J. Chem. Thermodynamics 2002, 34, 915–926
doi:10.1006/jcht.2002.0945
Available online at http://www.idealibrary.com on
Calorimetric investigation of excess molar heat
capacities for water + ethylene glycol from
T = 273.15 to T = 373.15 K
Zhaodong Nan,a Beiping Liu,b and Zhicheng Tanc
Thermochemistry Laboratory, Dalian Institute of Chemical Physics, Chinese
Academy of Sciences, Dalian 116023, P. R. C.
The molar excess heat capacity C Ep,m of (1 − x)H2 O + xHOCH2 CH2 OH has been
measured in the temperature range from 273.15 K to 373.15 K at 5 K intervals. The
C Ep,m values are negative and positive at all compositions between temperatures of (273.15,
283.15, 333.15 and 373.15) K, respectively. Between T = 288.15 K and T = 328.15 K,
C Ep,m values are positive for the mixtures rich in water and negative for the mixtures
rich in ethylene glycol with maxima at values of x about 0.07, 0.3 and with minima at
values of x about 0.6. The curve of C Ep,m against x at T = 303.15 K is unusual in
showing three maximum values at values of x at about 0.07, 0.3, and 0.4, respectively.
The curves of C Ep,m against T show that the effects of T on C Ep,m at x = 0.03124,
0.5372, and 0.7232 are more complex. The shapes of the curves of C Ep,m against x and
their changes with temperature can be accounted for by the structure of the binary system.
c 2002 Elsevier Science Ltd. All rights reserved.
KEYWORDS: an adiabatic calorimeter; excess heat capacity; binary system; ethylene
glycol; aqueous solution
1. Introduction
Ethylene glycol is an important chemical used in the petroleum and chemical industries.
Its solutions are also an advanced working fluid in heat transfer equipment and widely used
in the automobile, space and aviation industry. Song et al. (1, 2) studied the low temperature
heat capacities of the ternary systems of (water + ethylene glycol + ethanol). Hout et al. (3)
investigated the excess heat capacities of (water + ethylene glycol) at (278.15, 298.15 and
318.15) K. Kracht et al. (4, 5) studied excess molar enthalpies of binary mixtures of the three
glycols with methanol or ethanol, and glycols with water. However, the excess molar heat
a Also at Department of Chemical, Qufu Normal University, Qufu 273165, P. R. C
b Also at Department of Chemistry, Changde Normal College, Changde 415000, P. R. C.
c To whom correspondence should be addressed (E-mail: [email protected]).
0021–9614/02
c 2002 Elsevier Science Ltd. All rights reserved.
916
Zhaodong Nan, Beiping Liu, and Zhicheng Tan
capacity has not been reported for the binary systems of (water + ethylene glycol). It is
rather difficult to measure C Ep,m accurately compared to other thermodynamic functions. (6)
In order to explain the behaviour of the binary system of (water + ethylene glycol),
the excess molar heat capacities for these binary systems have been determined with an
adiabatic calorimeter over different compositions in the temperature range from 273.15 K
to 373.15 K. The polynomial equations of C Ep,m with respect to mole fraction x of ethylene
glycol and temperature T have been established by the least-squares method, respectively.
2. Experimental
Ethylene glycol (produced by Beijing Chemical Company) was purified by distillation.
The distillate was obtained in the temperature range from 469 K to 471 K. The density of
ethylene glycol is 1.111 g · cm−3 , and the refractive index is 1.4316. The water used for
preparing the aqueous solution of ethylene glycol was deionized and twice distilled.
An adiabatic calorimeter made in our thermochemistry laboratory was used to measure
the heat capacities of the binary system. The calorimetric apparatus and measuring
technique were described in detail previously. (7) Briefly, it is an adiabatic calorimeter with
intermittent energy inputs and temperature equilibration after each input. The calorimeter
cell with internal volume of 60 mL was made of stainless steel. In order to obtain good
adiabatic conditions, the calorimetric cell was surrounded by the adiabatic shield. The
calorimetric cell and the adiabatic shield were housed in a high vacuum can to reduce
the heat transfer between the cell and its surroundings. The high vacuum can was housed
in a Dewar vessel. The temperature in the Dewar vessel can be lowered to 193 K by dry
ice. The temperature control of the shield was carried out automatically. The temperature of
the calorimeter sample cell was measured by means of a platinum resistance thermometer.
The thermometer (R0 = 25 ) was calibrated by the National Institute of Metrology in
terms of ITS-90 temperature scale. The heat capacity of measurements of n-heptane from
T = 200 K to T = 370 K, which is the internationally accepted heat capacity standard
reference material, showed a precision of 0.5 per cent and agreed with those of the National
Institute of Science and Technology (formerly NBS) to within ±0.5 per cent. In order to
compare the results, the heat capacities of n-heptane determined in our experiments and
cited from reference 8 were given in table 1.
After filling the calorimeter cell with the sample, the cryostat was cooled down to
T = 190.15 K by dry ice. The molar heat capacity C p,m was measured by a step heating
method that involved the determination of the heating energy Qe and the corresponding
temperature increment 1T of the cell with the specimen. The molar heat capacity C p,m
was calculated by using the following equation:
C p,m = [(Qe/1T ) − H ]/m,
(1)
where H is the heat capacity of the empty container, m the mole number of the specimen.
The heat capacities of (water + ethylene glycol) are shown in table 2. The values of heat
capacities determined in our experiments and reported in reference 3 are shown in figure 1
at T = (278.15, 298.15 and 318.15) K in order to compare the results. From figure 1, it
can be seen that our results agree well with those presented in reference 3.
Calorimetric investigation of excess molar heat capacities
917
TABLE 1. Heat capacities of n-heptane at different temperatures
T /K
C p /(J · K−1 · mol−1 )
C ap /(J · K−1 · mol−1 )
102 (C p − C ap )/C p
200
201.65
201.31
210
210.98
201.68
0.15
220
202.53
202.74
−0.10
230
204.71
204.36
0.17
240
206.47
206.47
0
250
208.86
208.93
−0.03
260
211.55
211.73
−0.08
270
214.98
214.81
0.08
280
218.42
218.23
0.09
290
221.48
221.75
−0.12
300
225.26
225.44
−0.07
310
229.03
229.27
−0.10
320
233.14
233.25
−0.04
330
237.20
237.38
−0.07
340
241.31
241.67
−0.14
350
246.09
246.09
0
360
250.91
250.63
0.11
370
255.31
255.30
0.02
0.17
a Data gained from reference 8.
3. Results
The excess molar heat capacity for the binary system {(1 − x) water + x ethylene glycol}
was calculated by using the following equation:
C Ep,m = C p,m − xC ∗p,m,2 − (1 − x)C ∗p,m,1 ,
(2)
where C ∗p,m,1 and C ∗p,m,2 are the molar heat capacities for water and ethylene glycol,
respectively, and C p,m is the molar heat capacity of a mixture at the mole fraction
of ethylene glycol x. The C p,m , C ∗p,m,1 and C ∗p,m,2 were determined by the adiabatic
calorimeter. The values of C Ep,m are summarized in table 3.
It is difficult to fit the C Ep,m results to a simple least-squares representation over the
whole range of x at each temperature, since the results appear to be complex. The results
for the binary system from T = 273.15 K to T = 283.15 K with a interval of 5 K were
fitted to a Redlich–Kister type polynomial by the least-square method: (6)
C Ep,m = f (1 − f )
n
X
i=1
ai (1 − 2 f )i−1 ,
(3)
918
Zhaodong Nan, Beiping Liu, and Zhicheng Tan
TABLE 2. Heat capacities C p /J · K−1 · g−1 of {(1 − x) water + x ethylene glycol}
T
x
K
0
0.03124
0.06765 0.1106 0.1572 0.2250 0.3033 0.4038 0.5372 0.7232
1
273.15 4.2175
3.9790
3.7530
3.5438 3.3388 3.1254 2.9204 2.7405 2.5818 2.4142 2.2342
278.15 4.2020
3.9874
3.7740
3.5690 3.3723 3.1380 2.9581 2.7782 2.6150 2.4434 2.2635
283.15 4.1920
3.9957
3.7949
3.5940 3.4100 3.2008 2.9957 2.8116 2.6443 2.4727 2.2886
288.15 4.1857
4.0041
3.8158
3.6192 3.4392 3.2384 3.0334 2.8451 2.6736 2.5020 2.3221
293.15 4.1819
4.0083
3.8325
3.6443 3.4685 3.2761 3.0710 2.8786 2.7029 2.5271 2.3556
298.15 4.1794
4.0166
3.8535
3.6694 3.4978 3.3137 3.1084 2.9121 2.7280 2.5564 2.3849
303.15 4.1786
4.0250
3.8702
3.6903 3.5229 3.3472 3.1464 2.9455 2.7572 2.5815 2.4184
308.15 4.1781
4.0292
3.8869
3.7112 3.5522 3.3765 3.1798 2.9790 2.7824 2.6108 2.4434
313.15 4.1786
4.0376
3.8995
3.7321 3.5731 3.4058 3.2091 3.0125 2.8116 2.6359 2.4727
318.15 4.1794
4.0459
3.9162
3.7489 3.5940 3.4351 3.2426 3.0418 2.8368 2.6610 2.5020
323.15 4.1806
4.0501
3.9288
3.7698 3.6192 3.4644 3.2761 3.0752 2.8660 2.6903 2.5271
328.15 4.1823
4.0585
3.9413
3.7865 3.6359 3.4894 3.3054 3.1003 2.8911 2.7154 2.5522
333.15 4.1844
4.0668
3.9497
3.7991 3.6568 3.5146 3.3346 3.1296 2.9162 2.7405 2.5773
338.15 4.1865
4.0710
3.9581
3.8158 3.6736 3.5355 3.3598 3.1547 2.9414 2.7656 2.6024
343.15 4.1894
4.0794
3.9664
3.8284 3.6945 3.5564 3.3807 3.1798 2.9706 2.7949 2.6276
348.15 4.1928
4.0836
3.9748
3.8409 3.7112 3.5690 3.4016 3.2049 2.9957 2.8200 2.6526
353.15 4.1961
4.0920
3.9832
3.8535 3.7279 3.5857 3.4225 3.2259 3.0167 2.8451 2.6778
358.15 4.2003
4.0961
3.9874
3.8618 3.7447 3.6024 3.4392 3.2468 3.0418 2.8702 2.7029
363.15 4.2049
4.1045
3.9915
3.8744 3.7614 3.6150 3.4560 3.2635 3.0627 2.8911 2.7322
368.15 4.2104
4.1087
3.9957
3.8828 3.7782 3.6275 3.4685 3.2802 3.0878 2.9162 2.7572
373.15 4.2158
4.1170
4.0041
3.8911 3.7949 3.6443 3.4853 3.2970 3.1087 2.9414 2.7824
with
f = x/{x + k(1 − x)},
(4)
where f is a concentration factor and k is a constant pre-selected before computation. The
constant k is selected to yield f ≈ 0.5 at the maximum C Ep,m values.
In the temperature range from 288.15 K to 373.15 K (not containing 303.15 K), the
values of C Ep,m were divided into two parts: that is x 6 0.2250 and x > 0.2250 because
of C Ep,m values reaching the maxima at about x = 0.2250, and fitted to the following
polynomials, respectively:
at x 6 0.2250
C Ep,m =
n
X
i=1
ai x i ,
(5)
Calorimetric investigation of excess molar heat capacities
919
5
Cp /(J . K −1 . g −1)
T = 278.15 K
4
3
2
0
0.2
0.4
0.6
0.8
1
x
5
Cp /(J . K − 1 . g − 1)
T = 298.15 K
4
3
2
0
0.2
0.4
0.6
0.8
1
x
5
Cp /(J . K − 1 . g − 1)
T = 318.15 K
4
3
2
0
0.2
0.4
0.6
0.8
1
x
◦
FIGURE 1. Heat capacities C p of {ethylene glycol x + water (1 − x)} at different temperatures: ( )
results cited from reference 3, () results determined in our experiments.
at x > 0.2250
C Ep,m =
n
X
ai (1 − x)i .
(6)
i=1
At T = 303.15 K, the C Ep,m values were divided into three parts: that is x 6 0.1572,
920
Zhaodong Nan, Beiping Liu, and Zhicheng Tan
TABLE 3. Molar excess heat capacities, C Ep,m /(J · K−1 · mol−1 ) for {x ethylene glycol + (1 − x)
water}
T
x
K
0
0.03124
0.06765
0.1106
0.1572
0.2250
0.3033
0.4038
0.5372
273.15 0 −0.7660 −1.4273 −1.7868 −2.5615 −2.8258 −3.3840 −3.1701 −2.0657
0.7232
1
−0.9658 0
278.15 0 −0.1265 −0.5553 −0.8968 −1.5374 −1.7763 −2.3420 −2.2277 −1.3972
−0.6541 0
283.15 0 −0.1265 −0.3300 −0.6109 −0.9383 −1.1054 −1.7004 −1.7204 −1.0640
−0.3092 0
288.15 0
0.1093
0.1035 −0.1494 −0.4300 −0.4243 −1.0718 −1.2782 −0.8578
−0.3118 0
293.15 0
0.1930
0.3586
−0.5895 0
0.2459
0.4710
0.2117 −0.4792 −0.8883 −0.7674
298.15 0
0.3418
0.6607
0.6463
0.2839
0.8248
0.1890 −0.4106 −0.6817
−0.4233 0
303.15 0
0.4399
0.9471
0.8783
0.8390
1.3744
0.7505
−0.5967 0
1.0924 −0.5425
308.15 0
0.4788
1.1808
1.2082
1.3160
1.8330
1.3423
0.5583 −0.3493
−0.2653 0
313.15 0
0.5949
1.2809
1.5041
1.5852
2.1555
1.7068
1.0009 −0.0774
−0.3740 0
318.15 0
0.7159
1.5225
1.6356
1.8065
2.6393
2.1900
1.3174 −0.0217
−0.4270 0
323.15 0
0.6446
1.6695
1.9333
2.1590
3.0725
2.7460
1.8652
0.3339 −0.1125 0
328.15 0
0.7500
1.7604
2.1628
2.2449
3.4051
3.1624
2.1156
0.6045
0.0007 0
333.15 0
0.8321
1.7921
2.1739
2.5037
3.7403
3.5951
2.5253
0.7142
0.1723 0
338.15 0
0.8395
1.8330
2.4034
2.6774
3.9276
3.9001
2.7758
0.9148
0.2855 0
343.15 0
0.8879
1.8536
2.4815
2.9289
4.1310
4.0422
3.0126
1.2957
0.5443 0
348.15 0
0.9073
1.9164
2.5429
2.9875
4.0918
4.1849
3.0970
1.4812
0.6773 0
353.15 0
0.9256
1.9180
2.5927
3.1289
4.1670
4.3161
3.3193
1.4684
0.7536 0
358.15 0
0.8700
1.7793
2.5501
3.2489
4.1921
4.2830
3.3911
4.6388
0.8489 0
363.15 0
0.9237
1.7089
2.5066
3.2651
4.0922
4.2324
3.2160
1.5017
0.5856 0
368.15 0
0.8690
1.6266
2.4640
3.3852
4.0392
4.1017
3.1130
1.6722
0.6809 0
373.15 0
0.8570
1.6005
2.4215
3.5054
4.0643
4.0686
3.0448
1.6878
0.7760 0
0.1572 6 x 6 0.3033 and x > 0.3033, and fitted to the following polynomials,
respectively:
at x 6 0.1572
n
X
C Ep,m =
ai x i ,
(7)
i=1
at 0.1572 6 x 6 0.3033
C Ep,m =
n
X
ai x i ,
(8)
ai (1 − x)i .
(9)
i=0
at x > 0.3033
C Ep,m =
n
X
i=1
Calorimetric investigation of excess molar heat capacities
921
The standard deviation δ of the fits for each mixture was calculated by the equation (10):
E exp
fit
δ = [6{(C Ep,m
− C p,m )2 }/(n − 1)]1/2 ,
(10)
E exp
fit represent the
where n is the number of experimental points, and C p,m and C Ep,m
experimental measurement and the corresponding result calculated from the equations (3),
(5)–(9), respectively. The coefficients ai and the standard deviations δ are given in table 4.
Figure 2 shows the excess heat capacity isotherms of the ethylene glycol + water
mixtures as well as the corresponding Redlich–Kister curves. The fitting results are listed
in table 4. In order to see clearly the change of the curves in figure 2 at maxima, the
inserted figure was used within figure 2. The shapes of C Ep,m (x) curves in figure 2 and their
changes with temperature can be interpreted qualitatively by consideration of the molecular
interactions in solutions.
Figure 3 shows the excess heat capacities of (ethylene glycol + water) as well as the
corresponding fitting curves with the same composition.
The function of C Ep,m with respect to T was established at the same composition and
different temperature. In order to fit well, reduced temperature (X ) was used instead of
temperature T , were
(11)
X = (T − 323.15)/50.
The fitting results and the standard deviation δ are listed in table 5.
4. Discussion
It can be seen from figure 2 that the shapes of C Ep,m (x) curves change dramatically when
the temperature increases. At temperatures (273.15, 278.15 and 283.15) K, the C Ep,m values
are negative at all compositions with the minimum at x ≈ 0.3. In contrast, the values of
C Ep,m are all positive in the temperature range from 333.15 K to 373.15 K with the maxima
at 0.2250 < x < 0.3033. At temperatures between about 288.15 K and 328.15 K, C Ep,m (x)
has both positive and negative portions with the maximum values at x ≈ 0.07 and 0.25,
and the minima at x ≈ 0.65. The points with maximum values at x ≈ 0.07 changes into
inflexions as temperature increases, and the curves become smooth at these points when
temperature further increases. The C Ep,m (x) curve at T = 303.15 K is of special interest
in view of its shape: the C Ep,m of the mixture reaches maximum values at x ≈ 0.07, 0.25,
0.40, respectively.
The shapes of the C Ep,m (x) curves in figure 2 and their changes with temperature can
be interpreted qualitatively by consideration of the molecular interactions in the mixtures.
Water molecules build a three-dimensional latticed structure due to intermolecular hydrogen bonds. (4, 9–11) With increasing alcohol concentration, alcohol molecules displace water
molecules inside the lattice, which raises the stability of the system. A further increase of
alcohol breaks the water structure and leads to the characteristic inflection points in the
excess enthalpy curve. This region is described as a “pseudo-two-phase system” with clusters of water molecules as one phase and random mixture of (water + alcohol) as the other.
The structure of the (ethylene glycol + water) may be explained based on the same principles. A “pseudo-two-phase system” may be the stable structure in (ethylene glycol +
922
Zhaodong Nan, Beiping Liu, and Zhicheng Tan
TABLE 4. Coefficients ai and standard deviations δ
T /K
k
a1
273.15 0.4353
278.15 0.4353
283.15 0.5469
288.15
293.15
298.15
−13.025
−8.9396
−6.6292
x
x
x
x
x
6 0.2250
> 0.2250
6 0.2250
> 0.2250
6 0.2250
x > 0.2250
7.8866
4.0597
7.4907
−6.4131
9.0662
−0.07900
a2
a3
1.7720
2.2204
0.7544
7.9260
8.9192
9.0752
−122.47
351.11
−24.268
23.531
−8.6728 −577.86
29.652
−64.368
117.22
−1994.6
−9.4190
x 6 0.1572
0.1572 6 x 6 0.3033
x > 0.3033
21.101
−4.2432
36.377
−147.15
49.399
−281.64
308.15
x 6 0.2250
x > 0.2250
25.397
−2.5158
−178.68
2.4508
452.82
5.1754
313.15
x 6 0.2250
28.170
−183.88
449.05
x > 0.2250
−3.7732
x 6 0.2250
x > 0.2250
x 6 0.2250
34.418
−4.2643
33.816
−247.53
10.252
−206.90
x > 0.2250
−6.3135
21.690
x
x
x
x
x
x
6 0.2250
> 0.2250
6 0.2250
> 0.2250
6 0.2250
> 0.2250
38.508
9.1676
38.398
18.381
38.521
20.068
x
x
x
x
x
x
6 0.2250
> 0.2250
6 0.2250
> 0.2250
6 0.2250
> 0.2250
x
x
x
x
x
323.15
328.15
333.15
338.15
343.15
348.15
353.15
358.15
363.15
368.15
373.15
−8.9544
−3.3996
−5.2860
2164.8
48.077
6075.3
14.099
303.15
318.15
a4
275.16
−108.59
634.08
δ/(J · K−1 · mol−1 )
0.1166
0.09949
0.08823
0.01202
0.03705
0.006032
0.009925
0.0003458
0.01221
−434.32
0.03593
0.0001871
0.01293
0.04223
0.06597
0.03048
8.6873
0.06197
651.46
0.03773
0.08605
0.05790
519.99
−10.588
0.09730
−254.02
−2.3004
−243.12
−129.42
−223.25
−138.32
665.17
0.05985
0.1166
0.08557
0.08501
0.1001
0.02223
37.424
17.729
38.306
19.309
37.206
23.241
−192.54
−115.00
−192.71
−121.49
−168.01
−146.40
478.18
254.89
458.08
267.02
376.98
317.29
6 0.2250
6 0.2250
6 0.2250
> 0.2250
6 0.2250
31.717
20.581
30.607
17.622
25.949
−97.502
−125.92
−83.473
−115.07
−19.373
174.71
275.20
126.13
260.67
−70.861
x > 0.2250
x 6 0.2250
x > 0.2250
13.761
23.483
14.719
−83.352
16.219
−87.288
649.48
285.60
574.49
305.20
197.39
−177.46
195.50
−182.25
−195.82
−164.08
−172.29
−204.09
−179.11
−171.66
−130.99
−127.31
0.06363
0.0007155
0.006667
0.01962
0.04807
0.02726
0.01828
0.03541
0.02795
0.004287
0.05607
0.005175
0.09126
0.03733
Calorimetric investigation of excess molar heat capacities
923
C Ep,m
4.4
4.2
5
4.0
4
3
0.24
0.22
0.26
0.28
0.30
0.32
x
C Ep,m /(J . K− 1 . mol − 1)
2
1
3
2
B
0
4
C
6
5
D
c
E
F
7
f
G
d
−1
9
I
i
8
e
H
g
h
−2
−3
T = 373.15 K
T = 368.15 K
T = 363.15 K
T = 358.15 K
T = 353.15 K
T = 348.15 K
T = 343.15 K
T = 338.15 K
T = 333.15 K
T = 328.15 K
T = 323.15 K
T = 318.15 K
T = 313.15 K
T = 308.15 K
T = 303.15 K
T = 298.15 K
T = 293.15 K
T = 288.15 K
T = 283.15 K
T = 278.15 K
T = 273.15 K
−4
0.0
0.2
0.4
0.6
0.8
1.0
x
FIGURE 2. Experimental excess molar heat capacities C Ep,m plotted against mole fraction x for
{ethylene glycol x + water (1 − x)}.
water), so that C Ep,m reaches its maximum in the region of forming the “pseudo-two-phase
system”. At T = 303.15 K, the reason why the C Ep,m of the mixture reaches maximum
values at x ≈ 0.25 and 0.40, respectively, may be that the mixture contains two kinds of
“pseudo-two-phase system”. The “pseudo-two-phase system” may consist of clusters of
water molecules as one phase or ethylene glycol molecules as one phase and a random
924
Zhaodong Nan, Beiping Liu, and Zhicheng Tan
6
C Ep,m /(J . K− 1 . mol − 1)
4
2
0
−2
−4
273
293
313
333
353
373
T/K
x = 0.03123
x = 0.3033
x = 0.06765
x = 0.4038
x = 0.1106
x = 0.5372
x = 0.1572
x = 0.7232
x = 0.2250
FIGURE 3. Experimental excess molar heat capacities C Ep,m plotted against temperature for
{ethylene glycol x + water (1 − x)}.
mixture of (water + ethylene glycol) as the other. When the experimental temperature is
lower than 283.15 K, the structure of the mixture does not contain a “pseudo-two-phase
system” because of the difficulty of forming a random mixture of (water + ethylene) at
such low temperatures. It forms easily a random mixture of (water + ethylene) with temperature increasing. Therefore, when the experimental temperature is higher than 343.15 K,
the structure of the mixture contains a “pseudo-two-phase system” at all compositions, and
the curves of C Ep,m (x) become smooth at x ≈ 0.07.
Even though the heat capacity values determined in our experiments agree well with,
those reported in reference 3, the values of the excess heat capacities C Ep,m differ from each
other. This appears to occur because the excess heat capacity values are very much smaller
Calorimetric investigation of excess molar heat capacities
925
TABLE 5. Dependence of C Ep,m against reduced temperature X
x
Equation of C Ep,m (X )
0.03124
C Ep,m = −0.6301X 4 + 0.2538X 3 + 0.06510X 2 + 0.4762X + 0.6446
0.02077
0.06767
= −1.5139X 2 + 1.3043X + 1.6695
= −1.5378X 2 + 1.9602X + 1.9333
= −1.6157X 2 + 2.7413X + 2.1590
0.02087
= −2.4332X 2 + 3.3305X + 3.0724
0.01646
= −2.3411X 2 + 3.7897X + 2.7460
= −1.7958X 2 + 3.1650X + 1.8652
= −1.2973X 4 − 0.5183X 3 + 0.6573X 2 + 2.1176X + 0.3339
0.02915
0.5372
C Ep,m
C Ep,m
C Ep,m
C Ep,m
C Ep,m
C Ep,m
C Ep,m
0.7232
273.15 K 6 T 6 293.15 K
0.1106
0.1527
0.2250
0.3033
0.4038
C Ep,m = −25.692X 3 − 72.562X 2 − 64.803X − 18.905
δ/(J · K−1 · mol−1 )
0.01710
0.03081
0.05201
0.02916
0.01354
293.15 K 6 T 6 308.15 K
C Ep,m = 140.73X 3 + 194.12X 2 + 87.127X + 12.202
0.0003559
308.15 K 6 T 6 318.15 K
C Ep,m = 2.7850X 2 + 0.3055X − 0.4243
0.0002185
318.15 K 6 T 6 358.15 K
C Ep,m = 1.4677X − 0.1125
0.02463
353.15 K 6 T 6 368.15 K
C Ep,m = 119.53X 3 − 268.95X 2 + 198.78X − 47.512
0.0003082
T > 363.15 K
C Ep,m = 0.9520X − 0.1760
0.0002617
than values of the heat capacity, and the unit of the excess heat capacity is J · K−1 · mol−1
as (J · K−1 · g−1 ) × (g · mol−1 ) in order to analyse the interaction of water and ethylene
glycol molecules. At T = 298.15 K, the excess heat capacities of (water + ethylene glycol)
exhibit a maximum near x = 0.1 in reference 3, but x ≈ 0.07 in the present paper.
The results from figure 3 and table 5 indicate that the curves of C Ep,m plotted against
temperature are more sophisticated at x = 0.03124, 0.5327, and 0.7232 than those at other
compositions, and it is the most sophisticated at x = 0.7232. The phenomenon needs
further investigation. At this stage, we only put forward the comment that the dependence
of the structure with temperature is more sophisticated at x = 0.03124, 0.5327 and
0.7232.
The National Natural Science Foundation of China under the NSFC No. 20073047
financially supported this work. The China Postdoctoral Science Foundation supported
this project.
REFERENCES
1. Song, Y. J.; Tan, Z. C.; Meng, S. H.; Zhang, J. B. Thermochim. Acta 2000, 352–353, 255–264.
926
Zhaodong Nan, Beiping Liu, and Zhicheng Tan
2. Song, Y. J.; Tan, Z. C.; Meng, S. H.; Zhang, J. B. J. Chem. Thermodynamics 1999, 31, 1359–
1368.
3. Huot, J. Y.; Battistel, E.; Lumry, R.; Villeneuve, G.; Lavallee, J. F.; Anusiem, A.; Jolicoeur, C.
J. Solution Chem. 1988, 17, 601–636.
4. Kracht, C.; Ulbig, P.; Schulz, S. J. Chem. Thermodynamics 1999, 31, 1113–1127.
5. Kracht, C.; Ulbig, P.; Schulz, S. Thermochim. Acta 1999, 337, 209–217.
6. Ogawa, H.; Murakami, S. Thermochim. Acta 1986, 109, 145–154.
7. Tan, Z. C.; Zhou, L. X.; Chen, S. X.; Zheng, Q. J. Chemical Technology (Chinese) 1982, 4,
55–60.
8. Douglas, T. B.; Furukawa, G. T.; McCoskey, R. E.; Ball, A. F. J. Res. Natl. Bur. Stand. 1954,
53, 139–153.
9. Larkin, J. A. J. Chem. Thermodynamics 1975, 7, 137–148.
10. Mikhailov, V. A.; Pnormarovo, C. I. J. Struct. Chem. 1968, 9, 8–15.
11. Mikhailov, V. A. J. Struct. Chem. 1968, 9, 332–339.
(Received 10 September 2001; in final form 2 January 2002)
WE-319