Comment/Reply pubs.acs.org/jced
Comments on “Experimental Measurements of Vapor−Liquid Equilibrium Data for the Binary Systems of Methanol + 2‑Butyl Acetate, 2‑Butyl Alcohol + 2‑Butyl Acetate, and Methyl Acetate + 2Butyl Acetate at 101.33 kPa” Jaime Wisniak,*,† José R. Pérez-Correa,‡ Andrés Mejía,§ and Hugo Segura§ †
Department of Chemical Engineering, Ben-Gurion University of the Negev, Beer-Sheva 84105, Israel Escuela de Ingeniería, Departamento de Ingeniería Química y Bioprocesos, Pontificia Universidad Católica de Chile, Macul, Santiago 7820436, Chile § Departamento de Ingeniería Química, Universidad de Concepción, Concepción 4070386, Chile ‡
I
n the past years there have been an increasing number of papers about isobaric vapor−liquid equilibrium (VLE) data, which use the Herington test1 to determine the thermodynamic consistency of the data. This is most unfortunate because the Herington procedure has been proven to be inappropriate for this purpose.2 In addition, the test is being used in the wrong manner, leading to declare as consistent, data that are inconsistent according to the Herington criterion. An example of this situation is the paper recently published by Wang et al.3 reporting atmospheric vapor−liquid equilibrium (VLE) data for the binary systems methanol (1) + 2butyl acetate (2), 2-butyl alcohol (3) + 2-butyl acetate (2), and methyl acetate (4) + 2-butyl acetate (2). According to the authors, their VLE data were accurate because they satisfy the Herington’s integral consistency. The purpose of this contribution is to show not only that the data reported do not satisfy Herington’s test but also that the analysis of the data presents incoherencies and inaccuracies that become evident when they are analyzed in depth. (a). The Herington Test. Herington’s test is based on an attempt to evaluate the right-hand side of the following equation,
∫0
1
ln
γ1 γ2
dx1 =
∫T
T10
0 2
ΔH dT RT 2
in order to avoid (as shown below) the data becoming arbitrarily consistent or inconsistent. According to Herington (eq 11 in ref 1), the right-hand side of eq 1 satisfies the following constraint
∫T
0 2
|A+| − |A −| |A+| + |A −|
(1)
(2)
where A+ and A− represent the positive and negative areas of the plot (ln γ1/γ2) vs x1. Since one of these two areas will be smaller than the other, making D positive or negative according to which component is assigned the index 1, the value of D is always taken to be positive, D=
|A+| − |A −| |A+| + |A −|
(4)
Received: July 3, 2013 Accepted: September 30, 2013
(3) © XXXX American Chemical Society
ΔT ΔH dT < 150 max = J 2 Tmin RT
where ΔTmax and Tmin represent the maximum difference in boiling points and the minimum boiling point temperature (both in Kelvin), respectively, present in the VLE of the system. Herington declares the data to be consistent if |D| < J or |D − J| < 10 (eq 15 in ref 1) and not as used incorrectly by Wang et al.,3 that is, (D − J) < 10. It should be noted that the value of J, by its proper nature, increases as the difference in the boiling points of the pure components (T20 − T10) becomes larger. Consequently, following Wang et al.,3 J would allow a larger error in the experimental data and still declare the data consistent because (D − J) would become more negative, as calculated by the authors for two of the three systems they reported. A correct application of the Herington test to the numbers reported by Wang et al.3 indicates that |D − J| = 18.12 for the system methanol (1) + 2-butyl acetate (2) and |D − J| = 22.42 for the system methyl acetate (4) + 2-butyl acetate (2) and, hence, the data of these two systems are not consistent according to Herington. (b). Comments about Data Treatment and Reduction. Wang et al.3 used the γ − ϕ approach for calculating liquid phase properties. However, the information provided in their paper is not sufficient for calculating the reported activity coefficients, which are extremely important for qualitatively analyzing the coherency of the VLE data. In general, it is recommendable practice to report the second virial coef f icient data f rom which the activity coef ficients data were calculated. This is so because, although the calculation of virial coefficients from correlations is a standard procedure for treating vapor phase data, precautions have to be taken in order to avoid possible inaccuracies in the calculated activity coefficients of mixtures
which, according to the general Gibbs−Duhem equation, expresses the effect of the heat of mixing (ΔH) on the value of the ratio of the activity coefficients (ln γ1/γ2) in isobaric liquid mixtures. A plot of the left-hand side of eq 1 leads to the following definition of parameter D: D=
T10
A
dx.doi.org/10.1021/je400624t | J. Chem. Eng. Data XXXX, XXX, XXX−XXX
Journal of Chemical & Engineering Data
Comment/Reply
Table 1. Pure Component Data and Parameters Used in Tsonopoulos Correlation for Predicting Second Virial Coefficients Tc/K
component methanol 2-butanol methyl acetate 2-butyl acetate a
ω
Pc/bar a
a
512.50 536.20a 506.55a 561.00b
80.84 42.02a 47.50a 31.70b
102 a
Zc a
0.566 0.577a 0.331a 0.395a
a
0.222 0.254a 0.257a 0.264a
103 b c
8.780 0.000 −1.120d −0.762d
56.0c 0.0 0.0d 0.0d
Taken from Daubert and Danner.11 bTaken from Zhang et al.10 cRecommended by Tsonopoulos et al.8 dRecommended by Tsonopoulos et al.9
The recalculated activity coefficients are shown in Figures 1 and 2. According to the results reported in these figures, we can
characterized by large differences in boiling temperatures. Accordingly, the input data reported in Table 1 are reliable for accurately predicting the experimental second virial coefficient data of pure methanol,4 2-butanol,5 and methyl acetate6 according to Tsonopoulos correlation.7−9 To the best of our knowledge, no experimental data have been reported for 2butyl acetate so, in this case, predictions have been performed using Tsonopoulos’ recommendations for methyl acetate. In addition, as pointed out by Wang et al.,3 the vapor pressure data of 2-butyl acetate were taken from a report by Zhang et al.,10 according to which the experimental data were correlated by the following equation ln p20‐ butylacetate /MPa = 38.7855 −
6098 T /K
− 4.2398 × ln(T /K) + 2.1506 ·10−8(T /K)6
(5)
Equation 5 should replace the correlation wrongly reported by Wang et al.,3 and is equivalent to the vapor pressure correlation reported in ref 11 (which seems to be the unrecognized original source). For data treatment purposes, eq 5 may be conveniently (and accurately) simplified to the following Antoine’s type correlation log10 p20‐ butylacetate /kPa = 6.41703 −
1749.60 (T /K) − 49.50
(6)
Figure 1. Activity coefficient plot for the system methanol (1) + 2butyl acetate (2) at 101.33 kPa: blue ○,□, component 1 and 2, respectively, as recalculated in this work; red ●,■, component 1 and 2, respectively, as reported by Wang et al.3
which is valid over the temperature range of the VLE data reported in ref 3 (386 K > T > 329 K). Compared to eq 5, eq 6 predicts the vapor pressures of 2-butyl acetate with a negligible average deviation in pressure (∼ 0.01 %). As pointed out by Wang et al.,3 the activity coefficient γi for each one of the reported binaries may be determined from the relationship ln γi = ln
yp i xipi0
+
conclude that there is a large discrepancy between the present activity coefficients and those calculated by Wang et al.3 Moreover, it is interesting to note that the major discrepancies come when we compare the activity coefficient data of 2-butyl acetate in all the sets of binaries. In addition: • In the case of Figure 1, we observe that the activity coefficients of methanol calculated by Wang et al.3 do not asymptotically tend to 1 as the component becomes concentrated, a condition that seems to be better satisfied by the recalculated values. In addition, from Figure 1 it is also clear that the recalculated activity coefficients of 2-butyl acetate present an incoherent minimum which is not reflected by a maximum of γ1. • In the case of Figure 2, we can see that the activity coefficients calculated by Wang et al.3 asymptotically tend to 1 using the same vapor pressure data used in the previous case. However, contrary to the results of these authors, the recalculated activity coefficients of 2-butyl acetate negatively deviate from ideal behavior and, surprisingly, they do not intersect the curve of activity coefficients of methyl acetate thus suggesting a major inconsistency.
(Bii − ViL) p + yj2 (2Bij − Bjj − Bii ) RT RT (7)
pi0
where p is the total pressure and is the pure component vapor pressure, R is the universal gas constant, T is the equilibrium temperature, and xi and yi are the mole fractions of component i in the liquid and the vapor phases, respectively. ViL is the liquid molar volume of component i, Bii and Bjj are the second virial coefficients of the pure gases, and Bij is the cross second virial coefficient. In this work, and following the recommendations of Wang et al.,3 liquid molar volumes were estimated from the correlation proposed by Rackett.12 Second virial coefficients, in turn, were estimated from Tsonopoulos correlation7−9 using the properties and parameters reported in Table 1. Pure component vapor pressure correlations have been taken from Wang et al.,3 the exception being the case of 2-butyl acetate whose vapor pressure data have been predicted from eq 6. B
dx.doi.org/10.1021/je400624t | J. Chem. Eng. Data XXXX, XXX, XXX−XXX
Journal of Chemical & Engineering Data
Comment/Reply
Herington’s integral test was not satisfied. These incoherencies are unequivocally confirmed by the application of the more stringent consistency analysis proposed by Fredenslund et al.14 In fact, the point-to-point consistency results according to Fredenslund’s test are reported in Table 3, from which we Table 3. Point-to-Point Consistency Test Statistics for the Binary Systems system methanol + 2-butyl acetate 2-butanol + 2-butyl acetate methyl acetate + 2-butyl acetate
10·L0a
102·L1a
102·L2a
100·⟨δy2⟩b
⟨δp⟩/ kPac
12.306
12.961
−0.244
1.60
0.79
3.071
1.573
−3.330
0.52
0.18
1.953
−6.389
1.823
2.38
0.30
a
Parameters for the Legendre polynomial14 used in consistency. Average absolute deviation in vapor phase mole fractions δy = 1/N ∑ |yiexp − yical | (N: number of data points). cAverage absolute deviation in vapor pressure δp = 1/N ∑ | piexp − pical |. b
conclude that consistency criterion (⟨δy⟩ < 0.01) was effectively not met for the methanol (1) + 2-butyl acetate (2) and methyl acetate (4) + 2-butyl acetate (2) systems.
■
Figure 2. Activity coefficient plot for the system methyl acetate (4) + 2-butyl acetate (2) at 101.33 kPa: blue ○,□, component 4 and 2, respectively, as recalculated in this work; red ●,■, component 4 and 2, respectively, as reported by Wang et al.3
*E-mail:
[email protected].
• The overall trends of the recalculated activity coefficients are also observed if we assume ideal gas behavior for the vapor phase (Bii = Bjj = Bij = 0), although yielding slightly different values for γ values (maximum differences between corrected and noncorrected γ values occur in extremely diluted conditions, as expected, and are in the order of 7%). • According to Table 2, the paper of Wang et al.3 reports systematic and important differences between the
Notes
The authors declare no competing financial interest.
■
Tb/Kb
component
calculated
measured
methyl acetate methanol 2-butyl alcohol 2-butyl acetate
330.02 338.09 372.70 384.91
329.95 337.65 372.35 385.25
REFERENCES
(1) Herington, E. F. G. Tests for the consistency of experimental isobaric vapor−liquid equilibrium data. J. Inst. Petrol. 1965, 37, 457− 470. (2) Wisniak, J. The Herington test for thermodynamic consistency. Ind. Eng. Chem. Res. 1994, 33, 177−180. (3) Wang, H.-X. K.; Xiao, J.-J.; Shen, Y.-Y.; Ye, C.-S.; Li, L.; Qiu, T. Experimental measurements of vapor−liquid equilibrium data for the binary systems of methanol + 2-butyl acetate, 2-butyl alcohol + 2-butyl acetate, and methyl acetate + 2-butyl acetate at 101.33 kPa. J. Chem. Eng. Data 2013, 58, 1827−1832. (4) Bich, E.; Pietsch, R.; Opel, G. 2nd and 3rd Virial-coefficients of methanol vapor. Z. Phys. Chem., Leipzig 1984, 265, 396−400. (5) Cox, J. D. Thermodynamic properties of organic oxygen compounds. Part 4. Second virial coefficients of the propanols and butanols. Trans. Faraday Soc. 1961, 57, 1674−1678. (6) Lambert, J. D.; Clarke, J. S.; Duke, J. F.; Hicks, C. L.; Lawrence, S. D.; Morris, D. M.; Shone, M. G. T. The second virial coefficients of mixed polar vapours. Proc. R. Soc. (London) 1959, A249, 414−426. (7) Tsonopoulos, C. An empirical correlation of second virial coefficients. AIChE J. 1974, 20, 263−272. (8) Tsonopoulos, C.; Dymond, J. H.; Szafranski, A. M. 2nd virialcoefficients of normal alkanes, linear 1-alkanols and their binaries. Pure Appl. Chem. 1989, 61, 1387−1394. (9) Tsonopoulos, C. Second virial coefficients of water pollutants. AIChE J. 1978, 24, 1112−1115. (10) Zhang, W.; Du, W.; Meng, N.; Sun, R.; Shao, Y.; Li, C. Isobaric vapor-liquid equilibrium of hexamethyl disiloxane + sec-butyl acetate system at normal pressure. Energy Procedia 2012, 16 (Part B), 1078− 1083. (11) Daubert, T. E.; Danner, R. P. Physical and thermodynamic properties of pure chemicals. Data Compilation; Taylor and Francis: Bristol, PA, extant 2013. (12) Rackett, H. G. Equation of state for saturated liquids. J. Chem. Eng. Data 1970, 15, 514−517.
Table 2. Calculated and Reported Normal Boiling Temperatures of the Pure Components Tb/Ka
AUTHOR INFORMATION
Corresponding Author
a
Calculated from the vapor pressure correlations considered for data treatment by Wang et al.3 bExperimentally obtained by Wang et al.3 together with VLE determinations reported in their work.
experimentally determined boiling temperatures and the boiling temperatures predicted by the vapor pressure correlations used for treating the data. Such differences may result in inaccurately calculated activity coefficients. From the previous observations, and contrary to the trend observed in the γ values reported by Wang et al.3 we can conclude that the recalculated activity coefficients values do not satisfy the basic geometric constraints of consistency discussed in ref 13. It is interesting to observe that the worst cases of inconsistency appear for the systems methanol (1) + 2-butyl acetate (2) and methyl acetate (4) + 2-butyl acetate (2), which are precisely the same systems for which the criterion of C
dx.doi.org/10.1021/je400624t | J. Chem. Eng. Data XXXX, XXX, XXX−XXX
Journal of Chemical & Engineering Data
Comment/Reply
(13) Wisniak, J.; Apelblat, A.; Segura, H. An assessment of thermodynamic consistency tests for vapor−liquid equilibrium data. Phys. Chem. Liq. 1997, 35, 1−58. (14) Fredenslund, A.; Gmehling, J.; Rasmussen, P. Vapor−liquid Equilibria Using UNIFAC, a Group Contribution Method; Elsevier: Amsterdam, 1977.
D
dx.doi.org/10.1021/je400624t | J. Chem. Eng. Data XXXX, XXX, XXX−XXX
