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Excess enthalpies of { ethyl tert -butylether + hexane + heptane, or octane } at the temperature 298.15 K
J. Chem. Thermodynamics 2001, 33, 1181–1191 doi:10.1006/jcht.2001.0831 Available online at http://www.idealibrary.com on
Excess enthalpies of {ethyl tert-butylether + hexane + heptane, or octane} at the temperature 298.15 K Zhaohui Wang, Ding-Yu Peng,a George C. Benson,b and Benjamin C.-Y. Lu Department of Chemical Engineering, University of Ottawa, Ottawa, Ontario, Canada K1N 6N5
Excess molar enthalpies, measured at the temperature 298.15 K in a flow microcalorimeter, are reported for the ternary mixtures {x1 CH3 CH2 OC(CH3 )3 + x2 CH3 (CH2 )4 CH3 + (1 − x1 − x2 )CH3 (CH2 )5 CH3 } and {x1 CH3 CH2 OC(CH3 )3 + x2 CH3 (CH2 )4 CH3 + (1 − x1 − x2 )CH3 (CH2 )6 CH3 }. Smooth representations of the results are described and used to construct constant-enthalpy contours on Roozeboom diagrams. It is shown that useful estimates of the enthalpies of the ternary mixtures can be obtained from the Liebermann and Fried model, using only the physical properties of the components and c 2001 Academic Press their binary mixtures. KEYWORDS: excess enthalpy; ternary mixture; ethyl tert-butylether; n-alkanes; Liebermann and Fried model
1. Introduction A recent paper, (1)
from our laboratory, described measurements of excess molar enthalpies at T = 298.15 K for {ethyl tert-butylether (ETBE) + n-hexane (nC6), or n-heptane (nC7), or n-octane (nC8)}. To extend that investigation, we have made enthalpy measurements for {ETBE + nC6 + nC7, or nC8}.
2. Experimental The ETBE and n-alkanes used in the present measurements were the same as in our earlier work. (1) Apart from partial degassing, all of the components were used without further purification. Densities ρ(T = 298.15 K)/(kg · m−3 ), measured in an Anton–Paar densimeter, were 735.32, 655.53, 679.94, and 698.78 for ETBE, nC6, nC7, and nC8, respectively. These results are in reasonable agreement with values in the literature. (2,3) a Visiting Professor from the Department of Chemical Engineering, University of Saskatchewan, Saskatoon, Saskatchewan, Canada S7N 5C9. b To whom correspondence should be addressed.
0021–9614/01/091181 + 11 $35.00/0
c 2001 Academic Press
1182
Z. Wang et al. TABLE 1. Parameters h k and standard deviations s for the representation of E Hm,i j (i < j) at T = 298.15 K by equation (2) Component i
j
h1
h2
h3
ETBE
nC6a
950.11
57.96
28.62
ETBE
nC7a
1124.24
12.58
61.80
nC6
nC7b
ETBE
nC8a
nC6
nC8c
1.846 1242.87 7.353
0.453 −20.94 2.770
h4
s/(J · mol−1 ) 1.13
70.75
−0.219 56.10
0.633 59.69
−0.539
0.68 0.008 1.18 0.021
a Reference 1; b reference 5; c reference 6.
Excess molar enthalpies HmE were measured in an LKB flow microcalorimeter (Model 10700-1), at T = (298.150 ± 0.003) K. Details of the equipment and the operating procedure have been described previously. (3,4) In studying {x1 CH3 CH2 OC(CH3 )3 + x2 CH3 (CH2 )4 CH3 + (1 − x1 − x2 )CH3 (CH2 )ν CH3 } for E ν = 5 and 6, the excess molar enthalpy Hm,1+23 was determined for several pseudo-binary mixtures in which component 1 (ETBE) was added to binary mixtures, having fixed compositions, of components 2 (nC6) and 3 (nC7 or nC8). For this purpose, binary mixtures with selected values of x2 /(1 − x1 − x2 ) were prepared by mass. The excess E molar enthalpy Hm,123 of the ternary mixture was then obtained from the relation: E E E Hm,123 = Hm,1+23 + (1 − x1 )Hm,23 ,
(1)
E where Hm,23 is the excess molar enthalpy of the particular binary mixture. Over most of the mole-fraction range, the errors of the excess molar enthalpies and the mole fractions of the final ternary mixtures are estimated to be <0.005 · |HmE | and <5 · 10−4 , respectively.
3. Results and discussion E Excess molar enthalpies Hm,i j (i < j) at T = 298.15 K for the five constituent-binary mixtures of present interest have been reported previously: {ETBE(1) + nC6(2)}, (1) {ETBE(1) + nC7(3)}, (1) {ETBE(1) + nC8(3)}, (1) {nC6(2) + nC7(3)}, (5) and {nC6(2) + nC8(3)}. (6) For convenience, values of the coefficients h k for representations of these results by the smoothing function: E −1 Hm,i j /(J · mol ) = x i (1 − x i )
m X
h k (1 − 2xi )k−1 ,
(2)
k=1
are listed in table 1, along with the standard deviations s of the representations. The experimental results for the two ternary mixtures are reported in tables 2 and 3, E where values of Hm,1+23 are listed against the mole fraction x1 of ETBE. Also included
Enthalpies of {ethyl tert-butylether + hexane + heptane, or octane}
1183
E TABLE 2. Experimental excess molar enthalpies Hm,1+23 at the temperature 298.15 K for the addition of ETBE to (nC6 + nC7) mixtures to form {x1 CH3 CH2 OC(CH3 }3 + x2 CH3 (CH2 )4 CH3 + (1 − x1 − x2 )CH3 (CH2 )5 CH3 }, and E E values of Hm,123 calculated from equation (1) using the smooth representation of Hm,23 by equation (2)
x1
E Hm,1+23
J · mol−1
a
E Hm,123
J · mol−1
x1
E Hm,1+23
J · mol−1
a
E Hm,123
J · mol−1
x1
E Hm,1+23
J · mol−1
a
E Hm,123
J · mol−1
E /(J · mol−1 ) = 0.39 x2 /(1 − x1 − x2 ) = 0.3333, Hm,23
0.0500
50.53
50.90
0.4001
254.30
254.54
0.7001
220.84
220.96
0.1001
98.64
98.99
0.4507
262.19
262.41
0.7499
197.32
197.42
0.1501
139.12
139.45
0.4999
263.98
264.18
0.8000
168.77
168.85
0.1997
173.21
173.52
0.5500
258.89
259.07
0.8500
133.03
133.09
0.2500
199.06
199.35
0.6003
253.23
253.39
0.8999
94.66
94.70
0.2999
221.93
222.21
0.6496
239.59
239.73
0.9500
49.70
49.72
0.3502
243.64
243.90 E /(J · mol−1 ) = 0.46 x2 /(1 − x1 − x2 ) = 0.9995, Hm,23
0.0501
49.43
49.87
0.4002
247.27
247.55
0.7001
213.24
213.38
0.1001
98.13
98.55
0.4503
254.07
254.32
0.7498
190.16
190.28
0.1500
135.46
135.85
0.5002
255.39
255.62
0.8001
161.73
161.82
0.1999
169.31
169.68
0.5504
253.62
253.83
0.8499
128.48
128.55
0.2498
195.39
195.74
0.5995
245.05
245.23
0.8999
90.72
90.77
0.3003
218.35
218.67
0.6504
230.60
230.76
0.9501
45.42
45.44
0.3502
235.44
235.74 E /(J · mol−1 ) = 0.28 x2 /(1 − x1 − x2 ) = 2.9994, Hm,23
0.0501
49.64
49.90
0.4003
238.05
238.22
0.7007
202.51
202.59
0.1001
93.74
93.99
0.4506
244.89
245.04
0.7507
179.40
179.47
0.1500
133.00
133.24
0.4998
245.08
245.22
0.7998
156.12
156.18
0.1999
167.56
167.78
0.5000
247.60
247.74
0.8500
124.78
124.82
0.2499
191.16
191.37
0.5504
240.05
240.18
0.9000
87.28
87.31
0.3004
213.47
213.66
0.6000
233.29
233.40
0.9500
45.33
45.34
0.3504
226.44
226.62
0.6503
221.17
221.27
E a Ternary term for representation of H E −1 m,1+23 by equations (2) to (4): Hm,T /(J · mol ) = 2 x1 x2 {(1 − x1 − x2 )/(1 − x1 + x2 )}(−526.05 + 811.64x1 + 477.87x2 − 437.51x1 ), s = 1.46 J · mol−1 .
E in the table are the corresponding values of Hm,123 , calculated from equation (1). The E values of Hm,1+23 are plotted in figures 1 and 2, along with curves for the constituentbinary mixtures having x2 = 0 (1) and x1 + x2 = 1. (1) In all cases, the maximum values of E E E Hm,1+23 and Hm,123 occur near x1 = 0.5. The values of Hm,1+23 for the three mixtures fall
1184
Z. Wang et al.
E TABLE 3. Experimental excess molar enthalpies Hm,1+23 at the temperature 298.15 K for the addition of ETBE to (nC6 + nC8) mixtures to form {x1 CH3 CH2 OC(CH3 )3 + x2 CH3 (CH2 )4 CH3 + (1 − x1 − x2 )CH3 (CH2 )6 CH3 }, and E E values of Hm,123 calculated from equation (1) using the smooth representation of Hm,23 by equation (2)
x1
E Hm,1+23
J · mol−1
a
E Hm,123
J · mol−1
x1
E Hm,1+23
J · mol−1
a
E Hm,123
J · mol−1
x1
E Hm,1+23
J · mol−1
a
E Hm,123
J · mol−1
E /(J · mol−1 ) = 1.61 x2 /(1 − x1 − x2 ) = 0.3335, Hm,23
0.0500
53.75
55.28
0.3999
275.88
276.85
0.6500
261.25
261.81
0.1000
103.90
105.35
0.4503
285.43
286.32
0.7002
243.13
243.61
0.1499
148.20
149.57
0.5002
287.65
288.46
0.7501
216.98
217.38
0.1999
186.71
188.00
0.5003
288.15
288.96
0.8000
186.19
186.51
0.2500
217.40
218.61
0.5500
283.33
284.06
0.8499
148.80
149.04
0.2501
216.05
217.26
0.6001
277.03
277.68
0.8969
109.64
109.81
0.3000
239.38
240.51
0.6002
276.18
276.82
0.9500
54.27
54.35
0.3501
259.01
260.06 E /(J · mol−1 ) = 1.84 x2 /(1 − x1 − x2 ) = 1.0001, Hm,23
0.0500
50.81
52.56
0.3997
260.75
261.85
0.7000
227.26
227.81
0.1000
99.57
101.22
0.4500
268.63
269.64
0.7503
203.11
203.57
0.1501
143.02
144.58
0.4999
269.85
270.77
0.8001
174.12
174.49
0.2001
179.37
180.84
0.5001
271.01
271.93
0.8500
138.97
139.25
0.2501
209.53
210.91
0.5500
266.52
267.35
0.9001
95.10
95.28
0.2998
227.75
229.04
0.6003
260.46
261.19
0.9500
51.77
51.86
0.3503
248.74
249.93
0.6500
245.91
246.55
E /(J · mol−1 ) = 1.09 x2 /(1 − x1 − x2 ) = 2.9984, Hm,23
0.0501
49.69
50.73
0.4002
245.78
246.44
0.7004
211.84
212.17
0.1000
94.89
95.87
0.4503
253.67
254.27
0.7503
189.88
190.15
0.1500
134.25
135.18
0.5004
255.91
256.46
0.8002
160.74
160.96
0.2001
169.00
169.88
0.5502
250.14
250.63
0.8499
128.74
128.90
0.2504
194.44
195.26
0.6004
241.69
242.13
0.9000
90.66
90.77
0.3002
215.48
216.25
0.6498
229.73
230.11
0.9500
47.23
47.28
0.3498
235.27
235.98
E a Ternary term for representation of H E −1 m,1+23 by equations (2) to (4): Hm,T /(J · mol ) = x1 x2 {(1 − x1 − x2 )/(1 − x1 + x2 )}(−462.33+743.56x1 +396.49x2 −384.13x12 ), s = 1.45 J · mol−1 .
E between the curves for the two constituent-binaries, and at constant x1 , Hm,1+23 decreases monotonically as x2 /(1 − x1 − x2 ) increases. E The values of Hm,1+23 were represented as a sum of binary terms (7) with an added
Enthalpies of {ethyl tert-butylether + hexane + heptane, or octane}
1185
300
250
H Em,1+23 / (J . mol– 1)
200
150
100
50
0 0.0
0.2
0.4
0.6
0.8
1.0
x1 E FIGURE 1. Excess molar enthalpies, Hm,1+23 , for {x1 CH3 CH2 OC(CH3 )3 + x2 CH3 (CH2 )4 CH3 + (1 − x1 − x2 )CH3 (CH2 )5 CH3 } at the temperature 298.15 K plotted against mole fraction x1 . Experimental results: 1, x2 /(1 − x1 − x2 ) = 0.3333; , x2 /(1 − x1 − x2 ) = 0.9995; ∇, x2 /(1 − x1 − x2 ) = 2.9994. Curves: . . . , x1 + x2 = 1, reference 1; ·—·, x2 = 0, reference 1; ——, calculated E given in from the representation of the results by equations (2) to (4), using the ternary term Hm,T the footnote of table 2; - - - -, estimated from the Liebermann and Fried model.
◦
ternary contribution: E E E E Hm,1+23 = [x2 /(1 − x1 )]Hm,12 + [x3 /(1 − x1 )]Hm,13 + Hm,T ,
(3)
E where the values of Hm,i j were calculated from the appropriate smoothing functions. The form: E Hm,T /(J · mol−1 ) = x1 x2 {(1 − x1 − x2 )/(1 − x1 + x2 )}(c0 + c1 · x1 + c2 · x2 +
c3 · x12 + c4 · x1 · x2 + c5 · x22 + · · ·),
(4)
1186
Z. Wang et al. 350
300
H Em,1+23 / (J . mol– 1)
250
200
150
100
50
0 0.0
0.2
0.4
0.6
0.8
1.0
x1 E FIGURE 2. Excess molar enthalpies, Hm,1+23 , for {x1 CH3 CH2 OC(CH3 )3 + x2 CH3 (CH2 )4 CH3 + (1 − x1 − x2 )CH3 (CH2 )6 CH3 } at the temperature 298.15 K plotted against mole fraction x1 . Experimental results: 1, x2 /(1 − x1 − x2 ) = 0.3335; , x2 /(1 − x1 − x2 ) = 1.0001; ∇, x2 /(1 − x1 − x2 ) = 2.9984. Curves: . . . , x1 + x2 = 1, reference 1; ·—·, x2 = 0, reference 1; ——, calculated E given in from the representation of the results by equations (2) to (4), using the ternary term Hm,T the footnote of table 3; - - - -, estimated from the Liebermann and Fried model.
◦
which was adopted for the latter contribution is similar to the form used by Morris et al., (8) but with an extra skewing factor (1 − x1 + x2 )−1 inserted. Values of the coefficients ci were obtained from least-squares analyses in which equations (3) and (4) were fitted to E E the values of Hm,1+23 in tables 2 and 3. The resulting forms for Hm,T are given in the footnotes of those tables, along with the standard deviation s for each representation. The E solid curves for Hm,1+23 in figures 1 and 2 were calculated from equation (3) using these representations.
Enthalpies of {ethyl tert-butylether + hexane + heptane, or octane}
1187
nC6 20 400 6 0 8 00 1 0 12 0 14 0 16 0 18
a
0 20 0 22 0 23 23 0.
47
7.8
0 23 0 22 0 20 0 18 0 16 0 14 0 12 0 10 80 60 40
20
281.1
280 270 260 250 240
ETBE
nC7
nC6 20 400 6 0 8 00 1 0 12 0 14 0 16 0 18
b
0 20 0 22 0 23 8.6
23 0. 4
6
0 23 0 22 0
20
280 275 270 260 250 240
283.2
nC7
20
0 18 0 16 0 14 0 12 0 10 80 60 40 ETBE
E FIGURE 3. Contours for constant values of Hm,123 /(J · mol−1 ) for {x1 CH3 CH2 OC(CH3 )3 (ETBE) + x2 CH3 (CH2 )4 CH3 (nC6) + (1 − x1 −x2 )CH3 (CH2 )5 CH3 (nC7)} at the temperature 298.15 K. a, calculated from the representation of the experimental results by E from the footnote of table 2; b, estimated from the Liebermann and equations (1) to (4) with Hm,T Fried model.
1188
Z. Wang et al. nC6 20 400 6 0 8 00 1 0 12 0 14 0 16 0 18
a
0
20
0 22 0 23 7.8
23 1. 90
0 23 0 22 0
20
0 18 0 16 0 14 0 12 0 10 80 60 40
ETBE 20
310.7
305 300 290 280 270 260 250 240
nC8
nC6 20 400 6 0 8 00 1 0 12 0 14 0 16 0 18
b
0 20 0 22 0
23
8.6 23 1. 8
7
0 23 0 22 0 20
305 300 290 280 275 270 260 250 240
312.7
nC8
20
0 18 0 16 0 14 0 12 0 10 80 60 40 ETBE
E FIGURE 4. Contours for constant values of Hm,123 /(J · mol−1 ) for {x1 CH3 CH2 OC(CH3 )3 (ETBE) + x2 CH3 (CH2 )4 CH3 (nC6) + (1 − x1 −x2 )CH3 (CH2 )6 CH3 (nC8)} at the temperature 298.15 K. a, calculated from the representation of the experimental results by E from the footnote of table 3; b, estimated from the Liebermann and equations (1) to (4) with Hm,T Fried model.
Enthalpies of {ethyl tert-butylether + hexane + heptane, or octane}
1189
E Equations (2) to (4) were also used to calculate the constant Hm,123 contours plotted on the Roozeboom diagrams in figures 3(a) and 4(a). All of the contours extend to the edges of the triangle, and there is no indication of internal extrema. In both cases, the maximum E value of Hm,123 is located in the edge of the plot for the constituent-binary comprising ETBE and the larger n-alkane. In the past, the Flory theory (9,10) has been useful in predicting the excess enthalpies of a number of ternary mixtures involving ethers and hydrocarbons, from analyses of the excess enthalpies of their constituent-binaries. More recent work indicates that an extension of the model of Liebermann and Fried (11,12) has not only the potential for correlating the excess enthalpy of binary mixtures but also the potential for predicting the (vapor + liquid) equilibria of binary and ternary mixtures. (1,13,14) Accordingly, it is of interest to consider the application of this model to predicting the excess enthalpies of the present ternary mixtures, using only the properties of the components and their binary mixtures. In applying the Liebermann and Fried model to the molar excess enthalpy of a ternary E mixture, Hm,123 is represented as a sum of two terms H (A) and H (V ), where
H (A) = (RT /2) 2
3 X 3 X
x j xk ·
j=1 k=1
P3
(∂ A jk /∂ T ) (∂ Ak j /∂ T ) + Ak j − ln(A jk Ak j ) A jk
P3
p=1
xp A jp
p=1 x p (∂ A j p /∂ T ) P3 p=1 x p A j p
P3
q=1 x q Akq
P3
+
q=1 x q (∂ Akq /∂ T ) P3 q=1 x q Akq
, (5)
and H (V ) = RT
2
= RT
2
P3
P3
x j xk {(∂ Vk /∂ T ) − (Vk /V j ) · (∂ V j /∂ T )} P3 k=1 x k Vk
P3
P3
x j xk Vk [(α p )k − (α p ) j ] . P3 k=1 x k Vk
j=1
j=1
k=1
k=1
(6)
H (A) represents the deviation from ideal behavior due to intermolecular forces, where A jk and Ak j are parameters characteristic of the binary mixture comprising components j and k. It is assumed, with some justification, that ln(A jk Ak j ) 1 ∂ A jk β 1 ∂ Ak j = = , (7) A jk ∂ T T ln(A jk Ak j ) − 2 Ak j ∂ T and, based on previous experience, (13) a value of 2 was adopted for the parameter β. Evaluation of H (V ), the contribution due to the different sizes of the molecules, requires values of the molar volumes Vm and their variation with the temperature T . In the present work, the isobaric thermal expansivities α p are used for the latter purpose, as indicated in the left side of equation (6).
1190
Z. Wang et al. TABLE 4. Values of the interaction parameters Ai j and A ji , and isobaric thermal expansivity α p at T = 298.15 K, used in Liebermann and Fried model calculations α p /kK−1
Component i ETBE
j
Ai j
A ji
i
j
nC6
0.8609
0.9732
1.401a
1.387b 1.256b
ETBE
nC7
0.8726
0.9305
1.401a
nC6
nC7
0.9473
1.0529
1.387b
1.256b
0.8883
1.401a
1.164b
1.0005
1.387b
1.164b
ETBE nC6
nC8 nC8
0.8930 0.9906
a Reference 2; b reference 15.
Values of the interaction parameters Ai j and A ji , were obtained by fitting the Liebermann and Fried model to the excess enthalpies of the constituent binary mixtures. (1,5,6) In this process, the relative importance of H (A) and H (V ) varies considerably, depending on the mixture under consideration. For mixtures of the ether with one of the alkanes, H (V ) is relatively small. However, for binary mixtures of the alkanes, the two terms are of similar magnitude and opposite in sign. The resulting values of Ai j and A ji are listed in table 4 along with the values of the isobaric thermal expansivities α p , (2,15) used in evaluating the size contribution H (V ). E Estimates of Hm,1+23 , derived from the Liebermann and Fried model, are shown as dashed curves in figures 1 and 2. It can be seen, that for the binary mixtures (i.e. x2 = 0 and x1 + x2 = 1), which were used in determining the values of Ai j and A ji , there is fairly close agreement with the experimental curves. However, the model tends to yield values which are higher than the experimental results for the ternary mixtures. For the 58 points in table 2 and the 61 points in table 3, the root mean square deviations are 4.0 and 3.9 J · mol−1 , respectively. However, these are less than the deviations (5.4 and) 5.3 J · mol−1 obtained from applications of the Flory theory. E Constant Hm,123 contours, estimated on the basis of the Liebermann and Fried model, are shown in figures 3(b) and 4(b). It is clear from a comparison of the two parts in each E figure, that the Liebermann and Fried model provides useful estimates of Hm,123 for both of the present mixtures, without requiring any direct measurements on the ternary mixture. The financial support of the Natural Sciences and Engineering Research Council of Canada (NSERC) is gratefully acknowledged. REFERENCES 1. Peng, D.-Y.; Wang, Z.; Benson, G. C.; Lu, B. C.-Y. J. Chem. Thermodynamics 2001, 33, 83–93; doi:10.1006/jcht.2000.0720. 2. Obama, M.; Oodera, Y.; Kohama, N.; Yanase, T.; Saito, Y.; Kusano, K. J. Chem. Eng. Data 1985, 30, 1–5.
Enthalpies of {ethyl tert-butylether + hexane + heptane, or octane}
1191
3. TRC—Thermodynamic Tables—Hydrocarbons. Thermodynamic Research Center: The Texas A&M University System, College Station TX 77843-3111. 1988: Table 23-2-(1.101)-a, page 1, dated 31 October, 1977. 4. Tanaka, R.; D’Arcy, P. J.; Benson, G. C. Thermochim. Acta 1975, 11, 163–175. 5. Kimura, F.; Benson, G. C.; Halpin, C. J. Fluid Phase Equilib. 1983, 11, 245–250. 6. Hamam, S. E. M.; Kumaran, M. K.; Benson, G. C. Fluid Phase Equilib. 1984, 18, 147–153. 7. Tsao, C. C.; Smith, J. M. Chem. Eng. Prog. Symp. Ser. No. 7 1953, 49, 107–117. 8. Morris, J. W.; Mulvey, P. J.; Abbott, M. M.; Van Ness, H. C. J. Chem. Eng. Data 1975, 20, 403–405. 9. Flory, P. J. J. Am. Chem. Soc. 1965, 87, 1833–1838. 10. Abe, A.; Flory, P. J. J. Am. Chem. Soc. 1965, 87, 1838–1846. 11. Liebermann, E.; Fried, V. Ind. Eng. Chem. Fundam. 1972, 11, 350-–354. 12. Liebermann, E.; Fried, V. Ind. Eng. Chem. Fundam. 1972, 11, 354–355. 13. Wang, Z.; Lu, B. C.-Y. J. Chem. Thermodynamics 2000, 32, 175–186; doi:10.1006/jcht.1999.0580. 14. Peng, D.-Y.; Wang, Z.; Benson, G. C.; Lu, B. C.-Y. Fluid Phase Equilib. 2001, 182, 217–227. 15. Benson, G. C.; Luo, B.; Lu, B. C.-Y. Can. J. Chem. 1988, 66, 531–534. (Received 18 August 2000; in final form 24 January 2001)
WE-259
Excess enthalpies of {ethyl tert-butylether + hexane + heptane, or octane} at the temperature 298.15 K Zhaohui Wang, Ding-Yu Peng,a George C. Benson,b and Benjamin C.-Y. Lu Department of Chemical Engineering, University of Ottawa, Ottawa, Ontario, Canada K1N 6N5
Excess molar enthalpies, measured at the temperature 298.15 K in a flow microcalorimeter, are reported for the ternary mixtures {x1 CH3 CH2 OC(CH3 )3 + x2 CH3 (CH2 )4 CH3 + (1 − x1 − x2 )CH3 (CH2 )5 CH3 } and {x1 CH3 CH2 OC(CH3 )3 + x2 CH3 (CH2 )4 CH3 + (1 − x1 − x2 )CH3 (CH2 )6 CH3 }. Smooth representations of the results are described and used to construct constant-enthalpy contours on Roozeboom diagrams. It is shown that useful estimates of the enthalpies of the ternary mixtures can be obtained from the Liebermann and Fried model, using only the physical properties of the components and c 2001 Academic Press their binary mixtures. KEYWORDS: excess enthalpy; ternary mixture; ethyl tert-butylether; n-alkanes; Liebermann and Fried model
1. Introduction A recent paper, (1)
from our laboratory, described measurements of excess molar enthalpies at T = 298.15 K for {ethyl tert-butylether (ETBE) + n-hexane (nC6), or n-heptane (nC7), or n-octane (nC8)}. To extend that investigation, we have made enthalpy measurements for {ETBE + nC6 + nC7, or nC8}.
2. Experimental The ETBE and n-alkanes used in the present measurements were the same as in our earlier work. (1) Apart from partial degassing, all of the components were used without further purification. Densities ρ(T = 298.15 K)/(kg · m−3 ), measured in an Anton–Paar densimeter, were 735.32, 655.53, 679.94, and 698.78 for ETBE, nC6, nC7, and nC8, respectively. These results are in reasonable agreement with values in the literature. (2,3) a Visiting Professor from the Department of Chemical Engineering, University of Saskatchewan, Saskatoon, Saskatchewan, Canada S7N 5C9. b To whom correspondence should be addressed.
0021–9614/01/091181 + 11 $35.00/0
c 2001 Academic Press
1182
Z. Wang et al. TABLE 1. Parameters h k and standard deviations s for the representation of E Hm,i j (i < j) at T = 298.15 K by equation (2) Component i
j
h1
h2
h3
ETBE
nC6a
950.11
57.96
28.62
ETBE
nC7a
1124.24
12.58
61.80
nC6
nC7b
ETBE
nC8a
nC6
nC8c
1.846 1242.87 7.353
0.453 −20.94 2.770
h4
s/(J · mol−1 ) 1.13
70.75
−0.219 56.10
0.633 59.69
−0.539
0.68 0.008 1.18 0.021
a Reference 1; b reference 5; c reference 6.
Excess molar enthalpies HmE were measured in an LKB flow microcalorimeter (Model 10700-1), at T = (298.150 ± 0.003) K. Details of the equipment and the operating procedure have been described previously. (3,4) In studying {x1 CH3 CH2 OC(CH3 )3 + x2 CH3 (CH2 )4 CH3 + (1 − x1 − x2 )CH3 (CH2 )ν CH3 } for E ν = 5 and 6, the excess molar enthalpy Hm,1+23 was determined for several pseudo-binary mixtures in which component 1 (ETBE) was added to binary mixtures, having fixed compositions, of components 2 (nC6) and 3 (nC7 or nC8). For this purpose, binary mixtures with selected values of x2 /(1 − x1 − x2 ) were prepared by mass. The excess E molar enthalpy Hm,123 of the ternary mixture was then obtained from the relation: E E E Hm,123 = Hm,1+23 + (1 − x1 )Hm,23 ,
(1)
E where Hm,23 is the excess molar enthalpy of the particular binary mixture. Over most of the mole-fraction range, the errors of the excess molar enthalpies and the mole fractions of the final ternary mixtures are estimated to be <0.005 · |HmE | and <5 · 10−4 , respectively.
3. Results and discussion E Excess molar enthalpies Hm,i j (i < j) at T = 298.15 K for the five constituent-binary mixtures of present interest have been reported previously: {ETBE(1) + nC6(2)}, (1) {ETBE(1) + nC7(3)}, (1) {ETBE(1) + nC8(3)}, (1) {nC6(2) + nC7(3)}, (5) and {nC6(2) + nC8(3)}. (6) For convenience, values of the coefficients h k for representations of these results by the smoothing function: E −1 Hm,i j /(J · mol ) = x i (1 − x i )
m X
h k (1 − 2xi )k−1 ,
(2)
k=1
are listed in table 1, along with the standard deviations s of the representations. The experimental results for the two ternary mixtures are reported in tables 2 and 3, E where values of Hm,1+23 are listed against the mole fraction x1 of ETBE. Also included
Enthalpies of {ethyl tert-butylether + hexane + heptane, or octane}
1183
E TABLE 2. Experimental excess molar enthalpies Hm,1+23 at the temperature 298.15 K for the addition of ETBE to (nC6 + nC7) mixtures to form {x1 CH3 CH2 OC(CH3 }3 + x2 CH3 (CH2 )4 CH3 + (1 − x1 − x2 )CH3 (CH2 )5 CH3 }, and E E values of Hm,123 calculated from equation (1) using the smooth representation of Hm,23 by equation (2)
x1
E Hm,1+23
J · mol−1
a
E Hm,123
J · mol−1
x1
E Hm,1+23
J · mol−1
a
E Hm,123
J · mol−1
x1
E Hm,1+23
J · mol−1
a
E Hm,123
J · mol−1
E /(J · mol−1 ) = 0.39 x2 /(1 − x1 − x2 ) = 0.3333, Hm,23
0.0500
50.53
50.90
0.4001
254.30
254.54
0.7001
220.84
220.96
0.1001
98.64
98.99
0.4507
262.19
262.41
0.7499
197.32
197.42
0.1501
139.12
139.45
0.4999
263.98
264.18
0.8000
168.77
168.85
0.1997
173.21
173.52
0.5500
258.89
259.07
0.8500
133.03
133.09
0.2500
199.06
199.35
0.6003
253.23
253.39
0.8999
94.66
94.70
0.2999
221.93
222.21
0.6496
239.59
239.73
0.9500
49.70
49.72
0.3502
243.64
243.90 E /(J · mol−1 ) = 0.46 x2 /(1 − x1 − x2 ) = 0.9995, Hm,23
0.0501
49.43
49.87
0.4002
247.27
247.55
0.7001
213.24
213.38
0.1001
98.13
98.55
0.4503
254.07
254.32
0.7498
190.16
190.28
0.1500
135.46
135.85
0.5002
255.39
255.62
0.8001
161.73
161.82
0.1999
169.31
169.68
0.5504
253.62
253.83
0.8499
128.48
128.55
0.2498
195.39
195.74
0.5995
245.05
245.23
0.8999
90.72
90.77
0.3003
218.35
218.67
0.6504
230.60
230.76
0.9501
45.42
45.44
0.3502
235.44
235.74 E /(J · mol−1 ) = 0.28 x2 /(1 − x1 − x2 ) = 2.9994, Hm,23
0.0501
49.64
49.90
0.4003
238.05
238.22
0.7007
202.51
202.59
0.1001
93.74
93.99
0.4506
244.89
245.04
0.7507
179.40
179.47
0.1500
133.00
133.24
0.4998
245.08
245.22
0.7998
156.12
156.18
0.1999
167.56
167.78
0.5000
247.60
247.74
0.8500
124.78
124.82
0.2499
191.16
191.37
0.5504
240.05
240.18
0.9000
87.28
87.31
0.3004
213.47
213.66
0.6000
233.29
233.40
0.9500
45.33
45.34
0.3504
226.44
226.62
0.6503
221.17
221.27
E a Ternary term for representation of H E −1 m,1+23 by equations (2) to (4): Hm,T /(J · mol ) = 2 x1 x2 {(1 − x1 − x2 )/(1 − x1 + x2 )}(−526.05 + 811.64x1 + 477.87x2 − 437.51x1 ), s = 1.46 J · mol−1 .
E in the table are the corresponding values of Hm,123 , calculated from equation (1). The E values of Hm,1+23 are plotted in figures 1 and 2, along with curves for the constituentbinary mixtures having x2 = 0 (1) and x1 + x2 = 1. (1) In all cases, the maximum values of E E E Hm,1+23 and Hm,123 occur near x1 = 0.5. The values of Hm,1+23 for the three mixtures fall
1184
Z. Wang et al.
E TABLE 3. Experimental excess molar enthalpies Hm,1+23 at the temperature 298.15 K for the addition of ETBE to (nC6 + nC8) mixtures to form {x1 CH3 CH2 OC(CH3 )3 + x2 CH3 (CH2 )4 CH3 + (1 − x1 − x2 )CH3 (CH2 )6 CH3 }, and E E values of Hm,123 calculated from equation (1) using the smooth representation of Hm,23 by equation (2)
x1
E Hm,1+23
J · mol−1
a
E Hm,123
J · mol−1
x1
E Hm,1+23
J · mol−1
a
E Hm,123
J · mol−1
x1
E Hm,1+23
J · mol−1
a
E Hm,123
J · mol−1
E /(J · mol−1 ) = 1.61 x2 /(1 − x1 − x2 ) = 0.3335, Hm,23
0.0500
53.75
55.28
0.3999
275.88
276.85
0.6500
261.25
261.81
0.1000
103.90
105.35
0.4503
285.43
286.32
0.7002
243.13
243.61
0.1499
148.20
149.57
0.5002
287.65
288.46
0.7501
216.98
217.38
0.1999
186.71
188.00
0.5003
288.15
288.96
0.8000
186.19
186.51
0.2500
217.40
218.61
0.5500
283.33
284.06
0.8499
148.80
149.04
0.2501
216.05
217.26
0.6001
277.03
277.68
0.8969
109.64
109.81
0.3000
239.38
240.51
0.6002
276.18
276.82
0.9500
54.27
54.35
0.3501
259.01
260.06 E /(J · mol−1 ) = 1.84 x2 /(1 − x1 − x2 ) = 1.0001, Hm,23
0.0500
50.81
52.56
0.3997
260.75
261.85
0.7000
227.26
227.81
0.1000
99.57
101.22
0.4500
268.63
269.64
0.7503
203.11
203.57
0.1501
143.02
144.58
0.4999
269.85
270.77
0.8001
174.12
174.49
0.2001
179.37
180.84
0.5001
271.01
271.93
0.8500
138.97
139.25
0.2501
209.53
210.91
0.5500
266.52
267.35
0.9001
95.10
95.28
0.2998
227.75
229.04
0.6003
260.46
261.19
0.9500
51.77
51.86
0.3503
248.74
249.93
0.6500
245.91
246.55
E /(J · mol−1 ) = 1.09 x2 /(1 − x1 − x2 ) = 2.9984, Hm,23
0.0501
49.69
50.73
0.4002
245.78
246.44
0.7004
211.84
212.17
0.1000
94.89
95.87
0.4503
253.67
254.27
0.7503
189.88
190.15
0.1500
134.25
135.18
0.5004
255.91
256.46
0.8002
160.74
160.96
0.2001
169.00
169.88
0.5502
250.14
250.63
0.8499
128.74
128.90
0.2504
194.44
195.26
0.6004
241.69
242.13
0.9000
90.66
90.77
0.3002
215.48
216.25
0.6498
229.73
230.11
0.9500
47.23
47.28
0.3498
235.27
235.98
E a Ternary term for representation of H E −1 m,1+23 by equations (2) to (4): Hm,T /(J · mol ) = x1 x2 {(1 − x1 − x2 )/(1 − x1 + x2 )}(−462.33+743.56x1 +396.49x2 −384.13x12 ), s = 1.45 J · mol−1 .
E between the curves for the two constituent-binaries, and at constant x1 , Hm,1+23 decreases monotonically as x2 /(1 − x1 − x2 ) increases. E The values of Hm,1+23 were represented as a sum of binary terms (7) with an added
Enthalpies of {ethyl tert-butylether + hexane + heptane, or octane}
1185
300
250
H Em,1+23 / (J . mol– 1)
200
150
100
50
0 0.0
0.2
0.4
0.6
0.8
1.0
x1 E FIGURE 1. Excess molar enthalpies, Hm,1+23 , for {x1 CH3 CH2 OC(CH3 )3 + x2 CH3 (CH2 )4 CH3 + (1 − x1 − x2 )CH3 (CH2 )5 CH3 } at the temperature 298.15 K plotted against mole fraction x1 . Experimental results: 1, x2 /(1 − x1 − x2 ) = 0.3333; , x2 /(1 − x1 − x2 ) = 0.9995; ∇, x2 /(1 − x1 − x2 ) = 2.9994. Curves: . . . , x1 + x2 = 1, reference 1; ·—·, x2 = 0, reference 1; ——, calculated E given in from the representation of the results by equations (2) to (4), using the ternary term Hm,T the footnote of table 2; - - - -, estimated from the Liebermann and Fried model.
◦
ternary contribution: E E E E Hm,1+23 = [x2 /(1 − x1 )]Hm,12 + [x3 /(1 − x1 )]Hm,13 + Hm,T ,
(3)
E where the values of Hm,i j were calculated from the appropriate smoothing functions. The form: E Hm,T /(J · mol−1 ) = x1 x2 {(1 − x1 − x2 )/(1 − x1 + x2 )}(c0 + c1 · x1 + c2 · x2 +
c3 · x12 + c4 · x1 · x2 + c5 · x22 + · · ·),
(4)
1186
Z. Wang et al. 350
300
H Em,1+23 / (J . mol– 1)
250
200
150
100
50
0 0.0
0.2
0.4
0.6
0.8
1.0
x1 E FIGURE 2. Excess molar enthalpies, Hm,1+23 , for {x1 CH3 CH2 OC(CH3 )3 + x2 CH3 (CH2 )4 CH3 + (1 − x1 − x2 )CH3 (CH2 )6 CH3 } at the temperature 298.15 K plotted against mole fraction x1 . Experimental results: 1, x2 /(1 − x1 − x2 ) = 0.3335; , x2 /(1 − x1 − x2 ) = 1.0001; ∇, x2 /(1 − x1 − x2 ) = 2.9984. Curves: . . . , x1 + x2 = 1, reference 1; ·—·, x2 = 0, reference 1; ——, calculated E given in from the representation of the results by equations (2) to (4), using the ternary term Hm,T the footnote of table 3; - - - -, estimated from the Liebermann and Fried model.
◦
which was adopted for the latter contribution is similar to the form used by Morris et al., (8) but with an extra skewing factor (1 − x1 + x2 )−1 inserted. Values of the coefficients ci were obtained from least-squares analyses in which equations (3) and (4) were fitted to E E the values of Hm,1+23 in tables 2 and 3. The resulting forms for Hm,T are given in the footnotes of those tables, along with the standard deviation s for each representation. The E solid curves for Hm,1+23 in figures 1 and 2 were calculated from equation (3) using these representations.
Enthalpies of {ethyl tert-butylether + hexane + heptane, or octane}
1187
nC6 20 400 6 0 8 00 1 0 12 0 14 0 16 0 18
a
0 20 0 22 0 23 23 0.
47
7.8
0 23 0 22 0 20 0 18 0 16 0 14 0 12 0 10 80 60 40
20
281.1
280 270 260 250 240
ETBE
nC7
nC6 20 400 6 0 8 00 1 0 12 0 14 0 16 0 18
b
0 20 0 22 0 23 8.6
23 0. 4
6
0 23 0 22 0
20
280 275 270 260 250 240
283.2
nC7
20
0 18 0 16 0 14 0 12 0 10 80 60 40 ETBE
E FIGURE 3. Contours for constant values of Hm,123 /(J · mol−1 ) for {x1 CH3 CH2 OC(CH3 )3 (ETBE) + x2 CH3 (CH2 )4 CH3 (nC6) + (1 − x1 −x2 )CH3 (CH2 )5 CH3 (nC7)} at the temperature 298.15 K. a, calculated from the representation of the experimental results by E from the footnote of table 2; b, estimated from the Liebermann and equations (1) to (4) with Hm,T Fried model.
1188
Z. Wang et al. nC6 20 400 6 0 8 00 1 0 12 0 14 0 16 0 18
a
0
20
0 22 0 23 7.8
23 1. 90
0 23 0 22 0
20
0 18 0 16 0 14 0 12 0 10 80 60 40
ETBE 20
310.7
305 300 290 280 270 260 250 240
nC8
nC6 20 400 6 0 8 00 1 0 12 0 14 0 16 0 18
b
0 20 0 22 0
23
8.6 23 1. 8
7
0 23 0 22 0 20
305 300 290 280 275 270 260 250 240
312.7
nC8
20
0 18 0 16 0 14 0 12 0 10 80 60 40 ETBE
E FIGURE 4. Contours for constant values of Hm,123 /(J · mol−1 ) for {x1 CH3 CH2 OC(CH3 )3 (ETBE) + x2 CH3 (CH2 )4 CH3 (nC6) + (1 − x1 −x2 )CH3 (CH2 )6 CH3 (nC8)} at the temperature 298.15 K. a, calculated from the representation of the experimental results by E from the footnote of table 3; b, estimated from the Liebermann and equations (1) to (4) with Hm,T Fried model.
Enthalpies of {ethyl tert-butylether + hexane + heptane, or octane}
1189
E Equations (2) to (4) were also used to calculate the constant Hm,123 contours plotted on the Roozeboom diagrams in figures 3(a) and 4(a). All of the contours extend to the edges of the triangle, and there is no indication of internal extrema. In both cases, the maximum E value of Hm,123 is located in the edge of the plot for the constituent-binary comprising ETBE and the larger n-alkane. In the past, the Flory theory (9,10) has been useful in predicting the excess enthalpies of a number of ternary mixtures involving ethers and hydrocarbons, from analyses of the excess enthalpies of their constituent-binaries. More recent work indicates that an extension of the model of Liebermann and Fried (11,12) has not only the potential for correlating the excess enthalpy of binary mixtures but also the potential for predicting the (vapor + liquid) equilibria of binary and ternary mixtures. (1,13,14) Accordingly, it is of interest to consider the application of this model to predicting the excess enthalpies of the present ternary mixtures, using only the properties of the components and their binary mixtures. In applying the Liebermann and Fried model to the molar excess enthalpy of a ternary E mixture, Hm,123 is represented as a sum of two terms H (A) and H (V ), where
H (A) = (RT /2) 2
3 X 3 X
x j xk ·
j=1 k=1
P3
(∂ A jk /∂ T ) (∂ Ak j /∂ T ) + Ak j − ln(A jk Ak j ) A jk
P3
p=1
xp A jp
p=1 x p (∂ A j p /∂ T ) P3 p=1 x p A j p
P3
q=1 x q Akq
P3
+
q=1 x q (∂ Akq /∂ T ) P3 q=1 x q Akq
, (5)
and H (V ) = RT
2
= RT
2
P3
P3
x j xk {(∂ Vk /∂ T ) − (Vk /V j ) · (∂ V j /∂ T )} P3 k=1 x k Vk
P3
P3
x j xk Vk [(α p )k − (α p ) j ] . P3 k=1 x k Vk
j=1
j=1
k=1
k=1
(6)
H (A) represents the deviation from ideal behavior due to intermolecular forces, where A jk and Ak j are parameters characteristic of the binary mixture comprising components j and k. It is assumed, with some justification, that ln(A jk Ak j ) 1 ∂ A jk β 1 ∂ Ak j = = , (7) A jk ∂ T T ln(A jk Ak j ) − 2 Ak j ∂ T and, based on previous experience, (13) a value of 2 was adopted for the parameter β. Evaluation of H (V ), the contribution due to the different sizes of the molecules, requires values of the molar volumes Vm and their variation with the temperature T . In the present work, the isobaric thermal expansivities α p are used for the latter purpose, as indicated in the left side of equation (6).
1190
Z. Wang et al. TABLE 4. Values of the interaction parameters Ai j and A ji , and isobaric thermal expansivity α p at T = 298.15 K, used in Liebermann and Fried model calculations α p /kK−1
Component i ETBE
j
Ai j
A ji
i
j
nC6
0.8609
0.9732
1.401a
1.387b 1.256b
ETBE
nC7
0.8726
0.9305
1.401a
nC6
nC7
0.9473
1.0529
1.387b
1.256b
0.8883
1.401a
1.164b
1.0005
1.387b
1.164b
ETBE nC6
nC8 nC8
0.8930 0.9906
a Reference 2; b reference 15.
Values of the interaction parameters Ai j and A ji , were obtained by fitting the Liebermann and Fried model to the excess enthalpies of the constituent binary mixtures. (1,5,6) In this process, the relative importance of H (A) and H (V ) varies considerably, depending on the mixture under consideration. For mixtures of the ether with one of the alkanes, H (V ) is relatively small. However, for binary mixtures of the alkanes, the two terms are of similar magnitude and opposite in sign. The resulting values of Ai j and A ji are listed in table 4 along with the values of the isobaric thermal expansivities α p , (2,15) used in evaluating the size contribution H (V ). E Estimates of Hm,1+23 , derived from the Liebermann and Fried model, are shown as dashed curves in figures 1 and 2. It can be seen, that for the binary mixtures (i.e. x2 = 0 and x1 + x2 = 1), which were used in determining the values of Ai j and A ji , there is fairly close agreement with the experimental curves. However, the model tends to yield values which are higher than the experimental results for the ternary mixtures. For the 58 points in table 2 and the 61 points in table 3, the root mean square deviations are 4.0 and 3.9 J · mol−1 , respectively. However, these are less than the deviations (5.4 and) 5.3 J · mol−1 obtained from applications of the Flory theory. E Constant Hm,123 contours, estimated on the basis of the Liebermann and Fried model, are shown in figures 3(b) and 4(b). It is clear from a comparison of the two parts in each E figure, that the Liebermann and Fried model provides useful estimates of Hm,123 for both of the present mixtures, without requiring any direct measurements on the ternary mixture. The financial support of the Natural Sciences and Engineering Research Council of Canada (NSERC) is gratefully acknowledged. REFERENCES 1. Peng, D.-Y.; Wang, Z.; Benson, G. C.; Lu, B. C.-Y. J. Chem. Thermodynamics 2001, 33, 83–93; doi:10.1006/jcht.2000.0720. 2. Obama, M.; Oodera, Y.; Kohama, N.; Yanase, T.; Saito, Y.; Kusano, K. J. Chem. Eng. Data 1985, 30, 1–5.
Enthalpies of {ethyl tert-butylether + hexane + heptane, or octane}
1191
3. TRC—Thermodynamic Tables—Hydrocarbons. Thermodynamic Research Center: The Texas A&M University System, College Station TX 77843-3111. 1988: Table 23-2-(1.101)-a, page 1, dated 31 October, 1977. 4. Tanaka, R.; D’Arcy, P. J.; Benson, G. C. Thermochim. Acta 1975, 11, 163–175. 5. Kimura, F.; Benson, G. C.; Halpin, C. J. Fluid Phase Equilib. 1983, 11, 245–250. 6. Hamam, S. E. M.; Kumaran, M. K.; Benson, G. C. Fluid Phase Equilib. 1984, 18, 147–153. 7. Tsao, C. C.; Smith, J. M. Chem. Eng. Prog. Symp. Ser. No. 7 1953, 49, 107–117. 8. Morris, J. W.; Mulvey, P. J.; Abbott, M. M.; Van Ness, H. C. J. Chem. Eng. Data 1975, 20, 403–405. 9. Flory, P. J. J. Am. Chem. Soc. 1965, 87, 1833–1838. 10. Abe, A.; Flory, P. J. J. Am. Chem. Soc. 1965, 87, 1838–1846. 11. Liebermann, E.; Fried, V. Ind. Eng. Chem. Fundam. 1972, 11, 350-–354. 12. Liebermann, E.; Fried, V. Ind. Eng. Chem. Fundam. 1972, 11, 354–355. 13. Wang, Z.; Lu, B. C.-Y. J. Chem. Thermodynamics 2000, 32, 175–186; doi:10.1006/jcht.1999.0580. 14. Peng, D.-Y.; Wang, Z.; Benson, G. C.; Lu, B. C.-Y. Fluid Phase Equilib. 2001, 182, 217–227. 15. Benson, G. C.; Luo, B.; Lu, B. C.-Y. Can. J. Chem. 1988, 66, 531–534. (Received 18 August 2000; in final form 24 January 2001)
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