review of experimental and recommended data for the excess molar volumes of 1-alkanol + n-alkane...
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Fluid Phase Equilibria, 89 (1993) 31-56 Elsevier Science Publishers B.V., Amsterdam
31
Review of experimental and recommended data for the excess molar volumes of 1-alkanol + n-alkane binary mixtures
Andrzej J. Treszczanowicze, Teresa Treszczanowicz* and George C. Bensonb
“Ina~itute of Physical Chemistry, Polish Academy of Sciences, P.O. Box 49, 01-224 Warszawa 42, (Poland)
bDepartment of Chemical Engineering, University of Ottawa, 770 King Edward Ave., Ottawa, Ontario, KIN 9B4 (Canada)
Keywords: alkanol + n-alkane mixtures, excess volume, bibliography, review, recommended data, key systems, fitting equations.
ABSTRACT
A review of excess volume data for (l-alkanol + n-alkane) systems and recommended data sets are presented. The review covers 54 systems in 207 data sets published up to 1991. The experimental data are repre- sented in a reduced form as parameters of the best smoothing equation together with the standard and maximum deviations. For all data the tem- perature, pressure, number of data points, and method of measurement are given. Six recommended data sets are selected from the collected sys- tems: methanol + n-heptane, ethanol + n-hexane, ethanol + n-heptane, 1-propanol + n-heptane, l-butanol + n-heptane and 1-hexanol + n-hexane. Recommendation are also given for the five key systems of the IUPAC Project.
INTRODUCTION
Handa and Benson (1979) presented a review containing excess volume data which were collected up to 1978. The review gives parameters of the selected smoothing equation and standard deviation, number of data points, method and temperature of measurement.
037~3812/93/$06.00 01993 Elsevier Science Publishers B.V. AU rights rk?WNd
32
More complete information is presented in the “International DATA Se- ries, Selected Data for Mixtures” edited by Kehiaian. This Series should be recommended as an example adequately describing experimental data, where (cf. Benson (1986) all the necessary informations for verification of the data are reported about quality of measurement, numerical data, stan- dard and maximum deviation for the best fitting equation, illustrated by a plot of the measured property (VE) as a function of mole fraction .
Bibliographic data for excess volume of the 1-alkanol + n-alkane mix- tures were presented by us twice (Treszczanowicz et al, (1985, 1989) and the present paper is based on these compilations. The first successful re- view and critical evaluation of the data for binary systems formed by methanol with hydrocarbons was undertaken by Srivastava and Smith (1987), where the recommended data set for methanol + n-heptane system is given.
An aim of the present paper is to extend the part of collection given by Handa and Benson (1979) regarding (l-alkanol + n-alkane) systems up to 1991 and to select sets of recommended data.
The first part contains the data review and the second part considers recommended data for specific systems. The collection contains data for 54 binary 1-alkanol + n-alkane systems presented in 207 data sets. For data reduction there were applied various smoothing equations.
DATA REDUCTION AND CURVE FITTING
Our knowledge of fluid behavior is incomplete and so empirical and semiempirical equations have been used to represent experimental data of their properties. The most common is the polynomial equation, which in the case of excess properties of binary mixtures is expressed as powers of the differences of the mole fractions of the two components (x, - x2>.
Equation (1) is associated with the names of RedZich and Kister (RK). Acton (1970), Malanowski (1974) and King et al (1979) suggested the use of a rational function (R(m,,q)) to represent the data, with fewer coef- ficients than those required for the RK equation:
33
m,
where ml, m2 are numbers of parameters in numerator and denomina- tor, respectively. One commonly applied equation which is a particular case of the above expression is that proposed by Myers and Scott (MS) (1963) with one “skewing” parameter in denominator:
The equation is regarded as one of the best for the description of the pos- itive-negative shape of excess volume data for the alkanol + alkane systems. Another modification of the Redlich-Kister equation is the so- called switching fimction (SF):
lF ml
cm3 mar’ = xl x2 f expk~,) C vi (xl - ~2)”
i-1 m2
+ 11 - eW-~,)l~ 4 (x, - x2,‘,
i-1
proposed by Costigan et al (1980).
The equation proposed by Neau (NE) (1972) for alkanol + alkane sys- tems:
If/cd mof’ = x, x2 i vi yi (5) Cl
where
Yi- ( Xl - , +‘,, y 1
34
and parameter D is usually fitted as an integer. For excess volumes of the alkanol + alkane systems, D = 35 has been recommended (cf. Berro (1982)) and this value is used in this work.
Another type of equation which has been applied widely for excess prop erties with a complex shape is Missen’s square root of x (SR) equation for alkanol + alkane systems:
(6)
However, it should not be applied to data in the high dilution region due to infinite slope of the partial molar excess at infinite dilution (x =O>. It should be added that modifications of the above equations lead to better results only when mole fraction is replaced by volume or surface fractions (cf. Handa and Benson, (1977)).
For data in the dilute region a polynomial (P) of 1-alkanol mole frac- tion is applied:
(7)
A comparison of the data fits given by different equations and choice a proper number of parameters for recalculated data is made by calculation of the standard deviation, from the relation:
where: n - is the number of data points, m - number of parameters of the smoothing equation and i is the serial number of the data point. A nonlin- ear least squares Levenberg-Marquardt procedure (1988) is applied throughout the paper.
Excess volumes for alkanol + alkane systems are characterized usually by high asymmetry and positive - negative shape. Therefore it needs more parameters, but it is important to minimize their number to avoid system- atic error. A tendency observed during the last 20 years is to overestimate the number of fitting parameters even for sets with a low number of data points. To avoid over-fitting, it is recommended to use no less than 3-4 data points per parameter. Peneloux (1974) recommends an even more rig- orous rule:
n-4 m = 1 + integer 8
For numerical data recalculated in the paper a best fitting equation (usually rational function, Myers-Scott or Neau) needs no more than 6 pa- rameters. Further increase in their number (under mentioned above limitations) not lead to marked decrease in standard deviation. For data with insufficient number of points the methods based on theoretical mod- els are recommended.
ORGANIZATION OF EXCESS VOLUME TABLES
All the bibliographic data are presented in Table I in a grid. Apart from data used for selection of the recommended data and high dilution data, the grid contains some data (given in parenthesis) which are not included in Table II. These data can be: a) presented graphically only, b) set con- tains too low number of data points, c> data are not available, d) bad quality data.
All systems have been recalculated if there is a sufficient number of data points by all the equations given above. The parameters of the best fitting equation and the quality of fit given by standard and extreme devi- ations are presented together with information about the conditions of the measurement (temperature, and pressure if necessary), number of data points, method of measurement, and range of concentration.
In the case where the reference contains no experimental data except fitting equation parameters, these parameters are collected in Table II, but the column listing the number of data points is left blank.
Table II gives the following information in subsequent columns:
36
1) name of mixture: names of components are reduced to numbers of their carbon atoms and the respective number for the 1-alkanol precedes that for the n-alkane.
2) condition of measurement: temperature CC) and, if necessary, pressure (MPa) are given. If pressure is not reported then it is considered as normal (0.101325 MPa).
3) number of data points: n (in the case if source paper not contains numerical data but fitting equation parameters this column is blank
4) range of concentration: w- for measurements in the whole concentrations range, hd - for high dilution (conventionally assumed x 0.05). In the case of a miscibility gap, the letters ‘LLE’ are added.
5) smobthing equation initials: RK - for Redlich and Kister, es.(l), Rm,,m, - for the rational function given by eq.(2) MS - for Myers and Scott, eq.(3), NE for Neau eq.(5) RS - for Missen eq.(6) and P - for polynomial of xi given by eq.(7).
6) equimolar value: V&/ c~‘~oP calculated from the smoothing equation parameters.
7) l 12) contain up to 6 parameters of the smoothing equation indicated in column 5. In the case if source paper contains fitting equation parameters these parameters are listed.
13) standard deviation of the fit given by relation (8)
l~~.~nitia& of esperimental technique, the same as given in Handa and Benson’s (1979) paper (where each method is described and verified): D _ density measurements when a technique is not reported, DF- density by a magnetic float densimeter, DO - density by a mechanical oscillator densimeter,, DP - density by a pycnometer, VB - direct excess volume measurement by batch dilatometer, VD - direct excess volume measurement by dilution dilatometer.
16) reference paper.
Tab
le I
Th
e bi
blio
grap
hic
da
ta f
or e
xces
s vo
lum
e of
(1-
alka
nol
+ n
-alk
ane)
bi
nar
y sy
stem
s*)
Il-C
, -’
n-C
R
C,O
H
70
31 “A
&
(80)
I 1
&O
H
1 -
I (2
9),
33,
(4%
47
, 51
r, 5
4,64
,
(66)
C,O
H
- 29
,33,
(3
4)
(4%
42
,54,
(6
3,
66)
C,O
H
- 24
, (2
9,
41)
42,6
0
I I
C,O
H
- 1
C,O
H
14s,
7f
15’,
27,
(29)
, 31
h,
42,6
2,73
’
C,O
H
-
C,O
H
- (2
9),
42,6
2
n-C
, n
-C,
5’,
(61,
65)
, -
68h
, 71
’
6’,
33,
4Sh
, (2
), 6
4,
(67)
(58)
, 59
, 68
h,
69,
71’,7
7
4,7’
, 33
, (2
), 3
8
‘35,
46!5
2,
68
,71’
,76
8’,
25,4
4,
30,3
8,
49
45,
4Sh
, 52
, (6
7)
68h
, 69
,71
r
’ h
(5:)
@:2
32,3
8,49
,
68h
:72’
(6
7)
lo’,
4Sh
, 16
’,38,
73=
52,
68h
, 69
,
72’
C&
OH
-
Cl&H
16
’, 74
’ 19
*,
31h
,
42,6
2,74
’
&O
H
- _
$g$-
pg
- “;
:
I )
Nu
mbe
rs
are
attr
ibu
ted
to
*efe
reys
gi
ven
in
D
otn
ote
of t
he
Tab
le
pare
nth
esis
. S
upe
rscr
ipts
de
not
e:
nJ h
igh
dil
luti
on,
r, r
ecom
men
ded
data
, ”
sele
cted
dat
a.
II.
Dat
a,n
ot
incl
ude
d in
Tab
le
II a
re i
--I-
26
,53,
78
-
n-C
,, I
n-C
,, I
n-G
A
I n-
C,,
I I
I
55,5
6 55
,57
(63)
I I
!
36
22a,
31
h,
74
Y
Tab
le
II
Exc
ess
volu
me
data
(!llz
ble
IZ
, pa
ge:
1)
Nam
e t
p
Ran
ge
N
OC
M
Pa
XI
1+5
25
Eq
n.
ti5
Vl
v2
V
3 v
4
VS
v
6
8V
@
M
ref.
b’
typ
e cm
?m
ol
cm3/
mo
l cm
3/m
ol
R2,
2 0.
395
1.57
88
-1.8
150
-0.7
605
-0.4
667
- -
0.01
0 0.
021
DP
[7
0]
1+8
25
1+6
40
1+7
25
1+7
20
2.0
3.99
7.96
11.9
4
15.9
1
19.8
9
25.8
6
29.8
3
33.8
1
W
hd
w,ll
e
w,ll
e
hd
13
13
11
20
4
P NE
MS
P
0.61
6
5.4660
-54.991
325.76
3.2158
-3.3794
3.4120
1.8857
2.1375
2.5638
6.8189
-108.84
-
-679
.56
0.86
49
3.0528
0.93
79
0.97
88
0.0058
0.0083
DO
[31]
0.007
0.011
DO
WI
0.0008
0.0009
VD
[5,71]
0.0026
0.0026
VS
F81
2+6
25
2+6
25
2+6
10
2+6
25
2+6
35
2+6
15
2+6
25
2+6
25
2+6
25
2+6
25
2+6
25
2+6
25
2+6
25
2+6
25
2+6
25
2+6
25
2+6
35
2+6
25
2+7
25
2+7
25
W
W
W
W
W
W
W
W
W
W
W
W
W
W
W
W
W
W
w,h
d
W
15
7 28
34
30
8 13
13
13
13
13
13
13
13
13
13
8 11
55
RK
0.427
1.7095
-0.6490
1.2532
RK
0.402
1.8092
-1.8434
-1.0692
MS
0.344
1.3767
1.3116
0.6147
MS
0.4090
1.6361
1.3247
0.4741
MS
0.4630
1.8521
1.3387
0.3671
SR
0.358
4.4682
-8.2381
5.5788
NE
0.394
2.1642
-1.8588
0.6694
NE
0.368
1.9170
-1.3280
0.2603
NE
0.377
1.9396
-1.3367
0.0018
NE
0.342
1.8843
-0.8213
-0.4161
NE
0.344
1.6764
-1.2920
1.3828
NE
0.334
1.6270
-1.2421
1.3326
NE
0.327
1.7091
-1.3281
0.4946
NE
0.325
1.6909
-1.6756
1.7902
NE
0.315
1.6337
-1.6559
1.8405
NE
0.301
1.4717
-0.9943
0.4206
MS
0.470
1.8790
1.1562
0.9128
MS
0.444
1.7751
-0.7555
0.5914
MS
0.4714
1.8830
1.7452
0.827
NE
0.4753
2.5759
-2.9033
3.8810
-1.2792
0.5756
0.98
87
0.5536
0.97
68
0.5179
0.96
66
1.1921
1.0811
1.4391
1.5113
1.0610
0.99
30
-0.7453
0.8880
-1.9355
0.188
1.6098
0.024
0.020
0.002
0.0008
0.001
0.009
0.009
0.010
0.008
0.009
0.008
0.008
0.008
0.009
0.007
0.006
0.009
0.005
0.0010
0.0018
0.04
3 0.024
0.0070
0.0019
0.0019
0.013
0.017
0.013
0.014
0.011
0.011
0.010
0.012
0.013
0.013
0.013
0.013
0.008
0.0022
DP
W
I D
1471
VD
[51]
VD
[51]
VD
[51]
DO
PI
DO
PI
D
O
WI
DO
W
I D
O
WI
DO
W
I D
O
WI
DO
W
I D
o W
I D
O
WI
DO
P+
l D
O
WI
VD
W
l VD
[6,71]
DO
P31
2+7
25
- W
17
RK
0.475
1.9006
-0.0331
1.1055 -0.6538
- -
0.006
0.013
DP
[33]
(!lW
de I
I, pa
ge:
2)
Name
t p
Range
N Eqn.
65
Vl
v2
v3
v4
v5
V6
6V
SQ
M
WbJ
Oc
MPa
XI
type
cm3/mol
crn3/mol cm3/mol
2+7
25
- 2+7
15
-
2+7
25
- 2+7
25
2.0
2+7
25
3.99
2+7
25
7.96
2+7
25
11.94
2+7
25
15.91
2+7
25
19.89
2+7
25
25.88
2+7
25
29.83
2+7
25
33.81
2t7
35
- 2+7
20
- 2+7
25
- 2t7
30
- 2t7
25
- 2+7
45
-
2+8
25
- 2+9
25
- 2tlO
25
-
2+12
25
- 2+14
25
-
2t18
25
- 2tl5
45
-
3t8
25
- 3t8
25
-
3t8
10
-
hd
W
W
W
W
W
W
W
W
W
W
W
W
hd
W
W
W
W
W
W
hd
W
W
w,ll
e
w,lle
9 9 18
18
18
18
18
18
18
18
18
18
14
4
P RK
NE
NE
NE
NE
NE
NE
NE
NE
NE
NE
NE
P RK
RK
MS
MS
MS
NE
P MS
MS
SR
SR
7.4370
-179.64
2003.9
- -
- 0.0017
0.0024
VD
[46l
0.413
0.478
0.454
0.455
0.437
0.431
0.411
0.400
0.380
0.363
0.350
0.523
0.8617
-
-0.8444
-
-0.9951
- -1.2842
-
-1.4508
-
-1.0923
-
-0.8305
-
1.8534 -0.0002
1.1585
2.5431
-2.3215
1.8008
2.4383
-2.4964
2.4888
2.4623
-2.6164
2.6460
2.3787
-2.5673
2.5908
2.3407
-2.8258
3.6100
2.2202
-2.7224
3.6532
2.1943
-2.9433
4.1812
2.0394
-2.7058
4.1027
1.8590 -2.1777
3.3274
1.8297 -2.2158
3.1843
2.9245
-3.2786
3.1584
5.8195
-92.116
- 1.8223
-0.0888
1.5627
1.4478
-0.5901
0.3815
1.8504
1.7827
0.8714
2.4773
2.0390
0.7519
2.0460
-0.3928
1.1495
2.8157
-2.9616
4.6292
8.2542
-79.300
568.50
1.4737
1.7139
1.3243
1.1393
1.6055
1.3621
Q.OQ40
-41.913
103.25
11.347 -48.100
116.53
0.010
0.010
0.012
0.008
0.007
0.008
0.008
0.009
0.008
0.007
0.008
0.008
0.0046
-
0.017
0.017
0.022
0.012
0.012
0.015
0.015
0.016
0.013
0.013
0.015
0.022
0.0044
14
14
11
_ 11
10
18
19
24
0.456
0.362
0.463
0.519
0.512
0.517
0.368
0.285
0.534
0.7028
0.9784
0.002
0.7405
0.9695
0.004
-0.0137
- 0.003
-0.5098
-4.9390
5.2394
0.0022
-1459.0
- 0.005
0.8542
- 0.007
0.5295
0.9732
0.008
-122.06
56.964
0.005
-140.57
66.544
O.OOQ
0.003
0.006
0.008
0.008
0.011
0.011
0.012
0.017
Do
r5Q
j D
o W
I D
o PI
D
o W
I D
O
WI
Do
PI
DO
15
91
DO
W
I D
O
PI
DO
15
91
DO
W
I D
o PI
V
B
PI
DP
WI
DP
PI
VD
W
l V
D
[TII
V
D
WI
Do
P31
DO
[31]
VD
WI
VD
W
I V
D
WI
VD
PI
W
8 MS
0.172
0.8860
-0.4613
0.5711
W
11
RK
0.173
0.8920
-1.0147
0.2125
W
14
NE
0.1434
1.2188 -1.9144
1.1002
-0.OQO5
-
0.00
9 0.011
D
PQ
I 0.014
0.030
DP
PI
0.0011
0.0019
Do
w
3t6
25
- W
14
NE
0.1797
1.6329 -2.7785
1.8638 -0.5138
- -
0.0005
0.0006
Do
1421
$4
Nam
e t
p R
ange
N
OC
M
Pa
x1
3+8
40
- 3+
8 15
-
3+8
25
- 3
+ 8
25
2.0
3+8
25
3.99
3+
8 25
7.
98
3+8
25
11.9
4 3+
8 25
15
.91
3+8
25
19.8
9 3+
8 25
25
.86
3+8
25
29.8
3 3+
8 25
33
.81
3+8
35
- 3+
7 25
-
3+7
25
- 3+
7 25
-
3+7
25
- 3+
7 30
-
3+7
20
- 3+
7 25
-
3+8
30
- 3+
9 30
-
3+9
20
- 3+
9 25
-
3+9
60
- 3+
11
15
- 3+
11
25
- 3+
11
35
- 3+
11
45
-
W
W
W
W
W
W
W
W
W
W
W
W
W
W
W El
W
hd
W
W
W
W
W
W
W
W
W
W
14
8 9 9 9 9 9 9 9 9 9 9 8 7 39
17
10
(!R
h!e
II,
page
: 3)
8
Eqn.
\$
.s
Vl
v2
v3
v
4
v5
V
6 8V
S
P
M
,f.b’
type
cm
3/m
ol
cm3/
mol
cm
3/m
ol
NE
0.24
17
2.26
45
-4.0
788
3.18
33
-1.2
754
- -
0.00
12
0.00
21
DO
[4
2]
0.14
3 0.
164
0.15
7 0.
170
0.18
5 0.
170
0.18
9 0.
166
0.18
5 0.
180
0.14
2 0.
218
0.30
5 0.
2_q6
4 0.
301
0.33
7 5 14
7 14
28
14
20
20
20
20
SR
N
E N
E N
E N
E NE
NE
NE
NE
NE NE
SR
YS
MS
MS P RK
P MS
RK
R
K
R3,
2 R
3,2
R3,
2 R
3,2
R3,
2 R
3,2
R3,
2
0.31
2 0.
413
0.44
91
0.37
40
0.40
53
0.73
42
0.39
01
0.45
71
0.52
33
0.82
08
2.12
34
1.53
75
1.45
63
1.55
82
1.47
60
1.51
07
1 A06
5 1.
3481
1.
3568
1.
2862
1.
1813
3.
8298
1.
2214
1.
1877
1.
2033
7.
5621
1.
3472
5.
8281
1.
2475
1.
8534
1.
7968
1.
4961
1.
6210
2.
9367
1.
5604
1.
8284
2.
1131
2.
4831
-2.1
935
- -
-1.9
738
- -
-1.8
539
- -
-1.9
734
- -
-1.6
288
- -
-1.8
614
- -
-1.6
399
- -
-1.5
373
- -
-1.5
861
- -
-1.4
533
- -
-1.3
800
- -
-3.9
092
- -
0.54
66
- -
0.58
28
-0.0
650
0.33
23
0.44
65
-0.2
170
0.90
29
-259
.14
4053
.1
- 0.
4372
-0
.154
07
- -7
9.47
0 -
- 0.
6921
-0
.232
7 0.
9687
0.
5542
0.
5120
-
0.40
75
0.17
72
- -0
.138
9 -0
.371
6 0.
0686
-0
.267
0 -0
.536
4 0.
0186
-0
.628
9 -1
.151
8 0.
0594
0.
0998
0.
3634
0.
1023
0.
2851
0.
5409
0.
2300
0.
2212
0.
3745
0.
2199
0.
2804
0.
7758
0.
2482
-0.0
186
0.98
22
-0.5
958
-
-0.6
635
- -0
.688
0 -
-0.2
718
- -0
.204
5 -
-0.2
570
- -0
.158
2 -
0.02
3 0.
021
0.02
2 0.
024
0.02
3 0.
021
0.02
0 0.
018
0.02
0 0.
022
0.01
9 0.
035
0.01
2 0.
0002
0.
008
0.00
13
0.00
6 0.
005
0.01
1 0.
006
0.00
5 0.
0013
0.
0018
0.
0025
0.
0012
0.
0022
0.
0016
0.
0020
0.03
1 0.
034
0.03
7 0.
038
0.03
3 0.
036
0.03
4 0.
026
0.02
9 0.
034
0.03
0 0.
054
0.01
5 0.
0005
0.
015
0.00
16
0.00
5 0.
020
0.00
7
0.00
20
0.00
36
0.00
50
0.00
20
0.00
52
0.06
40
0.00
50
Do
WI
Do
WI
Do
WI
DO
W
I D
o W
I D
O
WI
DO
W
I D
O
WI
Do
WI
Do
WI
Do
WI
Do
WI
DC
[4
] VD
[7
,711
D
P [3
3]
VD
WI
VB
[52]
VS
WI
VD
W
I V
D
WI
VB
W
I D
O
WI
DO
W
I D
O
WI
Do
156,
551
DO
[5
6,55
l W
[5
6,55
l W
(5
6,55
1 3+
12
15
- W
20
R
3.2
0.41
22
1.64
85
0.43
54
0.44
92
0.25
97
-0.1
906
- 0.
0014
0.
0028
W
15
7,55
l_
Nam
e t
p R
ange
N
OC
M
Pa
XI
3+12
25
3+
12
35
3tl2
45
20
20
20
(Ta
bk
II,
pa
ge:
4)
Eqn.
ti
5 V
l v2
v3
v4
v5
V
6 &
a?
M
re
t.“’
type
cm
3/m
d cm
3/m
d cm
3/m
ol
R3.
2 0.
4848
1.
8584
0.
2185
0.
3798
0.
1871
-0
.283
1 -
0.00
18
0.00
30
DO
[5
7,55
1 R3
;2
R3,
2 0.
5398
2.
1594
0.
2188
0.
8084
0.
2013
-0
.184
3 0.
0015
0.
0027
D
o (5
7,55
1 0.
8289
2.
5075
0.
7053
0.
8981
0.
3855
-0
.130
8 0.
0018
0.
0025
D
O
[57,
551
4t8
25
4t8
IO
4+8
25
4t8
40
4+8
30
4+7
25
4t7
25
4t7
25
4t7
15
4+7
35
4t7
45
4+7
25
4t7
30
4+7
20
4t7
20
4+7
25
4t8
25
4t8
30
4t8
25
4tQ
30
4t
10
25
4t10
25
4t
lO
50
4tlO
75
4t
10
95
0.7
0.4
0.5
W
W
W
W
W
W
W
W
W
W
W
W
W
W
hd lz
W
W
W
W
W td
W
W
W
W
22
18
18
18
11
88
19
17
12
13
13
8 4
-2.5
881
0.00
23
0.00
08
0.00
18
0.98
50
0.00
13
0.00
8 0.
9753
0.
0008
0.
0027
0.
008
0.00
5 0.
002
0.00
7 0.
0015
0.
004
0.00
33
20
7 12
- 17
8 8 8 8
NE
MS
MS
MS
MS
MS
MS
MS
MS
MS
MS P RK
P RK
R
K
MS
MS
NE
RK
P RK
R
K
MS
MS
0.03
88
1.01
81
-2.1
401
0.92
13
-2.8
965
4.85
49
0.02
58
0.10
24
-0.8
311
-0.4
830
0.19
30
0.99
90
0.04
32
0.17
28
-0.7
857
-0.8
830
0.15
78
0.99
27
0.07
48
0.29
83
-0.9
180
-0.9
271
0.11
49
0.15
78
0.04
1 0.
1853
0.
9415
-0
.454
3 -
- 0.
1881
0.
7581
-0
.029
5 -0
.517
2 0.
1423
0.
0880
0.
1854
0.
7417
-0
.004
2 -0
.488
4 0.
9429
-
0.18
4 0.
7342
-0
.078
2 -0
.458
1 0.
9453
-
0.14
7 0.
5887
-0
.220
7 -0
.492
9 0.
9285
-
0.25
2 1.
0072
0.
0719
-0
.454
2 0.
9377
-
0.34
7 1.
3880
0.
3520
-0
.894
9 0.
9872
-
5.54
34
-137
.89
1528
.3
- -
0.21
9 0.
8773
0.
4334
0.
1451
-
- 5.
8235
-9
9.02
1 -
- -
0.27
27
1.09
07
-090
07
1.37
97
-1.1
428
- 0.
1797
0.
7188
-0
.880
2 0.
4773
-0
.510
5 -
0.31
51
1.24
52
0.30
53
0.84
12
-0.8
058
0.38
87
0.37
87
1.50
88
-1 .O
l37
-0.9
089
- -
0.27
23
1.73
19
-1.7
988
0.80
18
- -
0.38
5 1.
5388
0.
2857
0.
1000
-
- 4.
8948
-5
2.35
5 31
1.55
-8
57.1
8 -
0.38
3 1.
4508
-0
.382
8 0.
3377
-
- 0.
538
2.15
38
-0.7
404
0.71
03
- -
0.85
5 3.
4195
2.
0808
0.
8798
-
- 1.
218
4.88
34
2.53
87
0.84
18
- -
0.00
35
0.00
48
0.00
03
0.00
3 0.
004
0.00
7 0.
020
0.00
9 0.
008
o.oo
4o
Do
0.00
18
DO
0.
0038
D
o 0.
0030
D
o 0.
011
VD
0.00
21
VD
0.00
70
Do
0.01
7 D
P 0.
008
D
0.00
3 D
0.
009
D
0.00
28
VD
VB
0.00
34
VB
DP
DP
0.00
82
VD
0.00
59
VD
0.00
05
Do VB
0.
008
Do
0.01
1 D
F 0.
031
DF
0.01
1 D
F 0.
012
DF
M
WI
1311
[3
7l
P7l
[37l
P7
1 R
K
0.25
7 1.
0288
-0
.811
3 -0
.297
9 -1
.757
3 -
- -
- D
P 16
91
t 4t
10
25
- W
Nam
e t
p
Ran
ge
N
OC
MP
a X
I
(Tab
le Z
Z, p
age:
5)
ip
Eq
n.
es
Vl
v2
v3
v4
v5
V6
6V
aO
M
refb
’
typ
e cm
3/m
ol
cm3/
md
cm
3/m
d
5+6
15
5+6
25
5+6
35
5+7
25
5+7
30
5+7
25
5+7
30
5+7
20
5+6
0 5+6
5
5+8
25
5+8
35
5+8
45
5+8
30
5+8
25
5+9
30
5+lO
15
5+lO
25
5+10
35
5+lO
45
5+lO
25
5+l2
25
6+5
25
6+6
25
6+6
25
6+6
25
6+6
15
W
W
W
W tIl
W
hd
W
W
W
W
W
W
W
W
W
W
W
W
W
W
w,hd
w&d ttl
W
9 9 9 30
7 9 7 11
11
11
11
11
7 13
10
10
10
10
12
12
51
48
9 14
17
SR
SR
SR
M
S
MS
P RK
P RK
RK
RK
RK
RK
MS
NE
RK
NE
NE
NE
NE
MS
MS
MS
MS
MS
P NE
-0.116
1.0221 -1.7353
-0.5335
- -
- 0.007
0.010
DC
[l]
-0.198
1.6576 -3.7464
-0.2289
- -
- 0.010
0.015
W [l]
-0.250
3.3301
-9.1874
4.3348
- -
- 0.023
0.039
DO
[1]
0.0726
0.2896
-0.5079
-0.6696
0.0516
0.1039
0.9732
0.0006
0.0010
VD
[9,72]
0.2237
0.102
0.0985
0.1075
0.1075
0.1333
0.1636
0.2237
0.1881
0.269
0.216
0.291
0.347
0.382
0.321
0.3904
0.6946
0.4681
-0.3862
5.6430
-208.71
3425.1
0.4076
1.1036
0.0715
5.1591
-125.14
- 0.3939
0.6572
-0.1526
0.4301
0.6066
-0.1700
0.4299
0.6218
-0.1926
0.5333
0.6128
-0.2195
0.6543
0.6873
-0.2233
0.8946
0.4681
-0.3862
1.3056 -1.2884
0.1061
1.0759
0.5285
0.032
1.4309 -1.5831
0.7481
1.7934 -1.8076
0.8866
2.2971
-2.9159
1.9634
2.5709
-3.5729
2.7708
1.2849
0.8341
-0.3468
1.5616
1.1270
0.9080
_
0.00
3
0.0008
0.008
0.002
0.0006
0.0005
0.0004
0.0005
0.0006
0.003
0.002
0.003
0.003
0.002
0.005
0.006
0.002
0.003
0.00
4 0.0014
0.003
O.ooo8
0.0008
0.0008
0.0008
0.0009
0.004
0.004
0.004
0.003
0.006
0.008
0.003
0.004
VD
W
I V
D
WI
VB
W
I V
B
PI
Do
WI
Do
WI
W [321
W 1321
DO
WI
VD
W
I D
O
WI
VB
W
I D
O
PI
Do
PI
DO
V
I D
O
VI
DO
W
I D
o W
I
-0.5556
-2.2221
-2.7054
-0.3905
0.2166
0.2045
0.9809
0.0007
0.0019
VD
[14,73]
-0.2203
-0.6620
-1.5997
0.6367
0.1145
0.1655
0.9769
0.0004
0.0014
VD
[15,73]
-0.227 -0.9088
-1.5377
-0.5329
0.9932
- -
0.00
9 0.014
w [271
5.3250
-198.22
3036.0
-1648.0
- -
0.008
0.011
w pi]
-0.2032
-0.2687
-1.3346
0.7332
-1.6303
1.2618
- 0.0011
0.0018
W [42]
6+6
25
- W
18
NE
-0.2236
-0.2621
-1.7337
I.3971 -2.1230
1.2958
- 0.0010
0.0018
W 14
21
Nam
e t
p R
ange
N
OC
M
Pa
XI
6+6
35
6+6
50
6+6
25
6+7
25
6+7
25
6+7
30
6+7
20
6+7
25
6+6
25
6+6
30
6+9
30
6+9
20
6+9
25
6+9
60
6+10
25
6+
10
25
6+12
25
6+
16
25
7+10
25
6+
6 10
6+
6 25
6+
6 40
6+
6 25
8+
7 25
8+
7 20
8+
7 25
8+
7 30
8+
8 25
W
W
W
w,h
d hd
ii W
W
W
W
W
W
W
IYd
hd
hd
hd
W
W
W
W
W
hd
W
W
W
18
18
7 30
8
(!l’a
ble
II,
pag
e: 6
)
Eqn.
e.
5 V
l v
2
V3
v4
v
5
‘f6
SV
@
M
re
tb’
type
cm
3/m
d cm
?mol
cm
3/m
ol
NE
-0.2
470
-0.2
296
-2.3
795
2.53
21
-2.4
075
-0.2
035
1.16
61
0.00
11
0.00
16
w
[42]
-3
.934
2
0.13
61
3.79
06
0.97
11
5
0.00
28
0.00
36
0.01
6 0.
019
0.00
03
0.00
07
0.00
03
0.00
04
0.00
5 -
0.00
5 0.
005
42
7
-0.2
809
-0.1
047
-3.7
322
4.79
37
-2.4
705
-0.2
47
-0.4
358
-1.5
890
0.79
47
- -0
.024
6 -0
.099
0 -0
.825
5 -0
.658
2 0.
0278
4.
5714
-1
38.8
2 13
37.7
-
-0.0
35
-0.1
403
0.64
46
0.14
48
- 4.
2524
-8
5.45
8 -
- -0
.025
-0
.100
0 -0
.626
7 -0
.170
2 -0
.390
0 0.
0936
0.
3732
-0
.296
3 -0
.614
6 -0
.055
9 0.
102
0.40
59
0.64
57
-0.4
487
- 0.
192
0.76
75
0.20
89
0.15
98
- 0.
1590
0.
6360
0.
8785
0.
9787
0.
9235
0.
1732
0.
5926
0.
8406
0.
8159
0.
7781
0.
3422
1.
3688
0.
6654
0.
2188
0.
3935
0.
2418
0.
9656
0.
4323
-0
.441
6 -0
.099
8 5.
9904
-1
13.5
2 10
66.0
-3
469.
3 5.
5718
-8
8.85
7 76
2.32
-2
257.
6 6.
2860
-9
0.54
3 73
1.80
-2
100.
9 4.
1492
-6
5.59
3 36
2.95
-
-0.3
595
-1.4
380
-1.7
065
-0.2
169
0.14
73
-0.4
310
-1.7
262
-1.9
643
-0.1
726
0.08
62
-0.5
229
-2.0
916
-2.2
870
-0.0
615
0.04
44
-0.4
304
-1.4
102
-0.9
234
0.50
43
- -0
.213
9 -0
.857
2 -1
.281
6 -0
.367
8 -0
.013
1 3.
7860
-1
21.3
9 -
- -0
.210
8 -0
.843
3 -0
.275
4 -0
.160
7 -0
.786
3 -0
.295
0 -1
.180
0 -0
.328
6 0.
0898
1.
7010
-0
.095
0 0.
0244
-0
.938
5 -5
.946
2 24
.283
0.87
63
0.08
80
14
28
14
30
11
16
12
11
18
18
18
8 62
4
NE
NE
MS P RK
P RK
M
S M
S R
K
R1,
3 R
1,3
R1,
3 M
S P P P P MS
MS
MS
NE
MS P RK
0.05
99
0.96
29
0.15
86
0.98
56
0.11
90
0.97
98
0.07
47
0.98
80
0.06
50
0.97
25
0.00
04
0.00
09
0.00
8 0.
011
0.00
5 -
0.00
14
0.00
28
0.00
10
0.00
24
0.00
13
0.00
24
0.00
05
0.00
14
0.00
3 0.
004
0.00
4 0.
007
0.00
4 0.
008
0.00
2 0.
005
0.00
10
0.00
14
0.00
09
0.00
13
0.00
10
0.00
19
0.00
19
0.00
22
0.00
08
0.00
21
0.00
2 0.
003
0.85
03
-0.0
399
-32.
909
_ -2
.449
0 21
.177
-5
.697
DO
[4
2j
VS
PI
VD
[1
0,72
]
VD
WI
VB
PI
V
B
WI
DP
PI
VD
[16,
73]
VD
1381
VS
W
I D
O WI
DO
PI
DO
I7
81
VD
[17,
73]
Do
Bl]
DO
[3
1]
Do
[311
D
O
[31]
DO
t4
21
DO
[s
2)
DO
W
I V
B
Pl
VD
[11,
72]
VS
WI
Df’
PI
D
P PI
_
_ D
o Pl
8+
9 20
W
14
N
E 0.
0390
0.
6726
-1
.852
7 3.
1960
-4
.706
2 2.
3104
-
0.00
2 0.
003
DO
n8
1 2;
(Tab
le Z
J pa
ge:
7)
$
Name
t p
Range
N Eqn.
e.5
Vl
v2
v3
v4
V5
v6
8V
sv
M
re
tbJ
OC
MPa
XI
type
cm3/mol
cm3/md
cm3/mol
8+9
25
8+9
60
9+10
25
9+10
35
9+10
45
9+14
25
9t14
35
9t14
46
lOt5
25
10t6
25
lOt6
25
lOt6
10
lOt6
25
lOi
40
lOt6
25
lOt7
25
lOt7
25
lOt7
20
lOt7
25
lot8
25
lot8
25
lot9
25
lot9
20
lot9
25
lot9
40
lot10
25
lot10
25
W
28
NE
0.0362
0.6879
-2.0708
3.0157
-1.4470
-3.7895
3.3355
0.00
4 0.
006
~0
l781
W
42
NE
0.1148
1.6804 -4.7450
6.0176
-1.7803
-5.5433
4.2709
0.00
4 0.011
DO
I781
W
28
MS
0.0619
0.2475
-0.2080
-0.3702
-0.1294
0.9646
- 0.0015
0.00
31
DO
W
I W
22
MS
0.0801
0.3205
-0.1926
-0.3342
-0.1465
0.9523
- 0.0012
0.0028
DO
W
I W
23
MS
0.0954
0.3817
-0.2643
-0.3113
-0.0941
0.9346
- 0.0016
0.0034
DO
W
I W
18
NE
0.2517
1.5057 -2.3681
3.3113
1.1461 -7.4802
4.7674
0.0013
0.0022
Do
PA
W
17
NE
0.2837
1.7894 -2.9272
4.3848
-1.5502
-3.0702
2.1304
0.0011
0.0022
Do
WI
W
17
NE
0.3250
2.2093
-3.8413
5.1300
-1.9601
-1.0782
- 0.0020
0.0030
DO
W
I
W,h
d w,hd
hd
W
W
W
W
w,hd
IYd
W
W
W
W
W
W
W
w,hd
W
58
49
10
15
15
15
10
66
12
4
MS
M
S
P MS
MS
MS
NE
MS
RK
P RK
MS
RK
RK
MS
MS
MS
MS
RK
0.9831
0.9776
0.97
65
_
-0.9998
-3.9990
-2.8849
0.7865
-0.1682
0.1469
-0.5897
-2.3587
-2.0471
0.2532
-0.0566
0.0559
1.9587 -275.05
6524.4
-52796
-
-0.4734
-1.8936
-1.6780
0.2182
-0.0325
0.9895
-0.5874
-2.3494
-2.0041
0.3197
-8.6946
0.9789
-0.7226
-2.8903
-2.3726
0.4722
-0.1257
0.9621
-0.584 -2.4496
0.2579
- -
- -0.3532
-1.4135
-1.5063
-0.0158
-0.0131
0.0127
-0.401 -1.6055
-0.0152
0.0090
-0.7141
-
2.5957
-99.215
- -
-
-0.355 -1.4200
-0.9550
0.2011
6.0064
1.6864
-0.1897
-0.7590
-1.0462
-0.1625
-0.0063
0.0084
-0.204 -0.8160
-0.3689
0.1225
-0.4036
-
-0.074 -0.2958
-0.3489
0.1739
-0.2298
-
-0.073 -0.2902
-0.6324
-0.2961
-0.0916
0.9818
-0.076 -0.3019
-0.8761
-0.2723
-0.0567
0.9789
-0.0700
-0.2779
-0.9474
-0.1847
-0.0647
0.9221
0.0087
0.0341
-0.3616
-0.2492
-0.0708
-0.0131
-0.004 -0.0165
-0.5301
0.4582
- -
o.oo
o9
0.00
33
0.0007
0.0014
0.002
0.003
0.0020
0.0030
0.0013
0.0021
0.0014
0.0025
0.013
0.023
0.0008
0.0016
0.003
0.004
0.0012
0.0012
57
13
12
25
50
25
48
11
0.96
46
0.0005
0.0010
0.002
0.004
0.002
0.093
0.001
0.903
OS%?
0.005
0.002
0.003
0.0007
0.0016
0.0010
0.0014
VD
[18,74]
VD
[19,74]
DC
Pll
DC
WI
DO
W
I D
O
WI
VB
W
I VD
[12,72]
DC
[281
VS
[‘=
I D
P W
I VD
120,741
DC
P81
DC
WI
DO
Wl
DO
WI
~0
r/s1
VD
121,741
DC
PSI
lot10
25
hd
10
P -
3.7255
-63.388
333.68
- -
- 0.0024
0.0030
DC
Rll
Nam
e t
p R
ange
N
OC
M
Pa
XI
lo+1
6 25
-
w,h
d 45
lo
t16
25
- hd
11
(Tab
le
II, p
age:
8)
Eqn.
e.
5 V
l v2
v3
V
4 v5
V
6 6V
S
F M
fe
f.b’
type
cm
3/m
ol
cm3/
mol
cm
3/m
ol
MS
0.26
34
1.05
41
0.74
03
-0.0
393
-0.0
064
0.02
70
0.95
59
0.00
06
0.00
18
VD
[22,
74]
P -
4.56
90
-79.
666
662.
59
-202
1.2
- -
0.00
4 0.
006
DC
[3
1]
12t7
25
-
w,h
d 60
M
S -0
.449
4 -1
.796
9 -1
.516
3 -0
.309
9 -0
.026
8 0.
0249
0.
9763
0.
0006
0.
0013
VD
[1
3,75
1
12t7
30
-
W
RK
-0
.426
-1
.703
7 -0
.123
5 0.
1817
0.
0299
-
- -
- IX
’ PI
12
t7
40
- W
R
K
-0.4
66
-1.6
730
-0.0
621
0.00
98
0.17
45
- -
- -
DP
PI
12t9
25
-
W
50
MS
-0.1
57
-0.6
266
-0.7
576
-0.0
417
-0.0
791
0.95
66
- 0.
003
0.00
6 D
O
[76]
12t9
60
-
tYd
25
MS
-0.2
16
-0.6
721
-1.1
496
0.21
92
0.91
10
- -
0.00
2 0.
005
DO
[7
6]
12tlO
25
-
6 P
- 1.
4792
-1
7.44
5 47
.695
-
- -
0.01
1 0.
016
DO
13
11
*)
fitt
ing
eq
ua
tio
n
V!&
AId
-r
1x2~
Vix
$ w
ith
m
=
7pa
ram
eter
s
b,
Lit
era
ture
Ref
eren
ces:
i-
l
1 Al-
Du
jaili
an
d A
vvw
ad (1
O),
21
. B
enso
n (
lQ86
s),
2. A
mir
cnrl
sno
v an
d B
qir
zad
e (1
977)
. 22
. B
enso
n (
1 Sss
g,
3. A
ww
ad m
d
Pet
hri
ck (
1 Q
S?
),
23.
Ber
ro e
t al
(1 Q
92),
4.
Eie
nd
eret
al
(lsg
l),
24.
Be.
~‘ro
etal
(l
Q82
),
5. B
enso
n (
lsss
a).
25.
Bet
~o a
nd
Pen
elo
ux
(198
4),
6. B
enso
n (
1Qw
.q.
26.
Ber
roet
al
(lse
s),
7. B
enso
n (
lses
c),
27.
Bra
vo e
t al
(lQ
84),
a
Ben
son
(t9
86d
),
28.
Btw
oet
al
(IQ
Ql)
, 9.
Ben
son
(ls
sse)
, 20
. ar
ow
n e
t al
(1 Q
69).
10
. B
enso
n (
lsss
r),
30.
Ch
aud
har
i an
d K
atti
(lss
s),
11.
Ben
son
(19
Bsg
),
31.
Co
stas
etal
(l98
7),
12.
Ben
son
(lQ
Elm
l),
32.
DA
pra
no
stal
(l
0).
13.
Ben
son
(ls
esi)
, 33
.Dia
zPen
aan
dC
hed
a(19
70),
14.
Ben
son
(ls
ssi)
, 34
. E
rnst
et
al (
1979
),
15.
Ben
son
(lg
esk)
, 35
. F
ren
chet
al
(19
79),
16
. B
enso
n (
19&
t),
39.G
amia
del
aFw
nte
etal
(l9Q
2),
17.
Ben
son
(19
8&n
),
37.G
ates
&al
(196
6),
18.
Ben
son
(ls
esn
),
38.
Gu
pta
etai
(1
976)
,
19.
Ben
son
(ls
esp
),
39.
Gu
ruku
l an
d R
4u (1
966)
20
. B
enso
n (
199%
40
. Hab
ibul
lah a
nd A
khta
r (198
8),
41.
Hab
tbu
llah
an
d D
as~u
pta
(lQ
M),
42
. H
ein
tzet
al
(lse
s),
43.
Kia
Fp
roth
(lQ
40),
44
. K
um
aret
al(l
979)
. 45
. K
um
er (
1964
),
46.
Ku
mar
anan
d B
wso
n
(lQ
i33)
, 47
. L
evic
hev
(196
43,
48.
Liu
aal
(IQ
Ql)
, 49
. L
iu e
t al
(1
see)
, 50
. M
ach
wae
tal
(lae
s),
5l.M
afsh
and
Bw
litt(
lQ7s
),
52.
Nai
du
an
d N
aid
u (1
961)
, 53
. Nak
lu a
nd
Nak
iu (
1983
),
54.
Orm
mo
ud
iset
d
(IQ
Ql)
, 55
0rte
pet
al(1
Q8f
J),
56.
Cm
(1
~),
57.
ort
e9a
(lQ
lBb
),
56.
oza
wae
tal
(lse
o),
59
. P
apal
ow
lno
uet
al
(IQ
Ql)
, 60
. P
atd
oet
al
(lQ
Q2)
,
61.
Pat
il an
d M
ehta
, (1
QE
Q),
62
. P
erez
etal
(l
sss)
, 63
. R
ice
and
Tej
a (l
Q92
),
64.
Ru
el(1
973)
. 65
.9ad
ekan
dF
uo
ss(l
QS
l),
66.9
aleh
cnd
Sh
ah(l
QB
3),
67.
Sjo
blo
man
d L
iljj
om
(l
Q62
),
68.S
avel
eyan
d9p
ice(
l~52
),
69.9
lfln
el
and
ww
g
(lse
l),
70.T
enn
and
Mi(
tQ63
),
71.T
-an
dB
enso
n(l
QT
I),
72.
Trm
and
&
son
(1
978)
, 73
. Tm
an
d B
enso
n (I Q
BO
), 74
. T-e
ta
(Iset
), 75
. Tre
szcz
anow
kz an
d B
enso
n (19
&l)
, 76
.Van
Ne~
ssat
cd(1
967a
), 77
.van
Ne!
wet
al(l
967b
),
79. W
qner
mdH
ehQ
(168
6),
79.&
mly
kina
andz
otov
(196
3),
60. z
avbi
sza (1 9
85),
G
46
RECOMMENDED SYSTEMS
The review of the data for excess volumes presented above, together with results of recalculation by the chosen fitting equation, is applied as a basis for comparison of the quality of data sets and initial evaluation of the collected systems, followed by their verification and selection. In the case of methanol + n-alkane systems the result of a critical review by Srivastava and Smith (1987) is taken and methanol + n-heptane system is chosen as recommended.
Criteria for evaluation of the data and selection of the recommended sys- tems are as follows:
1) quality of experiment (ratings): low value of experimental error and high reproducibility of data.
2) low value of the standard error and maximum deviation observed for the chosen smoothing equations in comparison with experimental error.
3) extent of data point scatter, especially in the vicinity of extremes, inversion point (where VE - changes sign). the inflection point and in the high dilution region (ability to fit the properties at the limits of the concentration range).
4) relatively high number of properly distributed data points in set which allows to use smoothing equations as well as cubic splines and to calculate partial molar excess volumes of components.
5) method of measurementz a) direct methods of measurement of the volume changes on mixing are
preferred, b) the technique used avoids water contamination and absorption, as
well as evaporation effects, c) information on purification of components and purity tests are given
6) regular variation of VE in the series of mixtures formed by both homologues.
47
On the basis of the above criteria, the following recommendations can be made of six systems with the highest quality VE data: methanol + n-hep- tane (Treszczanowicz and Benson (19771, Benson (1986a)), ethanol + n-hexane (Marsh and Burfitt (197511, ethanol + n-heptane (Treszczanowicz and Benson (19771, Benson 1986b)), 1-propanol + n-heptane (Treszczanowicz and Benson (19771, Benson (1986c)), l-butanol + n-hep- tane (Treszczanowicz and Benson (1977), Benson (1986d)) and 1-hexanol + n-hexane (Treszczanowicz and Benson (1980), Benson (1986k)). For the data fits, the equations of Myers and Scott, eq.(3) and Neau, eq.(5) were chosen as the best ones for representation, and Missen’s square root of x1 , eq.(6) and Redlich-Kister, equation (1) were used for comparison. The re- sults of application of these fitting equations are illustrated in Table III in the case of ethanol + n-hexane. The coefficients of the best-fitting equation for each of these systems are given in Table II, and the deviations of the experimental data from the recommendations are shown in Figs. 1-6.
Table III. ETHANOL (1j + n-HEXANE (z, Condition T/K = 298.15, p/MPa = 0.1013
Molar volumes of the pure liquids: V&n3molW1= 58.678, e /cm3mol-‘= 131.597 Number of data points: N= 34
Experimental error: Sv”/ 1 flI= .002 at vicinity x1 = 0.5 Temperature reproducibility: 6T/K= 0.0002, 6T(IPTS68)/K= 0.01,
concentration: 6x, = 0.00005 Source: Marsh and Burfitt (1975)
48
Fig. 1. Difference of excess volume data recommended smoothed 298.15 K from available
la. System Methanol + r+Heptane: o - recommended data source Treszczanowicz and Benson (1977) and Benson (1986), recommended data represented by NE (eq.5) parameters given in Table II.
lb. System Ethanol + rrHexane: 0 - recommended data source Marsh and Burfii (1975), recom- mended data represented by MS (eq.3) parameters given in Table Ill, q . Diaz Pena (1970), l - Rue1 (197% A - Brown (1969).
0 0.2 0.4 0.6 0.6 x, 1.0
lc. System Ethanol + n-Heptane: 0 - recommended data source as Fig.la, recommended data presented by NE (eq.5) parameters given in Table II, q - Diaz Pena (1970). x - van Ness (1967), so/id curve - Berro (1962).
X0 X
0.04 2( x0 *n 0
0.02 - x XQ
x X
o-O-0 - 0 m n A 0” q x x X z
h * Y
0” 0 Q
Q -0.02 t
-0.04 -
-0.06-
I I I I I I 1 I I 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 '
Xl 3
Id. System 1-Propanol + r+Heptane: 0 - recommended data source as Fig.la, recommended data presented by MS (eq. 3) parameters given in Table II, q - Diaz Pena (1970), x - van Ness (1967)
1 e. System 1-Butanol + n-Heptane: o - recommended data source as Fig.la, recommended data presented by MS (eq.3) parameters given in Table II, q - Kumar (1979), X - Suhnel (1981), A - Berro (1984).
0.015 1 I I 1 I I 8 I I
-i “a E 0.010
“E e “3 0.005
i
0 0.2 0.4 0.6 0.6 x, 1.0 If. System l-He_ + n-Hexane: 0 - recommended data source Treszczanowicz and Benson
(1980) and Benson (1988) recommended data presented by MS (eq.3) parameters given in Table II, A - Perez (1985), q - Bravo (1984), V - Heintz (1988).
51
For the five key systems in the IUPAC Project, there are recommendations for ethanol + n-hexane (Marsh and Burfitt (1975)) and l-hexanol + n-hex- ane (Treszczanowicz and Benson (1980), Benson (1986k)) as described above. Uncertainties in experimental VE data are higher for the other sys- tems for which, at the present time, the selected data are as follows: methanol + n-hexane (Liu et al (1991)), ethanol + n-hexadecane (French et al (1979)) and l-butanol + n-decane (Gates et al (1986)).
CONCLUDING REMARKS
From the data of the excess volume for 1-alkanol + n-alkane presented in Table I, six systems are selected where the recommended VE data have the highest accuracy. These are methanol + n-heptane, ethanol + n-hex- ane, ethanol + n-heptane, 1-propanol + n-heptane, l-butanol + n-heptane and l-hexanol + n-hexane. Moreover, there are further twelve systems which could be recommended in the future. These systems are character- ized by properly distributed data points, high quality of measurement, direct excess volume measurement (dilatometer) and purity test of materi- als,as well as containing a large number of data points. The systems are (cf. Table II): 1-Pentanol + n-heptane, 1-Hexanol + n-pentane, n-heptane, n-octane, n-decane, 1-Decanol + n-pentane, n-hexane, n-heptane, n-octane, n-decane, n-hexadecane and 1-Dodecanol + n-heptane. These are mostly measured by Treszczanowicz et al (1978, 1980, 1981 and 1984) and veri- fied by Benson (1986). Unfortunately there is no reliable data for these systems from other sources for comparison. However, for the exceptional case of methanol + n-heptane the recommended system is chosen when no other systems for comparison but it was carefully tested by Srivastava and Smith (1987) as one of few systems with a miscibility gap where the excess volume has been measured. Of the selected systems two, ethanol + n-hex- ane and 1-hexanol + n-hexane, are among the five key systems of the IUPAC project. At this time, selected data for the other systems, methanol + n-hexane, ethanol + n-hexadecane and 1-butanol + n-decane, are of lower accuracy.
Analysis of the grid (Table I) and the contents of Table II indicates clearly the lack of data for 1-alkanol + n-alkane mixtures. The grid pres- ents sources of all available data for 1-alkanol ; n-alkane systems: those recommended (indicated by bold letters and superscript r) as well as those mentioned above, which are selected and can be regarded as recommended
52
in future (indicated by bold letters and superscript s), high dilution data denoted by superscript h and data initially not included to further verifica- tion (too low a number of data points or bad quality data) indicated by parenthesis.
There is particularly a lack of measurements for alkanol systems formed by alkanes shorter than n-hexane and longer than n-decane. Moreover, methanol as well as 1-dodecanol, 1-nonanol and 1-heptanol systems have not too much representatives. There are no VE data for mixtures with l- undecanol as well as longer molecule alkanols than 1-dodecanol and alkanes than n-hexadecane.
Other necessary experiments appear to be the testing of excess volume in large ranges of temperature and pressure. Only Heintz et al (1988) and Wagner et al (1988) data are sufficiently accurate. There is a lack of data on the isobaric thermal expansion (av/,~)~ and isothermal compressibility (av&)r for associated mixtures generally, and particularly for 1-alkanol + n-alkane mixtures. These are large fields for experimental investigations as well as for new accurate measuring techniques.
Lately, densities in wide pressure range have been measured for mix- tures formed by n-hexane with ethanol and 1-propanol by Ormanoudis et al (1991) and for ethanol + n-heptane by Papaloannou et al (1991).
Lack of data at high dilution can be also noted. However, accurate high dilution data are given by Kumaran and Benson (1983) and they are con- sistent for all the recommended systems. In addition, data by Staveley and Spice (1952) are of high quality but unfortunately have a low number of data points (four or five). Lately, good quality data of apparent molar vol- umes have been measured densimetrically by Costas et al (1987).
The excess volume for alkanol + alkane mixtures is characterized by complex positive-negative (“S”-shape) curves where the positive region is changing with the length of alkane and alkanol molecules as well as with temperature and pressure, being limited to an extremely small region, but possessing a relatively high value of the slope at infinite dilution of al- kanol. Therefore, it is difficult to describe the excess volume with one set of parameters in the whole concentration range, Treszczanowicz and Ben- son (1984). From this point of view for such cases it seems rational to have a separate treatment of the recommended data in the high dilution region
53
using a different fitting equation (polynomial) or cubic splines technique. Such a treatment allows the precise description of the complex shape of the excess volume and partial molar excess volume curves in the dilute al- kanol region as well as makes possible the extrapolation to infinite dilution for estimation of its limiting value Vy.
ACKNOWLEDGMENTS
The authors are indebted to the Institute of Physical Chemistry and to the University of Ottawa for financial support of the project as well as to professor J.H. Dymond of Glasgow University for discussion and advice.
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