Solubility of Dilute SO2 in Mixtures of N,N-Dimethylformamide +

Article pubs.acs.org/jced

Solubility of Dilute SO2 in Mixtures of N,N‑Dimethylformamide + Polyethylene Glycol 400 and the Density and Viscosity of the Mixtures Yanxia Niu,† Fei Gao,‡ Ruimin Zhu,† Shaoyang Sun,† and Xionghui Wei*,† †

Department of Applied Chemistry, College of Chemistry and Molecular Engineering, Peking University, Beijing 100871, China College of Chemical Engineering, Inner Mongolia University of Technology, Huhhot 010051, China

‡

S Supporting Information *

ABSTRACT: In this work, the isothermal gas−liquid equilibrium (GLE) data were measured for the system of polyethylene glycol 400 (PEG 400) + N,N-dimethylformamide (DMF) + SO2 + N2 at 308.15 K and 123 kPa with SO2 partial pressures in the range of (16.8 to 115) Pa. The Henry’s law constant (H′) and standard Gibbs free energy change (ΔG) were calculated from these GLE data. Furthermore, the densities and viscosities of binary mixtures of DMF + PEG 400 were also measured over the whole concentration range at T = (298.15 to 313.15) K. From the experimental data, including density and viscosity values, the excess molar volumes (VmE), and viscosity deviations (Δη), the calculated results are fitted to a Redlich−Kister equation to obtain the coefficients and estimate the standard deviations between the experimental and the calculated quantities. his co-workers10−18 carried out some studies on dilute SO2 in alcohol + water system in the latest several years. Our previous studies19 showed that polyethylene glycol 400 (PEG 400), with low vapor pressure, low toxicity, high chemical stability, and a low melting point, has a desirable solubility for SO2. However, its high viscosity may be a main barrier for application to industry in the future. Roizard et al.20,21 reported SO2 solubility in some organic solvents and found that N,N-dimethylformamide (DMF) has a strong absorption capability for SO2. But its high vapor pressure results in significant vaporization and solvent loss.22 Research23 shows that the carbonyl group of DMF can interact with the hydroxyl groups of ethylene glycol, which indicates that the mixture of DMF + PEG 400 will result in moderate viscosity and vapor pressure. Therefore, this work reported the gas−liquid equilibrium (GLE) data for dilute SO2 in various binary mixtures of DMF + PEG 400 at 308.15 K and 123 kPa. Moreover, the knowledge such as densities and viscosities of the DMF + PEG 400 solutions are also extremely

1. INTRODUCTION Air pollution has become a serious problem for years and has drawn worldwide attention. Sulfur dioxide (SO2) emitted from the burning of fossil fuels is a significant contributor to atmospheric pollution that threatens the environment and human health.1 Therefore, it is necessary to remove SO2 from gaseous streams before released. Many technologies of removing SO2 have been proposed, of which the conventional procedures, such as limestone scrubbing and ammonia scrubbing, have some inherent disadvantages, including high capital and operating costs, a larger water requirement, poor quality of byproduct, and secondary pollution.2,3 Because of the favorable absorption and desorption properties for acid gases in industrial processes, organic solvents have become the subject of increasing interest for many years.4−9 In previously reported works, most were focused on the solubility of SO2 in solvent within a relatively high range of SO2 partial pressure. For instance, Sciamanna and Lynn4 and Kurt et al.5 have reported the solubility data of SO2 in a few poly(ethylene glycols) ethers with the SO2 partial pressure range up to several bars. Yet the solubility data on dilute SO2, with the partial pressure less than 1 kPa, are scarce, so Wei and © 2013 American Chemical Society

Received: October 10, 2012 Accepted: January 23, 2013 Published: February 15, 2013 639

dx.doi.org/10.1021/je3011002 | J. Chem. Eng. Data 2013, 58, 639−647

Journal of Chemical & Engineering Data

Article

important for investigating the removal of SO2. However, a survey in the literature showed that these mixtures have not been studied in sufficient detail. Considering all of these facts, the densities and viscosities of binary mixtures of DMF + PEG 400 were measured over the whole concentration range in temperature range of (298.15 to 313.15) K and under atmospheric pressure. Meanwhile, the excess molar volumes (VmE) and viscosity deviations (Δη) were calculated.

2. EXPERIMENTAL SECTION 2.1. Materials. The analytical grade DMF and PEG 400 were obtained from Beijing Reagent Company (Beijing, China). The chemicals were dried over molecular sieves (type 4A) and degassed ultrasonically before use. The purity of DMF (99.5 %) and PEG 400 (99 %) was checked by measuring and comparing the densities and viscosities of the samples with corresponding literature values in the temperature range of (298.15 to 313.15) K. The measured results agreed reasonably well with the literature values24−38 and are shown in Table 1. Bidistilled water and chromatographic grade ethanol

Figure 1. Experimental setup of GLE measurement: (1) absorption bottle; (2) cold trap; (3) thermostatic bath; (4) gas circulatory pump; (5) GC; (6) regulating valve; (7) thermometer; (8) pressure meter; (9) SO2/N2 gas cylinder; (10) buffer; (11) waster gas treating bottle; (12) temperature-stabilizing water circulatory pump.

this work, only the gas phase (SO2/N2) was recycled by the gas circulatory pump (4) (type: PCF 5015 N-24 V; flow rate: 15 L·min−1; vacuum degree: 50 kPa. KV: 24 V, DC. Manufacturer: Chengdu Xinweichengkeji Co., Ltd., Chengdu, China), and the concentration of SO2 in gas phase was determined online using an Agilent GC (5) with PDF detector. Before experiment, the liquid used as absorbent is first put into the absorption bottle (1). Second, the mixtures gas (SO2/N2) from gas cylinder (9), through switching the regulating valves K1 and K2 (6), are poured into the bottom of absorption bottle and contact fully with the liquid. The residual gases out of absorption bottle are recycled in major by a gas circulatory pump to be absorbed more adequately and quickly by the solution, and only a small fraction is used for the online quantitative test of SO2 content at the same time. When the peak area responding the concentration of SO2 changes no longer with time, we consider the equilibrium to have arrived. Meanwhile, the peak areas are recorded, and the just enough liquid sample is taken from absorption bottle to measure the concentration of SO2 dissolved in the liquid phase. After performing one GLE experiment, the mixture gas is discharged out by switching the regulating valve (6) and passing buffer (10) and waster gas treating bottle containing alkaline solution (11). A series of GLE data are gained by repeating operation above. During the experiment process, liquid temperatures are controlled using the thermostatic bath (3) and a standard thermometer (7) with an uncertainty of 0.01 K. System pressures are inspected by a pressure meter (8) with the accuracy of ± 0.1 kPa. Data Treatment. The concentrations of SO2 in the gas phase were determined by a gas chromatograph (Agilent 6890N) equipped with a 2 m × 3.2 mm Porapak Q packed column, an FPD detector, and an HP6890 workstation. To determine the relationship between concentrations of SO2 and the response values of the gas chromatograph, a calibration curve was constructed using an external standard method. The sulfur(IV) concentration in the liquid phase (CSO2, mol·m−3) was examined by adding a known volume of liquid sample to another known volume of standard iodine solution. The excess iodine solution was back-titrated with the standard sodium thiosulfate solution.39 At the same time, the blank experiment was also done too, which is an improvement in comparison with the reported method.19 Each experimental value is an average of at least three measurements.

Table 1. Comparison of Experimental Densities (ρ) and Viscosities (η) of Polyethylene Glycol 400 and N,NDimethylformamide with Literature Values at Various Temperatures ρ/g·cm−3 T/K

expt.

298.15

1.1221

303.15

1.1181

308.15

1.1139

313.15

1.1101

298.15

0.9441

303.15

0.9394

308.15

0.9344

313.15

0.9294

η/mPa·s lit.

expt.

Polyethylene Glycol 400 1.121824 88.29 1.1216225 1.122626 1.118127 71.50 1.118024 1.118525 1.113926 52.56 1.113828 1.114224 1.110226 45.31 1.109827 N,N-Dimethylformamide 0.944223 0.820 0.943924 0.939425 0.767 0.939524 0.934423 0.721 0.934725 0.92954926 0.679 0.929223

lit. 89.7326 84.7129 69.8926 69.11124 51.6629

44.7726

0.813634 0.813535 0.767536 0.76537 0.721734 0.71131 0.67338

were used in present work. The certified standard gas of SO2 in N2 (8000 ppmv), which were purchased from the Beijing Gas Center, Peking University (China), were employed to determine the GLE data for DMF + PEG 400 mixtures with SO2. 2.2. Measurements. Binary mixtures were prepared by mass using an analytical balance (Sartorius BS 224S) with ± 0.0001 g accuracy. The possible error in the mole fraction for each binary mixture is less than ± 0.0001. 2.2.1. GLE Measurements. Apparatus and Experimental Procedure. The gas−liquid equilibrium (GLE) data for DMF + PEG 400 mixtures with SO2 were obtained using a dynamic analytic method, and the apparatus was given in Figure 1. In 640



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Table 2. GLE for DMF (1) + PEG 400 (2) + SO2 (3) + N2 (4) at 308.15 K and 123 kPa w1

106·ΦSO2

CSO2/mol·m−3

pSO2/Pa

w1

106·ΦSO2

CSO2/mol·m−3

pSO2/Pa

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.1001 0.1001 0.1001 0.1001 0.1001 0.1001 0.1950 0.1950 0.1950 0.1950 0.1950 0.1950 0.2998 0.2998 0.2998 0.2998 0.2998 0.2998 0.4000 0.4000 0.4000 0.4000 0.4000 0.4000 0.4973 0.4973

81.5 148 250 362 504 606 711 796 886 234 468 598 722 781 826 177 378 566 727 771 825 137 407 619 781 820 871 159 379 603 645 701 821 232 452

7.22 8.89 10.8 12.0 13.4 15.2 16.8 18.1 19.3 11.5 15.9 17.6 21.5 23.5 26.0 10.9 15.0 19.7 25.0 25.8 27.6 9.91 17.8 23.7 29.5 31.5 34.0 10.6 19.5 28.9 30.5 33.0 38.2 13.0 23.1

10.02 18.2 30.7 44.4 61.8 74.4 87.2 97.7 108 28.7 57.4 73.3 88.6 95.8 101 21.7 46.4 69.4 89.1 94.6 101 16.8 49.9 76.0 95.8 100 106 19.5 46.5 74.0 79.1 86.0 100 28.4 55.5

0.4973 0.4973 0.4973 0.6013 0.6013 0.6013 0.6013 0.6013 0.6013 0.7000 0.7000 0.7000 0.7000 0.7000 0.7000 0.7986 0.7986 0.7986 0.7986 0.7986 0.7986 0.9000 0.9000 0.9000 0.9000 0.9000 0.9000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

586 706 781 233 433 549 653 722 818 184 372 512 648 748 824 172 323 447 583 706 819 156 334 526 658 772 863 223 302 337 412 578 657 765 941

30.3 37.6 39.2 13.2 25.4 30.2 38.9 43.5 50.8 5.45 10.4 14.8 19.1 22.5 26.3 4.89 10.3 14.8 20.7 25.9 32.5 6.06 11.9 22.6 29.8 37.4 42.5 20.3 26.9 31.6 38.4 52.7 61.3 72.3 90.8

71.9 86.6 95.8 28.6 53.1 67.3 80.1 88.6 100 22.6 45.6 62.8 79.5 91.7 101 21.1 39.6 54.8 71.5 86.6 100 19.1 40.9 64.6 80.7 94.7 105 27.3 37.1 41.4 50.5 70.9 80.5 93.8 115

The sulfur(IV) concentration (CSO2, mol·m−3) was calculated from the following expression CSO2 = 1000·C Na 2S2O3(Vblank − V )/(2V ′)

viscometer, calibrated with high pure water and chromatographic grade ethanol at the experimental temperature whose viscosity and density were well-known, as has been described in literatures.40−45 The flow times of the solutions were recorded by an electronic timer with an accuracy of 0.01 s. The same circulating water bath used for density measurement was used for the viscosity measurement. Measurements were repeated at least 10 times at each temperature for all solutions, and the results were averaged. The kinematic viscosity (ν) was calculated from the following equation

(1)

where CNa2S2O3 is the concentration of the standard sodium thiosulfate solution (mol·L−3); Vblank is the volume of sodium thiosulfate solution consumed in blank experiment; V is the volume of sodium thiosulfate solution consumed in real sample determined; and V′ is the known volume of liquid sample to be determined. All units of volume are represented with mL. 2.2.2. Density and Viscosity Measurements. Densities of pure liquids and their mixtures were determined using a 25 cm3 bicapillary pycnometer. The volume of pycnometer was calibrated using distilled, deionized, and degassed water at each temperature. The pycnometer filled with liquid was kept in a thermostatic controlled and well-stirred water bath of sensitivity 0.01 K for 20 min to attain thermal equilibrium. The density measurements were carried out at T = (298.15 to 313.15) K. Each experimental density value was an average of at least three measurements. The uncertainty of the density measurement was estimated to be ± 0.01 %. The kinematic viscosity in both the pure components and their mixtures was measured using an Ubbelohde capillary

ν = At − B /t

(2)

where ν is the kinematic viscosity; t is flow time of liquids in the viscometer; and A and B are instrument constants calculated from measurements with the calibration fluids of water and ethanol. The absolute viscosity (η) was calculated by multiplying the kinematic viscosity by the corresponding density (η = νρ). It was estimated that the uncertainty of the viscosity measurement to be lower than ± 0.3 %.

3. RESULTS AND DISCUSSION 3.1. GLE Data. A series of GLE experiments for DMF (1) + PEG 400 (2) + SO2 (3) + N2 (4) were performed at 308.15 K 641



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sulfur(IV) concentration in liquid phase. From the reported data, it was found that the GLE curve is linear and nearly passes through the coordinate origin, which implies a physical process for SO2 dissolved in PEG 400. Yet there is a crossing point between the linearly lengthened CLE curve and the horizontal axis for this work data, which disclose that the absorbed process of SO2 by PEG 400 may involve both chemical absorption and physical absorption. This conclusion was proven to be correct from the desorption experiment performed using the N2 extraction method at the temperature of 338.15 K with a constant N2 flow rate of 2 L·min−1. The corresponding desorption result was given in Figure S1 (see the Supporting Information). From which, it can be seen that the process of SO2 desorption from PEG 400 is divided into two steps. Within 30 min the SO2 concentration in liquid reduces quickly, but the concentration changes slowly after that. Even the desorption time reaches 120 min, there is still 30 % of SO2 remaining in PEG 400. This is well in accordance with the GLE result in this work, so the data of this work is more reasonable. Figure 3 and Table 2 display the solubility of SO2 in pure DMF as more than in pure PEG 400 within the region of pressure investigated, and the solubility of DMF + PEG 400 mixtures are in the range of 13.9 mol·m−3 (pure PEG 400) to 47.1 mol·m−3 (pure DMF) when the volume fraction of SO2 in the gas phase is 5·10−4. Furthermore, it is also found that the absorption capabilities of the binary mixtures of DMF + PEG 400 present a maximum at w1 = 0.6013, which gave us important information to optimize the composition of mixture solutions during the absorption processes. As shown in Figure 3, the GLE curves are fitted with second-order polynomial functions (correlation coefficients, see the Supporting Information) when w1 is equal to 0.0000, 0.1001, 0.1950, 0.2998, and 0.4000, respectively, and the remaining GLE curves are well smoothed linearly within the regions investigated here. 3.2. Henry’s Law Constant and Standard Gibbs Free Energy. For a gas substance, its solubility in a liquid can be generally described in terms of Henry’s law, which is defined as:46−48

and 123 kPa. These GLE data are listed in Table 2, and the comparison on the GLE data of SO2 in pure PEG 400 between this work and previous work19 is shown in Figure 2. Other GLE curves were plotted in Figure 3.

Figure 2. Comparison on the GLE data of SO2 in PEG 400 between this work and previous work:19 △, the data of this work; □, the data of a previous work.

H ≡ lim

Cl → 0

p fl ≈ Cl Cl

(3)

where H is the Henry’s law constant, with the units of Pa·m3·mol−1, Cl is the molarity concentration of gas dissolved in the liquid phase, with the units of mol·m−3, f l is the fugacity of vapor in the liquid phase, and p is the pressure of the gas. Equation 3 implies that the solubility of gas which behaves nearly ideally is linearly related to the pressure. As shown in Figure 3, the experimental results for SO2 in the mixtures with the DMF mass fraction from 0.4973 to 1.0000 can be reasonably explained by Henry’s law. Therefore, those Henry’s law constants were acquired by calculating the linear slope of the GLE curves. Yet, Henry’s law constants are equal to the limiting slope as the pressure (or solubility) approaches zero for SO2 in other mixtures. According to ref 49, the dimensionless Henry’s law constant (H′) is defined as:

Figure 3. GLE curves for DMF (1) + PEG 400 (2) + SO2 (3) + N2 (4): ■, w1 = 0.0000; ●, w1 = 0.1001; ▲, w1 = 0.1950; ▼, w1 = 0.2998; ◀, w1 = 0.4000; □, w1 = 0.4973; △, w1 = 0.6013; ▽, w1 = 0.7000; ☆, w1 = 0.7986; ∗, w1 = 0.9000; ○, w1 = 1.0000; , the fitted line.

In Table 2, w1 is the mass fraction of DMF in the actual operation, ΦSO2 is the volume fraction of SO2 in the gas phase as ΦSO2 ≈ pSO2/(pSO2 + pN2 + pDMF + pPEG 400) = (pSO2/ Ptotal), pSO2 and Ptotal are the partial pressures of SO2 in the gas phase and the total pressure of the GLE system, respectively, and CSO2 denotes the molarity concentration of SO2 in the liquid phase. The GLE data were obtained with relative uncertainties within ± 2.5 % for SO2 concentration in the gas phase and ± 1 % for SO2 concentration in the liquid phase. According to Figure 2, it can be noted that there are differences in the two sets of data, which may be mainly attributed to the improved determination method for the

H = Cg /C l

(4)

where Cg is the gas concentration in gas phase, it can be derived from the ideal gas law (p = [n/V]RT = Cg·RT). Correlating these two expressions, the H′ is obtained as: 642



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H′ = H /RT

Table 4. Experimental Densities (ρ) of N,NDimethylformamide (1) + Polyethylene Glycol 400 (2)

(5) −1

−1

where R is the ideal gas constant (8.314 Pa·m ·mol ·K ) and T is the absolute temperature (K). Actually, for these systems with the GLE curves being linear, the phase equilibrium equation of SO2 is described as follows: 3

SO2 (g) ↔ SO2 (L)

ρ/g·cm−3

(6)

The equilibrium constant (K) is expressed as K = CSO2 /p

(7)

where CSO2 is the SO2 concentration dissolved in the liquid phase and p is the SO2 equilibrium pressure in gas phase. So the Henry’s law constant (H′) is the reciprocal of dimensionless equilibrium constant. The standard Gibbs free energy change (ΔG) when SO2 reaches phase equilibrium can be expressed as ΔG = −RT ln 1/H′

(8)

x1

T/K = 298.15

T/K = 303.15

T/K = 308.15

T/K = 313.15

0.0000 0.1204 0.2523 0.3796 0.5778 0.7007 0.7856 0.8446 0.8914 0.9274 0.9563 0.9801 1.0000

1.1221 1.1177 1.1110 1.1029 1.0841 1.0655 1.0471 1.0295 1.0111 0.9932 0.9770 0.9606 0.9441

1.1181 1.1136 1.1071 1.0990 1.0802 1.0618 1.0429 1.0253 1.0069 0.9898 0.9726 0.9559 0.9394

1.1139 1.1093 1.1026 1.0947 1.0759 1.0571 1.0383 1.0207 1.0021 0.9851 0.9679 0.9511 0.9344

1.1101 1.1055 1.0987 1.0907 1.0717 1.0531 1.0343 1.0163 0.9978 0.9805 0.9634 0.9465 0.9294

where ΔG denotes the standard Gibbs free energy of phase transition when SO2 reaches phase equilibrium. According to these formulas above, the Henry’s law constants (H′) and standard Gibbs free energy change (ΔG) can be calculated from the measured GLE data. All of these values are given in Table 3. Table 3. Henry’s Law Constants (H′) and Standard Gibbs Free Energy (ΔG) for SO2 in DMF + PEG 400 Mixtures at 308.15 K w1 0.0000 0.1001 0.1950 0.2998 0.4000 0.4973 0.6013 0.7000 0.7986 0.9000 1.0000

104·H′

ΔG/kJ·mol−1

± ± ± ± ± ± ± ± ± ± ±

−17.9 −18.3 −16.6 −17.2 −17.8 −19.5

0.559 12.0 8.32 10.0 8.36 9.37 7.76 15.3 12.0 9.47 4.97

0.373 0.456 0.282 0.278 0.103 0.255 0.257 0.508 0.577 0.476 0.0713

Figure 4. Experimental densities with mole fraction for N,Ndimethylformamide (1) + PEG 400 (2): □, 298.15 K; ○, 303.15 K; △, 308.15 K; +, 313.15 K.

VmE =

⎛ M x1M1 + x 2M 2 M ⎞ − ⎜⎜x1 1 + x 2 2 ⎟⎟ ρm ρ2 ⎠ ⎝ ρ1

(9)

where ρm is the density of the mixture and x1, ρ1, M1, x2, ρ2, and M2 represent the mole fractions, densities, and molecular weights of pure DMF and pure PEG 400, respectively. The results of VmE are listed in Table 5, and the dependence of VmE at temperatures (298.15 and 313.15) K is displayed in Figure 5. From Figure 5, VmE values are negative over the entire range of composition at all temperatures. The well-defined minimum was found at about x1 ≈ 0.70. Additionally, the VmE values become more negative at higher temperature. A Redlich−Kister relation was used to correlate the excess volume data.

Table 3 shows that the values of ΔG are always less than zero and more than −40 kJ·mol−1 in the liquids with the linear GLE curve trend, which reveal that the dissolving processes of SO2 in these liquids are spontaneous and reversible behavior at given conditions. The results inform us that SO2 can be captured by these liquids from a mixed gas stream and also recovered due to the reversible release. 3.3. Density and Viscosity Data. Experimental densities of DMF + PEG 400 mixtures at T = (298.15 to 313.15) K throughout the whole concentration range are listed in Table 4 and shown in Figure 4. Figure 4 shows that the density values decrease with the increasing DMF concentration. Meanwhile, the density values decrease with the augment of temperature at the same concentration. The excess mole volume (VmE) was calculated from density measurements using the following equation

n

VmE/cm 3·mol−1 = x1x 2 ∑ Ai (2x1 − 1)i i=0

(10)

where x1 is the mole fraction of DMF, x2 is the mole fraction of PEG 400, Ai are the polynomial coefficients which were evaluated from the least-squares method, and n is the polynomial degree. 643



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Table 5. Excess Molar Volumes (VmE) for N,NDimethylformamide (1) + Polyethylene Glycol 400 (2)

Table 7. Experimental Viscosities (η) of N,NDimethylformamide (1) + Polyethylene Glycol 400 (2)

VmE/cm3·mol−1

η/mPa·s

x1

T/K = 298.15

T/K = 303.15

T/K = 308.15

T/K = 313.15

x1

T/K = 298.15

T/K = 303.15

T/K = 308.15

T/K = 313.15

0.0000 0.1204 0.2523 0.3796 0.5778 0.7007 0.7856 0.8446 0.8914 0.9274 0.9563 0.9801 1.0000

0.000 −0.213 −0.271 −0.381 −0.501 −0.513 −0.508 −0.441 −0.323 −0.191 −0.179 −0.111 0.000

0.000 −0.194 −0.316 −0.432 −0.560 −0.607 −0.535 −0.474 −0.359 −0.308 −0.201 −0.108 0.000

0.000 −0.175 −0.259 −0.441 −0.589 −0.587 −0.543 −0.490 −0.360 −0.325 −0.222 −0.123 0.000

0.000 −0.189 −0.262 −0.439 −0.582 −0.636 −0.604 −0.511 −0.401 −0.343 −0.256 −0.153 0.000

0.0000 0.1204 0.2523 0.3796 0.5778 0.7007 0.7856 0.8446 0.8914 0.9274 0.9563 0.9801 1.0000

88.3 75.9 62.1 48.1 26.9 15.8 9.49 6.01 3.89 2.65 1.87 1.37 0.820

71.5 61.8 50.7 39.8 22.9 13.9 8.55 5.53 3.64 2.53 1.82 1.36 0.767

52.6 45.7 37.9 30.1 17.8 11.0 6.92 4.57 3.05 2.17 1.59 1.23 0.721

45.3 39.5 33.0 26.4 16.0 10.1 6.50 4.38 2.99 2.15 1.57 1.20 0.679

Figure 5. Excess molar volumes with mole fraction for N,Ndimethylformamide (1) + PEG 400 (2): □, 298.15 K; △, 313.15 K.

Figure 6. Experimental viscosities with mole fraction for N,Ndimethylformamide (1) + PEG 400 (2): □, 298.15 K; ○, 303.15 K; △, 308.15 K; +, 313.15 K.

The standard deviation values, σ, between the calculated and the experimental data points are obtained by the following equation E σ VmE = [∑ (Vcalc − VmE)2 /(N − m)]1/2

The experimental values of η for the various mixtures have been used to calculate the viscosity deviation (Δη), defined by the following equation

(11)

Δη = η − (x1η1 + x 2η2)

where N is the total number of experimental points and m is the number of Ai coefficients considered. The coefficients Ai and corresponding standard deviations, σ, are listed in Table 6. Experimental viscosities of the DMF + PEG 400 system at temperatures (298.15 to 313.15) K are listed in Table 7 and shown in Figure 6. In all cases, the viscosities decrease with the increasing DMF concentration and decrease with the increasing temperature at the same concentration.

(12)

where η is the viscosity of the mixtures, and x1, η1, x2, and η2 represent the mole fractions and the viscosities of pure DMF and pure PEG 400, respectively. The results of the viscosity deviation, Δη, are listed in Table 8 and plotted in Figure 7. From Figure 7, Δη values are negative over the entire range of composition and at all temperatures. The well-defined minimum is at about x1 ≈ 0.70. Additionally, the Δη values become less negative with the increasing temperatures.

Table 6. Coefficients and Standard Deviations of Excess Molar Volumes, VmE, for N,N-Dimethylformamide (1) + Polyethylene Glycol 400 (2) T/K

A0

A1

A2

A3

A4

σ/cm3·mol−1

298.15 303.15 308.15 313.15

−1.781 −2.090 −2.215 −2.173

−1.439 −1.373 −1.558 −1.782

−1.266 −0.716 0.891 0.070

1.018 0.150 0.066 0.265

−0.182 −0.906 −3.166 −2.481

0.0275 0.0144 0.0180 0.0239

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Table 8. Viscosity Deviations (Δη) for N,NDimethylformamide (1) + Polyethylene Glycol 400 (2)

system of DMF + PEG 400 at temperatures (298.15 to 313.15) K. The GLE data show that the solubility of SO2 in pure DMF is more than in pure PEG 400 within the region of partial pressure investigated, and the absorption capabilities of the binary mixture of DMF + PEG 400 present a maximum at w1 = 0.6013. Furthermore, the Henry’s law constant (H′) and standard Gibbs free energy change (ΔG) were calculated from the GLE data. The values of ΔG are in the range of (−40 to 0) kJ·mol−1 in the liquids with the linear GLE curve trend, which reveal that the dissolving processes of SO2 in these liquids are spontaneous and have reversible behavior at given conditions. The experimental data on the densities and viscosities of the binary system of DMF + PEG 400 have been used to compute excess properties of the system. The calculated excess molar volumes (VmE) and viscosity deviations (Δη) values for DMF + PEG 400 mixtures are negative at all temperatures and compositions. The minimum value of the excess mole volume and viscosity deviation is at about x1 ≈ 0.70.

Δη/mPa·s x1

T/K = 298.15

T/K = 303.15

T/K = 308.15

T/K = 313.15

0.0000 0.1204 0.2523 0.3796 0.5778 0.7007 0.7856 0.8446 0.8914 0.9274 0.9563 0.9801 1.0000

0.000 −1.867 −4.129 −6.993 −10.854 −11.203 −10.086 −8.404 −6.430 −4.521 −2.773 −1.191 0.000

0.000 −1.197 −2.969 −4.850 −7.730 −8.037 −7.382 −6.229 −4.809 −3.372 −2.038 −0.815 0.000

0.000 −0.631 −1.592 −2.807 −4.824 −5.248 −4.924 −4.213 −3.305 −2.317 −1.398 −0.523 0.000

0.000 −0.462 −1.051 −1.962 −3.518 −3.934 −3.746 −3.233 −2.535 −1.768 −1.059 −0.367 0.000

■

ASSOCIATED CONTENT

S Supporting Information *

Desorption result on SO2 out of PEG 400 at the temperature of 338.15 K and under the constant nitrogen flow rate of 2 L·min−1 (Figure S1); fitting functions and correlation coefficients on the GLE curves (Table S1). This material is available free of charge via the Internet at http://pubs.acs.org.

■

AUTHOR INFORMATION

Corresponding Author

*Telephone: +86-010-62751529. Fax: +86-010-62670662. Email: [email protected]. Funding

This work was supported by Boyuan Hengsheng HighTechnology Co., Ltd., Beijing, China. Notes

The authors declare no competing financial interest.

■

Figure 7. Viscosity deviations with mole fraction for N,Ndimethylformamide (1) + PEG 400 (2): □, 298.15 K; ○, 303.15 K; △, 308.15 K; +, 313.15 K.

The viscosity deviations were also represented by the Redlich−Kister equation as follows n

Δη /mPa·s = x1x 2 ∑ Bi (2x1 − 1)i

(13)

i=0

REFERENCES

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The coefficients Bi and the standard deviation σ are presented in Table 9.

4. CONCLUSIONS This paper reports the fundamental data on the isothermal GLE data of dilute SO2 in DMF + PEG 400 mixtures at 308.15 K and 123 kPa and the densities and viscosities of the binary

Table 9. Coefficients and Standard Deviations of Viscosity Deviation (Δη) for N,N-Dimethylformamide (1) + Polyethylene Glycol 400 (2) T/K

B0

B1

B2

B3

B4

σ/mPa·s

298.15 303.15 308.15 313.15

−38.495 −27.055 −16.458 −11.819

−38.469 −27.757 −20.336 −16.323

−5.953 −9.124 −8.379 −7.794

11.159 4.767 3.426 3.425

0.205 5.641 4.077 3.369

0.0718 0.0856 0.0659 0.0620

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Solubility of Dilute SO2 in Mixtures of N,N-Dimethylformamide +

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