Liquid-liquid equilibria data and thermodynamic modeling for ternary system of mesityl oxide + diethoxymethane + water at 303.15, 313.15, 323.15 K under 101.325

doi:10.21203/rs.3.rs-3425562/v1

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Liquid-liquid equilibria data and thermodynamic modeling for ternary system of mesityl oxide + diethoxymethane + water at 303.15, 313.15, 323.15 K under 101.325

https://doi.org/10.21203/rs.3.rs-3425562/v1

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published 19 Sep, 2024

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Liquid-liquid equilibria (LLE) data for the ternary mixture of mesityl oxide + diethoxymethane + water were measured at 303.15, 313.15, 323.15 K under 101.325 kPa. The extraction ability of mesityl oxide for separating diethoxymethane from water was evaluated using distribution coefficients (D) and selectivity coefficients (S). The reliability of experimental data of the ternary mixture was validated by the Bachman and Hand method, in which the linear correlation (R²) ≥ 0.99. This experimental data were correlated with the NRTL and UNIQUAC thermodynamic model with all of the RMSD values below 0.47% meaning that the ternary system had satisfactory agreement at temperatures studied. Both models successfully correlated experimental data.

Liquid-liquid equilibria

mesityl oxide

diethoxymethane

NRTL

UNIQUAC

Diethoxymethane is an important organic compound, which is widely used in the chemical industry, pharmaceutical extraction, and organic intermediate synthesis. Due to its low boiling point, low affinity with water, and good stability, diethoxymethane is usually used as a solvent for phase transfer reactions, sodium hydride reactions and copper catalyzed conjugate addition reactions[1]. Diethoxymethane is a functional diesel additive that can increase the octane number and reduce carbon monoxide emissions[2]. At present, the synthesis of diethoxymethane from formaldehyde and ethanol is the most economical and reasonable method, but diethoxymethane will form an azeotropic mixture with the byproduct water and the ethanol[3], and it is difficult to simply obtain high-purity diethoxymethane. The solvent extraction method overcomes the influence of azeotrope well.

Solvent extraction is one of the effective separation methods that is widely used in various types of applications, including separation of chemistry[4], wastewater treatment[4–7], pharmaceutical processes[7–9], and food engineering[10, 11]. The availability of accurate liquid-liquid equilibrium (LLE) data is critical to the design and management of the separation processes and equipment. Therefore, to investigate the thermodynamic behavior of multiple systems at different temperatures, the phase equilibrium, and properties of the mixtures are investigated by many researchers[12, 13]. After screening, it was found that mesityl oxide was a kind of dephenolic extractant with excellent performance[14]. Mesityl Oxide is a medium boiling point strong solvent, often used as nitrous acid cellulose and a variety of resins, especially vinyl resins and paint solvents. By consulting the literature, it is known that there is no report on the equilibrium distribution of diethoxymethane in water and the treatment of diethoxymethane in industry.

This paper mainly studies the effect of temperature on extraction. The liquid-liquid equilibrium data of mesityl oxide + diethoxymethane + water ternary systems were measured at 303.15, 313.15, 323.15 K. The distribution coefficients (D) and selectivity coefficients (S) were used to evaluate the ability of mesityl oxide to extract diethoxymethane from water. The Bachman[15] and Hand[16] were used to analyze the reliability of the experimental data. The thermodynamic models NRTL[17] and UNIQUAC[18]. were associated with phase equilibrium experimental data to obtain binary interaction parameters. The accuracy of the two methods was compared by calculating the root mean square deviation (RMSD).

2.1. Materials

The details information of chemical reagents used in this work are listed in Table 1. In this study, homemade distilled water was used. The purity of these chemicals was evaluated by gas chromatography (GC6820, Agilent Technologies). There were no note-worthy impurity peaks of the spectrum, so all substances were used straightforwardly and were not used further purification.

Table 1

Chemical reagents
Compound	CAS Reg. NO.	Supplier	Mass fraction purity
Mesityl oxide	141-79-7	Aladdin reagent company	༞0.99 ^b
Diethoxymethane	462-95-3	Aladdin reagent company	༞0.995 ^b
Distilled water	7732-18-5	Self-made	≥ 0.990

^a Confirmed by gas chromatography.

^b The purity of the reagents provided by the supplier.

2.2. Experimental apparatus and procedures

All reagents were prepared by weighing the AL204 analytic balance with precision of ± 0.0001 g. The LLE experiment was performed using a 100 ml equilibrium glass cell equipped with a water bath in which temperature was kept constant at 303.15, 313.15, and 323.15 K to maintain a constant temperature. The temperature of the cell was controlled by a thermostat bath with precision of ± 0.1 K. First, the mass ratio of mesityl oxide to water was 1:1 as the initial component of the solution. Then the diethoxymethane was added to the equilibrium cell and stirred at a certain temperature to make it completely mixed. After 2 hours of stirring, the mixture was stopped and then stood at a constant temperature for 8 hours to achieve thermodynamic equilibrium and phase separation. Finally, the aqueous and organic phases were sampled and analyzed.

2.3. Analysis

Each of the liquid phases separated samples was analyzed using the Gas chromatography Agilent 6820 GC by applying an internal standard method. Isopropanol was used as the internal standard substance. The device was used with a thermal conductivity detector (TCD) and Porapak N column (length of 3 m, 3mm id) and with hydrogen as a carrier gas at the rate of 60 mL∙min^− 1 for analysis. Meanwhile, the injection amount of each sample was 0.6 uL. The temperatures of the injector and the detector were 493.15 K. The temperature program started at 373.15 K and hold for 1 min, followed by a 10 K per minute ramp to 453.15 K and maintained at this temperature for 2 min. The process of sampling analysis was repeated at least three times. The Relative standard deviation was measured to be less than 1% to ensure the precision of the equilibrium composition of each phase.

3.1. Experimental LLE data

LLE data for the ternary system of mesityl oxide + diethoxymethane + water in the organic and aqueous phases at 303.15, 313.15, and 323.15 K are shown in Table 2. The reported values are mass fractions measured by gas chromatography. The experimental LLE phase diagrams of the ternary system are shown in Figs. 1. The distribution coefficient (D) and selectivity coefficients (S) are the essential parameters available for conducting liquid-liquid equilibrium operations, in particular, to check the suitability of a solvent for liquid extraction[4]. The distribution coefficient and selectivity were calculated with the following formula:

$$D={w}_{2}^{\text{I}}/{w}_{2}^{\text{I}\text{I}}$$

$$S=\left({w}_{2}^{\text{I}}/{w}_{2}^{\text{I}\text{I}}\right)/\left({w}_{3}^{\text{I}}/{w}_{3}^{\text{I}\text{I}}\right)$$

where w₂ and w₃ are mass fractions of diethoxymethane and water in organic(Ⅰ), and aqueous(Ⅱ) phases, respectively. The distribution coefficient and selectivity values are reported in Table 2. The distribution coefficient changes with the increase of diethoxymethane content in water at different temperatures, as shown in Fig. 2 and also, and the selectivity is shown in Fig. 3.

Table 2

Experimental LLE data in mass fraction for mesityl oxide (1) + diethoxymethane (2) + water (3) ternary system at 303.15, 313.15, 323.15 K at 101.3 kPa, together with the distribution coefficient (D) and selectivity coefficients (S). ^a
T / K	FEED		Organic phase (I)		Aqueous phase (II)		D	S
T / K	${w}_{1}^{\text{I}}$	${w}_{2}^{\text{I}}$	${w}_{1}^{\text{I}}$	${w}_{2}^{\text{I}}$	${w}_{1}^{\text{I}\text{I}}$	${w}_{2}^{\text{I}\text{I}}$	D	S
303.15	0.4936	0	0.9645	0	0.0226	0	-	-
	0.4767	0.0176	0.9318	0.0333	0.0215	0.0019	17.49	489.52
	0.4457	0.0486	0.8725	0.0930	0.0189	0.0042	21.98	622.22
	0.4315	0.0629	0.8455	0.1206	0.0175	0.0052	23.39	673.99
	0.4146	0.0793	0.8138	0.1526	0.0153	0.0060	25.50	744.09
	0.3976	0.0972	0.7805	0.1872	0.0147	0.0072	26.00	786.06
	0.3761	0.1194	0.7386	0.2305	0.0137	0.0082	27.95	883.11
	0.3475	0.1482	0.6847	0.2865	0.0104	0.0099	28.94	982.23
	0.3302	0.1662	0.6502	0.3217	0.0102	0.0107	30.02	1048.59
	0.3125	0.1838	0.6155	0.3565	0.0095	0.0111	32.03	1120.85
313.15	0.4916	0	0.9612	0	0.0219	0	-	-
	0.4769	0.0156	0.9327	0.0299	0.0212	0.0014	21.88	572.46
	0.4614	0.0318	0.9022	0.0611	0.0207	0.0026	23.50	624.47
	0.4467	0.0457	0.8744	0.0882	0.0190	0.0033	26.93	704.05
	0.4317	0.0615	0.8460	0.1187	0.0175	0.0043	27.35	757.98
	0.3570	0.1381	0.7012	0.2673	0.0128	0.0089	29.94	928.98
	0.3560	0.1395	0.6997	0.2700	0.0123	0.0090	29.96	968.00
	0.3300	0.1658	0.6482	0.3217	0.0117	0.0099	32.48	1057.56
	0.3134	0.1823	0.6161	0.3541	0.0107	0.0104	33.93	1114.13
	0.3003	0.1957	0.5902	0.3807	0.0103	0.0106	35.74	1202.62
323.15	0.4902	0	0.9617	0	0.0186	0	-	-
	0.4751	0.0158	0.9318	0.0305	0.0184	0.0010	30.33	789.75
	0.4654	0.0258	0.9129	0.0500	0.0180	0.0016	31.04	818.46
	0.4461	0.0458	0.8750	0.0887	0.0172	0.0028	31.54	853.26
	0.4324	0.0601	0.8486	0.1166	0.0162	0.0036	32.45	914.21
	0.4162	0.0764	0.8177	0.1486	0.0148	0.0043	34.64	1007.11
	0.4000	0.0928	0.7867	0.1806	0.0133	0.0050	36.21	1087.27
	0.3800	0.1137	0.7476	0.2215	0.0124	0.0060	37.20	1179.58
	0.3598	0.1337	0.7091	0.2606	0.0104	0.0068	38.30	1244.69
	0.3113	0.1839	0.6134	0.3592	0.0092	0.0087	41.26	1479.15

^a Standard uncertainties u are u(T) = 0.1 K, u(p) = 0.1 kPa, u(w) = 0.0015.

Table 3 lists the experimental and literature values of the solubility of water and solvents, which shows that the experimental values are in good agreement with the literature values. It is related to the method of use or measurement accuracy [19].

Table 3

The solubility data (mole fraction) of the experimental and literature values.
T/K	Water in solvent			Solvent in water
T/K	w_exp.	w_lit.	δ	w_exp.	w_lit.	δ
303.2	0.0355	0.0367[20]	-3.39	0.0226	0.0266[20]	-17.83
		0.0409[21]	-15.19		0.0230[21]	-1.65
		0.0392 ^b [22]	-10.38		0.0240 ^b [22]	-6.28
313.2	0.0388	0.0382[20]	1.48	0.0219	0.0256[20]	-16.84
		0.0420[22]	-8.25		0.0214[22]	2.30
		0.0417[21]	-7.45		0.0219[21]	-0.10
323.2	0.0383	0.0451[21]	-17.75	0.0186	0.0203[21]	-9.14
323.2	0.0383	0.0455[22]	-18.80	0.0186	0.0196[22]	-5.38
^a The binary data were taken from the interpolated data in the literature. [22]

^b Relative deviation: δ = $100\times ({x}_{exp}-{x}_{lit})/{x}_{exp}$.

The LLE phase diagrams of the ternary system are shown in Fig. 1. It can be seen from the figure that the feed is on the tie-line and follows the principle of leverage, indicating that the LLE data complies with the law of conservation of mass [23, 24]. Meanwhile, since diethoxymethane + mesityi oxide is a miscible binary mixture, and water + mesityl oxide and water + diethoxymethane are partially miscible binary mixtures, the system conforms to Treybal's type II ternary phase behavior [25].

As shown in Table 2 and Fig. 3, the selectivity coefficients are all greater than 1, indicating that the mesityl oxide has a good selective extraction effect on diethoxymethane. As can be seen from Figs. 2 and 3, with the increase of diethoxymethane in the organic phase, D and S of the mesityl oxide system increase simultaneously. At the same time, it can be seen from the figure that the D and S of the mesityl oxide system increase with the increase in temperature, indicating that the increase in temperature is conducive to improving the selective extraction ability of the mesityl oxide system. It can be seen from Fig. 2 and Fig. 3 that the extraction capacity of mesityl oxide to extract diethoxymethane from water is found to be ethyl acetate, mesityl oxide, MTBE, MIBK, isoamyl alcohol by comparison with the literature values. The selective order is MTBE, ethyl acetate, mesityl oxide, MIBK, and isoamyl alcohol.

3.2. Reliability of LLE data

The reliability of the experimental data was verified by the Bachman[15] and Hand[16] equation. The expressions of Bachman and Hand are as follows:

$${w}_{1}^{I}=A+B\left(\frac{{w}_{1}^{I}}{{w}_{3}^{II}}\right)$$

$$\text{l}\text{n}\left(\frac{{w}_{2}^{\text{I}}}{{w}_{1}^{\text{I}}}\right)=C+D\text{l}\text{n}\left(\frac{{w}_{2}^{\text{I}\text{I}}}{{w}_{3}^{\text{I}\text{I}}}\right)$$

where A and B are Bachman parameters, and C and D are the Hand parameters. ${w}_{1}^{\text{I}}$ and ${w}_{2}^{\text{I}}$denote the mass fractions of mesityl oxide and diethoxymethane in the organic phase; while ${w}_{2}^{\text{I}\text{I}}$ and ${w}_{3}^{\text{I}\text{I}}$ denote the mass fractions of diethoxymethane and water in the aqueous phase. The parameters and linear coefficient (R²) of equations A, B, C, and D were obtained through fitting, and their values were shown in Table 4, R² greater than 0.99, indicating that the experimental data had good reliability.

Table 4

Bachman and Hand parameters at various temperatures.
T / K	Bachman			Hand
T / K	A	B	R²	C	D	R²
303.15	0.0049	0.9719	1.0000	6.2977	1.5582	0.9931
313.15	0.0022	0.9752	1.0000	5.8547	1.4294	0.9915
323.15	-0.0286	1.0197	0.9907	5.5005	1.3134	0.9889

3.3. Thermodynamic modeling

In this study, the NRTL[17] and UNIQUAC[18] thermodynamic models have been used to correlate with the experimental LLE data.

In this work, the optimum binary interaction parameters and NRTL non-randomness parameters were obtained by fitting experimental LLE data to the NRTL and UNIQUAC thermodynamic models. The UNIQUAC structural parameters r (molecular-geometric volume) and q (molecular-geometric surface) were taken from the Aspen Plus V11 physical properties data bank. The values r and q used in the UNIQUAC equation were provided in Table 5.

Table 5

The UNIQUAC structural parameters (r and q) for pure components.
Component	r	q
Mesityl oxide	3.8600	4.3632
Diethoxymethane	3.7960	4.3131
Water	0.9200	1.4000

The corresponding binary interaction parameters in the NRTL and UNIQUAC models were calculated by minimizing the objective function(OF)[27]:

$$\text{O}\text{F}=\sum _{k=1}^{M}\sum _{j=1}^{2}\sum _{i=1}^{3}\left[{\left({w}_{ijk}^{exp}-{w}_{ijk}^{cal}\right)}^{2}\right]$$

where w^exp and w^cal are the experimental and calculated mass fractions. Subscripts i, j, and k refer to the components i in phase j on tie-line k. and M is the number of tie-lines.

The accuracy of the two models was evaluated by the root mean square deviation (RMSD), and the equation is as follows [28]:

$$RMSD\left(\text{\%}\right)=100\times {\left\{\sum _{k=1}^{M}\sum _{j=1}^{2}\sum _{i=1}^{3}{\left({w}_{ijk}^{exp}-{w}_{ijk}^{cal}\right)}^{2}/6M\right\}}^{1/2}$$

where, k, j, i, M, w^exp, w^cal are the same as those of Eq. (5). The RMSD of both models at different temperatures is given in Table 6. which is less than 0.47%. It shows that both models can be applied to this system. Meanwhile, In Figs. 1–3, the calculated values of the two models are compared with the experimental data, which further proves that the two models can be applied to the system.

Table 6

The NRTL and UNIQUAC binary interaction parameters for the studied ternary systems.
model	i-j	a_ij	b_ij/K	a_ji	b_ji/K	α	RMSD/%
NRTL	1–2	-25.16	8642.43	9.29	-3313.33	0.3	0.4730
	1–3	-0.33	491.90	5.40	-151.68	0.3
	2–3	6.25	-1381.74	10.74	-2036.59	0.3
UNIQUAC	1–2	2.43	-592.07	-13.63	-6848.46		0.3129
	1–3	-0.49	-155.36	-0.77	77.04
	2–3	-3.63	18.40	-0.34	-44.07

LLE experimental data of mesityl oxide + diethoxymethane + water system at 303.15, 313.15, and 323.15K were represented. The results indicated that mesityl oxide had a better extraction effect on diethoxymethane. In the experimental temperature range, as the temperature increased, the selectivity and distribution coefficients gradually increased. It shows that the extraction effect of mesityl oxide increases with increasing temperature. Meanwhile, the selectivity was greater than 1, which indicated that the distribution at each of these temperatures was satisfactory. The R²༞0.99 for Bachman and Hand equation validates LLE experimental data. The NRTL and UNIQUAC models used for experimental data correlations are well to the mesityl oxide + diethoxymethane + water system. Binary interactions were represented for both models. By calculating the RMSD values, which were lower than 0.47% for both models, the use of these two models found quite satisfactory results.

Conflict of interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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Liquid-liquid equilibria data and thermodynamic modeling for ternary system of mesityl oxide + diethoxymethane + water at 303.15, 313.15, 323.15 K under 101.325

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Abstract

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1. Introduction

2. Experimental

2.1. Materials

2.2. Experimental apparatus and procedures

2.3. Analysis

3. Results and discussion

3.1. Experimental LLE data

3.2. Reliability of LLE data

3.3. Thermodynamic modeling

4. Conclusions

Declarations

References

Additional Declarations

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