P_c is the critical pressure, T_c the critical temperature, T_r the reduced temperature, κ₁ the adjustable parameter characteristic of each pure compound, and ω the acentric factor.

The van der Waals one-fluid mixing rule was used for the vapor phase as follows:

\(a_{\mathrm{m}}=\sum_{i} \sum_{j} x_{i} x_{j} a_{i j}\)            (6)

\(b_{\mathrm{m}}=\sum_{\mathrm{i}} x_{i} b_{\mathrm{i}}\)            (7)

\(a_{i j}=\sqrt{a_{i} a_{j}}\left(1-k_{i j}\right)\)            (8)

where k_ij is the binary interaction parameter

The Wong-Sandler mixing rule was used for the liquid phase as follows:

\(\frac{a_{\mathrm{m}}}{R T}=Q \frac{D}{(1-D)}\)            (9)

\(b_{\mathrm{m}}=\frac{Q}{(1-D)}\)            (10)

where Q and D are defined as:

\(Q=\sum_{i} \sum_{j} x_{i} x_{j}\left(b-\frac{a}{R T}\right)\)            (11)

\(D=\sum_{i} x_{i} \frac{a_{i}}{b_{i} R T}+\frac{A_{\infty}^{E}}{C R T}\)            (12)

and where (b-a/ RT)_ij and C are defined as:

\(\left(b-\frac{a}{R T}\right)_{i j}=\frac{\left(b_{1}-\frac{a_{i}}{R T}\right)+\left(b_{j}-\frac{a_{j}}{R T}\right)}{2}\left(1-k_{i}\right)\)            (13)

\(C=\frac{1}{\sqrt{2}} \ln (\sqrt{2}-1)\)            (14)

Because excess Gibbs free energy (G^E) is approximately equal to excess Helmholtz free energy at infinite pressure (A^E_∞ ), at low pressure G^E can be substituted for A^E_∞. To obtain G^E, we used the NRTL model, the UNIQUAC model and the Wilson model. The non-randomness parameter (α_ij) was fixed at 0.47, and the coordination number (z) was fixed at 10. The correlating procedure is the same as in the previous work [3].

The vapor pressures of the pure propylene oxide at three different temperatures (303.15, 318.15, and 333.15) K and of pure 1-pentanol at 333.15 K were measured. The measured vapor pressures and literature values [10,11] are listed in Table 3 they deviated slightly from each other. Pure parameters for PRSV EOS are presented in Table 4, and the correlation results and average absolute deviations of pressure (AADp) are presented in Table 5.

Table 3. Comparison of pure component vapor pressures

u(T) = 0.1K

^aReference [10]

^bReference [11]

Table 4. Parameters used in the correlation

^aVan der Waals volume of the molecule relative to those of a standard segment, UNIQUAC volume parameter

^bVan der Waals area of the molecule relative to those of a standard segment, UNIQUAC area parameter

^cPure-component liquid molar volume

^dReference [12]

Table 5. The interaction parameters and average absolute deviations of pressure for propylene oxide + 1-pentanol system

^aNRTL, A₁₂ = Δg₁₂/R, A₂₁ = Δg₂₁/R; UNIQUAC, A₁₂ = Δu₁₂/R, A₂₁ = Δu₂₁/R, Wilson, A₁₂ = Δγ₁₂/R, A₂₁ = Δγ₂₁/R

^bBinary interaction parameter

The interaction parameters were regressed by minimizing the objective function, AADp, using a simplex algorithm. The AADp is defined as follows:

\(\mathrm{AAD} p=\frac{1}{\mathrm{N}} \sum_{i}^{\mathrm{N}}\left|\frac{p_{\mathrm{i}}^{\mathrm{exp}}-p_{\mathrm{i}}^{\mathrm{cal}}}{p_{\mathrm{i}}^{\mathrm{exp}}}\right|\)            (15)

where N is the number of experimental data points, p_i^exp the experimental pressure, and p_i^cal the calculated pressure.

As shown in Table 5, the experimental (propylene oxide + 1-pentanol) equilibrium data were correlated within 0.515%, 0.606%, and 0.609% AADp for the NRTL, UNIQUAC, and Wilson models, respectively. In all cases, the NRTL model showed the best correlated results among the three models. Therefore, the NRTL model is appropriate for the systems studied in this work, and the UNIQUAC and Wilson models showed similar correlation results. Figs. 2, 3, 4 show the experimental data and correlated values for the (propylene oxide + 1- pentanol) system, by NRTL, UNIQUAC, Wilson, respectively.

Fig. 2. Experimental (vapor + liquid) equilibrium data and correlated data by the NRTL for propylene oxide (1) + 1-pentanol (2) at temperatures from (303.15 to 333.15) K: ●, 303.15 K; □,318.15 K; ▲, 333.15 K; solid lines, NRTL.

Fig. 3. Experimental (vapor + liquid) equilibrium data and correlated data by the UNIQUAC for propylene oxide (1) + 1-pentanol (2) at temperatures from (303.15 to 333.15) K: ●, 303.15 K;□, 318.15 K; ▲, 333.15 K; solid lines, UNIQUAC.

Fig. 4. Experimental (vapor + liquid) equilibrium data and correlated data by the Wilson for propylene oxide (1) + 1-pentanol (2) at temperatures from (303.15 to 333.15) K: ●,303.15 K; □, 318.15 K; ▲, 333.15 K; solid lines, Wilson.

4. Conclusions

Isothermal (vapor + liquid) equilibrium data measurements were undertaken for the binary mixtures of (propylene oxide + 1-pentanol) system at three different temperatures (303.15, 318.15, and 333.15) K. The correlation results were obtained from PRSV EOS with the van der Waals one-fluid mixing rule for the vapor phase and with the Wong-Sandler mixing rule for the liquid phase. The NRTL, UNIQUAC, and Wilson models were used to calculate the excess Gibbs free energy. The experimental data were in good agreement with the correlation results obtained by all three models within less than 1% AADp. The NRTL model is more suitable than the UNIQUAC and Wilson models for the systems studied in this work.