MEASUREMENTS AND THERMODYNAMIC MODELING OF VAPOR-LIQUID EQUILIBRIA FOR BINARY SYSTEMS OF ISOPROPYL CHLOROACETATE WITH CYCLOHEXANE, ISOPROPANOL AND BENZENE AT 101.3 kPa

Abstract

In this work, the vapor-liquid equilibrium experimental data for the systems of isopropyl chloroacetate + isopropanol, isopropyl chloroacetate + cyclohexane and isopropyl chloroacetate + benzene were measured by a modified Rose-type recirculating still under the pressure of 101.3 kPa. The thermodynamic consistency of the measured data was verified by the Herington and van Ness methods, respectively. The experimental data were correlated by the NRTL, Wilson, and UNIQUAC activity coefficient models, and the corresponding interaction parameters of the three models were obtained. The root-mean-square deviations between the experimental data and calculated results for the temperature and the mole fraction of the vapor phase were less than 0.58 K and 0.0066, respectively. In addition, the excess Gibbs energy was calculated for the three systems.

Keywords:
Vapor-liquid equilibrium; Isopropyl chloroacetate; Correlation; Thermodynamic model

INTRODUCTION

Isopropyl chloroacetate is a raw material and intermediate, which is widely used in the synthesis of nonsteroidal anti-inflammatory drugs, such as naproxen, ketoprofen and ibupofen. Generally, isopropyl chloroacetate can be synthesized by esterification of chloroacetic acid and isopropanol with a catalyst, such as cation exchange resin (Patwardhan and Sharma, 1990), inorganic salts (Liu and You, 2013), and ionic liquids (Liu et al., 2007). During the esterification process, the water-carrying agent is required to remove water continuously to increase the esterification yield. Ma et al. (2006) reported the synthesis of isopropyl chloroacetate using cyclohexane as a water-carrying agent in their work. Wang et al. (2003) used benzene as a water-carrying agent to separate water from the esterification process. After the reaction, a mixture of isopropyl chloroacetate, unreacted isopropanol and water-carrying agent is obtained. To separate isopropyl chloroacetate from the mixture by distillation, vapor-liquid equilibrium (VLE) data are required.

Until now, some works have reported the preparation of isopropyl chloroacetate (Xu et al., 2011; Liu and You, 2012). However, for separation of isopropyl chloroacetate from the reacted solution, the VLE data for the systems of isopropyl chloroacetate + isopropanol, isopropyl chloroacetate + cyclohexane and isopropyl chloroacetate + benzene have not been reported in the NIST database. Therefore, it is necessary to generate the VLE data for these systems, which can be useful for the separation and purification of isopropyl chloroacetate from the mixture by distillation.

In this work, the VLE data for the systems isopropyl chloroacetate + isopropanol, isopropyl chloroacetate + cyclohexane and isopropyl chloroacetate + benzene were measured under the pressure of 101.3 kPa. To ensure the reliability of the measured VLE data, the thermodynamic consistency test was performed by the Herington and van Ness method. The non-random two-liquid (NRTL) (Renon and Prausnitz, 1968; Liu et al., 2019), Wilson (Wilson, 1964; Li, 2014), and the universal quasi-chemical (UNIQUAC) (Abrams and Prausnitz, 1975) activity coefficient models were used to correlate the experimental VLE data and the binary interaction parameters for the three models were regressed. In addition, the calculation of the excess Gibbs energy for the three systems from the VLE data was listed.

EXPERIMENTAL

Chemicals

Isopropyl chloroacetate, cyclohexane, isopropanol and benzene were commercial grade chemicals in this work. The mass purities of isopropyl chloroacetate, cyclohexane, isopropanol and benzene were 0.980, 0.995, 0.997 and 0.995, respectively, which were confirmed by gas chromatography (GC) and all the reagents were used directly. The boiling point temperatures for the chemicals were determined by a modified Rose-type recirculating still. The relevant information of the chemicals, such as CAS number, supplier, boiling temperature and so on, is given in Table 1.

Table 1
Information of the chemicals.

Name	CAS	Supplierc	Mass fraction	Tb/Kb		Analysis method
				This work	Literature
Isopropyl chloroacetate	105-48-6	(1)	≥0.980	422.85	422.63 (Dorris et al., 1934)	GCa
Isopropanol	67-63-0	(2)	≥0.997	355.11	355.45 (Chen et al., 2011)	GCa
Cyclohexane	110-82-7	(2)	≥0.995	353.83	353.65 (Gupta and Lee, 2012)	GCa
Benzene	71-43-2	(3)	≥0.995	353.23	353.25 (Li et al., 2017)	GCa

• ^a Gas chromatography. ^b The boiling temperature was measured at 101.3 kPa. The standard uncertainties u of P and T are u(P)=0.35kPa, u(T)=0.35 K. ^c Suppliers: (1) TCI (Shanghai) Development Co., Ltd.; (2) Tianjin Kemio Chemical Co., Ltd., (3) Tianjin Fuyu Chemical Co., Ltd.

Apparatus and procedure

The apparatus used in this work was a modified Rose-type recirculating still which is presented in detail in Figure 1. The equilibrium temperature was determined by a mercury thermometer with the accuracy of ± 0.1 K. The pressure was measured by a mercury U-shaped manometer and the accuracy of the manometer was ± 0.1333 kPa. In each experiment, a liquid mixture of 50 ml was charged into the equilibrium still and heated. The vapor condensate was recirculated and mixed with the liquid in the still, which could make enough contact for the two phases. To reach the equilibrium state, the recirculation time for the two phases was maintained for at least 50 min at a constant temperature, then the equilibrium temperature was recorded. At the same time, 0.3 ml of the vapor and the liquid phases were withdrawn by syringe for analysis, respectively. All the samples were analyzed by GC.

Figure 1
The vapor-liquid equilibrium apparatus: 1, heating rod; 2, liquid phase sample port; 3, thermometer sleeve tube; 4, mercury thermometer; 5, condenser; 6, vapor phase sample port, 7, mercury U-shaped manometer, 8, needle valve, 9, buffer tank, 10, vacuum pump.

Gas chromatography (GC7900, Shanghai Tianmei Scientific Instrument Co., Ltd.) was used to analyze the samples, which was equipped with a flame ionization detector (FID) and a capillary column. The carrier gas was high-purity nitrogen with the purity of 99.999 wt%. The compositions of all samples were obtained by a T2000P GC workstation. The detailed operating conditions are shown in Table 2.

Table 2
Operating conditions for the gas chromatograph.

Name	Characteristic	Description
Column	Type	DB-WAX, 30 m × 0.53 m × 0.5 µm
	Temperature	393.15 K
Carrier gas	Type	Nitrogen
	Flow rate	10 mL/min
	Pressure	0.3 MPa
Injector	Injection volume	0.2 μL
	Temperature	443.15 K
Detector	Type	Flame ionization detector (FID)
	Temperature	433.15 K

Analysis

Before analyzing the compositions of the samples, the area correction normalization method (Dai et al., 2014; Wu et al., 2018) was applied to calibrate the GC in this work. First, five different standard samples were prepared gravimetrically with an AR1140 electronic balance (Ohaus Corporation) with an accuracy of ± 0.0001 g. The five different standard samples with known compositions were analyzed by GC and the peak area of GC was calibrated. The samples of the vapor and liquid phases were analyzed at least three times, and the average values were recorded.

RESULTS AND DISCUSSIONS

Experimental VLE results

The experimental VLE data of isopropyl chloroacetate + isopropanol, isopropyl chloroacetate + cyclohexane and isopropyl chloroacetate +benzene were measured at the pressure of 101.3kPa and are listed in Table 3. The T-x-y profiles for the three systems are plotted in Figures 2-4.

Table 3
Experimental VLE data for temperature T, liquid phase mole fraction x _i , vapor phase mole fraction y _i , activity coefficient γ, excess Gibbs energy G ^E , the results for cyclohexane (1) + isopropyl chloroacetate (2), isopropanol (1) + isopropyl chloroacetate (2) and benzene (1) + isopropyl chloroacetate (2) at 101.3kPa.^a

T (K)	x1	y1	γ1	γ2	GE (J·mol−1)
Cyclohexane (1) + Isopropyl chloroacetate (2)
353.83	1.0000	1.0000	-	-	0.00
355.65	0.9333	0.9894	1.0046	1.6575	112.32
357.64	0.8000	0.9685	1.0818	1.5090	431.71
360.60	0.7001	0.9519	1.1149	1.3574	503.03
366.02	0.5667	0.9239	1.1470	1.1921	468.21
370.33	0.4870	0.8961	1.1503	1.1599	444.25
376.60	0.3932	0.8549	1.1510	1.0789	317.42
381.35	0.3297	0.8162	1.1603	1.0393	237.34
385.20	0.2835	0.7755	1.1645	1.0352	217.65
389.60	0.2366	0.7215	1.1662	1.0344	201.46
394.96	0.1837	0.6508	1.1932	1.0125	139.85
400.25	0.1403	0.5634	1.1976	1.0116	117.18
405.30	0.1035	0.4668	1.2017	1.0100	94.14
410.45	0.0700	0.3560	1.2117	1.0043	59.49
416.85	0.0323	0.1903	1.2270	1.0041	36.62
418.96	0.0215	0.1325	1.2288	1.0011	19.18
422.85	0.0000	0.0000	-	-	0.00
Isopropanol (1) + Isopropyl chloroacetate (2)
355.11	1.0000	1.0000	-	-	0.00
356.22	0.9393	0.9921	1.0204	1.3246	106.71
357.35	0.8894	0.9858	1.0240	1.2454	134.78
359.79	0.7955	0.9716	1.0260	1.2157	180.56
362.53	0.7006	0.9545	1.0305	1.1879	218.83
368.66	0.5283	0.9102	1.0383	1.1638	280.17
371.49	0.4636	0.8865	1.0411	1.1587	301.70
375.45	0.3785	0.8511	1.0657	1.1285	309.71
380.45	0.2962	0.8063	1.0888	1.0777	246.29
385.90	0.2273	0.7512	1.1060	1.0379	165.69
390.95	0.1734	0.6897	1.1351	1.0164	115.13
399.05	0.1055	0.5654	1.1980	1.0059	80.69
405.45	0.0662	0.4446	1.2493	1.0053	66.31
409.75	0.0457	0.3548	1.2820	1.0016	43.87
415.00	0.0235	0.2283	1.3933	1.0011	30.60
422.85	0.0000	0.0000	-	-	0.00
Benzene (1) + Isopropyl chloroacetate (2)
353.23	1.0000	1.0000	-	-	0.00
356.77	0.8825	0.9868	1.0039	1.1169	48.72
359.88	0.7916	0.9734	1.0063	1.1131	81.69
361.80	0.7342	0.9633	1.0150	1.1121	117.83
368.34	0.5828	0.9251	1.0192	1.1114	168.89
373.95	0.4761	0.8834	1.0214	1.1093	200.30
378.05	0.4102	0.8490	1.0217	1.0944	194.90
385.05	0.3141	0.7789	1.0223	1.0706	171.97
389.55	0.2590	0.7234	1.0297	1.0602	164.84
396.65	0.1875	0.6209	1.0294	1.0445	134.57
401.45	0.1414	0.5418	1.0655	1.0230	95.11
407.85	0.0892	0.4121	1.1125	1.0132	72.75
413.65	0.0456	0.2718	1.2652	1.0057	55.55
415.90	0.0262	0.2089	1.6134	1.0023	51.07
418.85	0.0135	0.1272	1.7921	1.0022	34.98
422.85	0.0000	0.0000	-	-	0.00

• ^a Standard uncertainties u of T, P, x and y are u(T)=0.35 K, u(p)=0.35 kPa, u(x)=0.0116, u(y) =0.0122.

Figure 2
T-x-y phase equilibrium for the system cyclohexane (1) + isopropyl chloroacetate (2) at 101.3 kPa: ●, experimental data; -, calculated by the NRTL model.

Figure 3
T-x-y phase equilibrium for the system isopropanol (1) + isopropyl chloroacetate (2) at 101.3 kPa: ●, experimental data; -, calculated by the NRTL model.

Figure 4
T-x-y phase equilibrium for the system benzene (1) + isopropyl chloroacetate (2) at 101.3 kPa: ●, experimental data; -, calculated by the NRTL model.

The equilibrium relationship of the system is represented by the following equation (Smith et al., 2001):

$${\widehat{\varphi }}_i{y}_{i}p=x_i{\gamma }_i{\varphi }_i^s{p}_i^s\exp \left[\frac{V_i^L\left(p-p_i^s\right)}{RT}\right]$$ (1)

Generally, the exponential term exp[V_i ^L((p - p_i ^s)/RT)] is approximately equal to 1 under atmospheric pressure. In addition, the vapor phase could be regarded as an ideal gas, thus φ_i and φ_i ^s are equal to 1. Thus, Eq. 1 can be simplified as follows:

$$y_{i}p=x_i{\gamma }_i{p}_i{}^s$$ (2)

The p_i ^s can be calculated by the Wagner 25 equation (Forero and Velásquez, 2011; Gao et al., 2016b):

$$\text{ln}\left({\text{p}}_{\text{i}}^{\text{s}}\right)\text{=ln}\left({\text{p}}_{\text{ci}}\right)\text{+}\frac{{\text{C}}_{\text{1i}}\left({\text{1-T}}_{\text{ri}}\right){\text{+C}}_{\text{2i}}{{\text{(1-T}}_{\text{ri}}\text{)}}^{\text{1}\text{.5}}{\text{+C}}_{\text{3i}}{{\text{(1-T}}_{\text{ri}}\text{)}}^{\text{2}\text{.5}}{\text{+C}}_{\text{4i}}{{\text{(1-T}}_{\text{ri}}\text{)}}^{\text{5}}}{{\text{T}}_{\text{ri}}}$$ (3)

and

$${\text{T}}_{\text{ri}}\text{=}\frac{\text{T}}{{\text{T}}_{\text{ci}}}$$ (4)

The Wagner 25 parameters C _1i to C _4i , as well as the T _ri and T _ci for each pure component i, were taken from the Aspen Plus physical properties databank and listed in Table 4. In the meantime, the activity coefficient was calculated by Eq. 2, and the results are listed in Table 3.

Table 4
Parameters of the Wagner 25 equation.^a

Component	C1i	C2i	C3i	C4i	pci/kPa	Tci/K	Tlower/K	Tupper/K
Isopropyl chloroacetate	-8.3736	2.2903	-3.9060	-3.7705	3420.33	614.00	190.00	614.00
Cyclohexane	-7.0580	1.7024	-2.1203	-3.1898	4070.44	553.40	279.82	553.40
Isopropanol	-8.5396	1.5379	-7.6671	2.3246	4751.67	508.27	185.24	508.27
Benzene	-7.1463	1.9153	-2.2948	-3.2081	4894.12	562.02	278.47	562.02

• ^a Taken from the Aspen Plus Physical Properties Databank.

To evaluate the non-ideality of the three binary systems, the excess Gibbs energy G ^E (Acevedo et al., 1988; Shi et al., 2017) was calculated as follows:

$$G^E=RT\left(x_1\ln {\gamma }_1+x_2\ln {\gamma }_2\right)$$ (5)

The calculated results of G ^E are presented in Table 3 and Figure 5. As shown in Figure 5, the three binary systems exhibit positive deviations from Raoult′s law, which indicates the non-ideality of the solutions for three binary systems. Furthermore, the values of the excess Gibbs free energy for three binary systems follow the order of isopropyl chloroacetate + cyclohexane > isopropyl chloroacetate + isopropanol > isopropyl chloroacetate + benzene.

Figure 5
Excess Gibbs energy for the three systems at 101.3 kPa: ▲, cyclohexane (1) + isopropyl chloroacetate (2); ●, isopropanol (1) + isopropyl chloroacetate (2); ■, benzene (1) + isopropyl chloroacetate (2), --, calculated by the NRTL model.

Thermodynamic consistency tests

For the binary mixtures, the Herington and van Ness method were used to check the consistency of the experimental data.

The Herington method (Herington and Inst, 1951; Alinejhad et al., 2018) based on the Gibbs−Duhem theory was adopted which can be described as follows:

$$D=100\times \left|\frac{S_{+}-S_{-}}{S_{+}+S_{-}}\right|=100\times \frac{\left|{\displaystyle {\int }_0^1\ln (\gamma 1/\gamma 2)dx1}\right|}{{\displaystyle {\int }_0^1\left|\ln (\gamma 1/\gamma 2)\right|dx1}}$$ (6)

$$J=150\times \left|\frac{T_{\max }-T_{\min }}{T_{\min }}\right|$$ (7)

The ln(γ₁/γ₂) vs x diagram is shown in Figure 6 and T _max and T _min are the maximum and minimum boiling points, respectively. The criterion of the Herington test is that the absolute value of |D-J| should be less than 10. As shown in Table 5, the results of thermodynamic consistency for all three systems are all less than 10, which indicates that the experimental data of the three systems passed the thermodynamic consistency test.

Figure 6
ln(γ₁/γ₂) vs. x ₁ plot for the three systems: ■, cyclohexane (1) + isopropyl chloroacetate (2); ●, isopropanol (1) + isopropyl chloroacetate (2); ▲, benzene (1) + isopropyl chloroacetate (2), --, calculated by the NRTL model.

Table 5
Herington test for thermodynamic consistency check.

System	D	J	|D-J| < 10
Cyclohexane (1) + Isopropyl chloroacetate (2)	37.73	29.26	8.47
Isopropanol (1) + Isopropyl chloroacetate (2)	37.68	28.61	9.08
Benzene (1) + Isopropyl chloroacetate (2)	37.89	29.19	8.69

The van Ness test method (Van Ness et al., 1973; Gao et al., 2016a) is expressed by the following equations:

$$\Delta y=\frac{1}{N}{\displaystyle \sum _{i=1}^N\Delta y_i}=\frac{1}{N}{\displaystyle \sum _{i=1}^{N}100\left|y_i{}^{cal}-y_i{}^{\exp }\right|}$$ (8)

$$\Delta P=\frac{1}{N}{\displaystyle \sum }_{i=1}^N\Delta p_i=\frac{1}{N}{\displaystyle \sum }_{i=1}^{N}100\left|\frac{P_i^{\exp }-P_i^{cal}}{P_i^{\exp }}\right|$$ (9)

The obtained VLE data can pass the thermodynamic consistency test if the values ofΔy andΔP are both less than 1. The test results are presented in Table 6. As seen from Table 6, the results of Δy andΔP are all less than unity, which indicates that the measured VLE data are thermodynamically consistent.

Table 6
van Ness test for thermodynamic consistency check.

System		ΔP < 1	Δy < 1
Cyclohexane (1) + Isopropyl chloroacetate (2)	NRTL	0.16	0.5082
	Wilson	0.15	0.4951
	UNIQUAC	0.15	0.4901
Isopropanol (1) + Isopropyl chloroacetate (2)	NRTL	0.06	0.2745
	Wilson	0.06	0.2495
	UNIQUAC	0.08	0.2745
Benzene (1) + Isopropyl chloroacetate (2)	NRTL	0.09	0.4439
	Wilson	0.06	0.2604
	UNIQUAC	0.08	0.4974

VLE data correlation

The measured experimental VLE data were correlated by the NRTL, Wilson and UNIQUAC activity coefficient models. For the UNIQUAC model, the structural parameters r and q are presented in Table 7. The expressions of the activity coefficient models are as follows:

NRTL:

$$\ln {\gamma }_i=\frac{{{\displaystyle \sum }}_j{x}_j{\tau }_{ji}{G}_{ji}}{{{\displaystyle \sum }}_k{x}_k{G}_{ki}}+{\displaystyle \sum }_j\frac{x_j{G}_{ij}}{{{\displaystyle \sum }}_k{x}_k{G}_{kj}}\left({\tau }_{ij}-\frac{{{\displaystyle \sum }}_m{x}_m{\tau }_{mj}{G}_{mj}}{{{\displaystyle \sum }}_k{x}_k{G}_{kj}}\right)$$ (10)

$${\tau }_{ij}=a_{ij}+\frac{b_{ij}}{T},G_{ij}=\exp \left(-{\alpha }_{ij}{\tau }_{ij}\right)$$ (11)

α_ij = 0.3

Wilson:

$$\text{ln}{\gamma }_{\text{i}}=1-\text{ln}\left({\displaystyle \sum }_{\text{j}}{\text{A}}_{\text{ij}}{\text{x}}_{\text{j}}\right)-{\displaystyle \sum }_{\text{j}}\frac{{\text{A}}_{\text{ji}}{\text{x}}_{\text{j}}}{{{\displaystyle \sum }}_{\text{k}}{\text{A}}_{\text{jk}}{\text{x}}_{\text{k}}}$$ (12)

$${\text{lnA}}_{\text{ij}}={\text{a}}_{\text{ij}}+\frac{{\text{b}}_{\text{ij}}}{\text{T}}$$ (13)

UNIQUAC:

$$\ln {\gamma }_i=\ln \frac{{\Phi }_i}{x_i}+\frac{z}{2}{q}_i\ln \frac{{\theta }_i}{{\Phi }_i}-q_i^t\ln t_i^t-q_i^t\frac{{{\displaystyle \sum }}_j{\theta }_j^t{\tau }_{ij}}{t_j^t}+l_i+q_i^t-\frac{{\Phi }_i}{x_i}{\displaystyle \sum }_j{x}_j{l}_j$$ (14)

$${\tau }_{\text{ij}}=\text{exp}\left({\text{a}}_{\text{ij}}+\frac{{\text{b}}_{\text{ij}}}{\text{T}}\right)$$ (15)

$${\text{l}}_{\text{i}}=\left(\frac{\text{z}}{2}\right)\left({\text{r}}_{\text{i}}-{\text{q}}_{\text{i}}\right)\left({\text{r}}_{\text{i}}-1\right)$$ (16)

$${\Phi }_{\text{i}}=\frac{{\text{r}}_{\text{i}}{\text{x}}_{\text{i}}}{{{\displaystyle \sum }}_{\text{k}}{\text{r}}_{\text{k}}{\text{x}}_{\text{k}}}$$ (17)

$${\theta }_{\text{i}}=\frac{{\text{q}}_{\text{i}}{\text{x}}_{\text{i}}}{{{\displaystyle \sum }}_{\text{k}}{\text{q}}_{\text{k}}{\text{x}}_{\text{k}}}$$ (18)

Table 7
Structural parameters for the UNIQUAC equation.^a

Component	r	q
Isopropyl chloroacetate	4.663	4.064
Cyclohexane	4.047	3.240
Isopropanol	2.914	2.528
Benzene	3.191	2.400

The interaction parameters of the above three models were obtained based on the maximum likelihood method by minimizing the following objective equation:

$$Q={\displaystyle \sum _{i=1}^N\left[{\left(\frac{T_i{}^{\exp }-T_i{}^{cal}}{{\sigma }_T}\right)}^2+{\left(\frac{p_i{}^{\exp }-p_i{}^{cal}}{{\sigma }_p}\right)}^2+{\left(\frac{x_i{}^{\exp }-x_i{}^{cal}}{{\sigma }_x}\right)}^2+{\left(\frac{y_i{}^{\exp }-y_i{}^{cal}}{{\sigma }_y}\right)}^2\right]}$$ (19)

The obtained interaction parameters of the NRTL, Wilson and UNIQUAC models in Aspen plus simulator (2013) are listed in Table 8. The root-mean-square deviations (RMSD) were employed to evaluate the difference between the experimental and the calculated results. The RMSD (y _i) and RMSD (T) are as follows:

$${\text{RMSDy}}_{\text{i}}\text{=}\sqrt{{{\displaystyle \sum }}_{\text{i=1}}^{\text{N}}\frac{{{\text{(y}}_{\text{i}}^{\text{exp}}{\text{-y}}_{\text{i}}^{\text{cal}}\text{)}}^{\text{2}}}{\text{N}}}$$ (20)

$$RMSD{T}_i=\sqrt{{{\displaystyle \sum }}_{i=1}^N\frac{{\left(T_i^{\exp }-T_i^{cal}\right)}^2}{N}}$$ (21)

The calculated RMSD values with the correlated parameters are presented in Table 8, which are less than 0.58 K and 0.006 respectively. As is shown in Table 8, the NRTL, Wilson and UNIQUAC models could correlate the VLE data for the three binary systems. Since the calculated results by the three model were graphically similar, the results correlated by the NRTL model were plotted in Figures 2-4.

Table 8
The interaction parameters and root-mean-square deviations (RMSD) for binary systems.

Model	aij	aji	bij / K	bji / K	RMSD(y1)	RMSD（T）
Cyclohexane (1) + Isopropyl chloroacetate (2)
NRTL	-2.7539	0.4169	1533.43	-395.50	0.0060	0.58
Wilson	0.2585	1.7588	53.88	-1074.49	0.0057	0.54
UNIQUAC	0.3081	0.1710	-348.10	84.15	0.0058	0.54
Isopropanol (1) + Isopropyl chloroacetate (2)
NRTL	-10.0839	20.3022	3438.09	-6918.72	0.0038	0.26
Wilson	-12.0894	5.4616	3991.10	-3936.35	0.0035	0.26
UNIQUAC	4.6921	-10.2046	-1827.72	3360.08	0.0037	0.23
Benzene (1) + Isopropyl chloroacetate (2)
NRTL	-10.2641	24.2028	3497.51	-8392.13	0.0064	0.23
Wilson	-16.4172	5.1950	5562.50	-1693.54	0.0043	0.17
UNIQUAC	4.8828	-12.9678	-1552.45	4364.27	0.0066	0.21

• ^a NRTL, τ_ij = α_ij + b_ij/T, the value of α_ij was set at 0.3 for binary systems.
• ^b UNIQUAC, τ_ij = exp(α_ij + b_ij/T).
• ^c Wilson, lnA_ij = α_ij + b_ij/T.

According to the residuals of temperature and vapor mole fraction, the reliability of VLE data measured for each system has been checked (Orchillés et al., 2017; Mathias, 2017; Ma et al., 2018). Since the values of RMSD by the NRTL model were relatively larger than those of the Wilson and UNIQUAC models, the residuals of temperature and vapor mole fraction were calculated based on the difference between experimental values and the calculated values in the NRTL model. The residuals for the vapor mole fraction and temperature are less than 0.016 and 0.010 and are presented in Figures 7 and 8. As shown in Figures. 7 and 8, the distributions of the vapor phase mole fraction and temperature residuals are randomly distributed around zero. The fluctuations of the vapor phase mole fraction and temperature residual values are within the range between -0.016 and 0.012, and -0.005 and 0.010 respectively.

Figure 7
Residual plot of vapor mole fraction for the three systems: ■, cyclohexane (1) + isopropyl chloroacetate (2); ●, isopropanol (1) + isopropyl chloroacetate (2); ▲, benzene (1) + isopropyl chloroacetate (2).

Figure 8
Residual plot of temperature for the three systems: ■, cyclohexane (1) + isopropyl chloroacetate (2); ●, isopropanol (1) + isopropyl chloroacetate (2); ▲, benzene (1) + isopropyl chloroacetate (2).

CONCLUSIONS

The VLE data for the binary solutions of isopropyl chloroacetate + cyclohexane, isopropyl chloroacetate + isopropanol and isopropyl chloroacetate + benzene were generated at 101.3 kPa. The calculated excess Gibbs energy results indicate that the three systems show positive deviations from Raoult′s law. The thermodynamic consistency test for the experimental data was checked by the Herington and van Ness methods, and the measured VLE data passed the consistency tests. The thermodynamic models NRTL, Wilson, and UNIQUAC were adopted to fit the measured VLE data for the investigated systems and the binary interaction parameters of the models were regressed. The RMSD values for the mole fraction of vapor phase and the temperature were all less than 0.58 K and 0.0066, respectively.

ACKNOWLEDGEMENTS

This work was supported by the Shandong Provincial Key Research & Development Project (2018GGX107001), National Natural Science Foundation of China (21878178) and Project of Shandong Province Higher Educational Science and Technology Program (J18KA072).

REFERENCES

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NOMENCLATURE

• T  Equilibrium temperature (K)
• p  Pressure (kPa)
• N  The point of the experimental data
• α  Non-randomness parameter in the NRTL model
• r  Area parameter of UNIQUAC
• q  Volume parameter of UNIQUAC
• z  Lattice coordination number in the UNIQUAC model
• θ  Area fraction in the UNIQUAC model
• u  Uncertainty
• x  Mole fraction in the liquid phase
• y  Mole fraction in the vapor phase
• φ_i  Fugacity coefficient of the vapor phase
• φ_i ^s  Fugacity coefficient at the saturated pressure
• γ  Activity coefficient
• V_i ^L  Liquid molar volume
• R  Universal gas constant (8.314 J.K^-1.mol^-1)
• p_i ^s  Saturation vapor pressure
• p_ci  Critical pressure of pure component
• a, b  Binary interaction parameters
• σ  Standard deviation
• i,j  Component i, j
• cal  Calculated property
• exp  Experimental property

Publication Dates

• Publication in this collection
  13 Jan 2020
• Date of issue
  Oct-Dec 2019

History

• Received
  01 Mar 2019
• Reviewed
  24 Apr 2019
• Accepted
  03 June 2019