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Acta Chim. Slov. 2007, 54, 538–544
Scientific paper
Temperature and Pressure Dependence
of Volumetric Properties for Binary Mixtures
of n-heptane and n-octane†
Darja Pe~ar* and Valter Dole~ek
Faculty of Chemistry and Chemical Egineerig, University of Maribor, Smetanova 17, 2000 Maribor, Slovenia.
Tel: +386 2 2294 442, Fax.: +386 2 2527 774,
* Corresponding author: E-mail: darja.pecar@uni-mbsi
Received: 15-06-2007
†Dedicated to Prof. Dr. Jo`e [kerjanc on the occasion of his 70th birthday
Abstract
The densities of n-heptane, n-octane and their binary mixtures were measured at 298.15, 323.15 and 348.15 K and within the pressure range 0.1 to 40 MPa using a vibrating tube densimeter. The reliability of this technique has been verified in our previous works. The partial molar volumes, excess molar volumes, isothermal compressibilities, isobaric thermal expansivities and internal pressures were calculated from the obtained densities. This study presents the dependence of densities, partial molar volumes, excess molar volumes, isothermal compressibilities, isobaric thermal expansivities and internal pressures on composition, temperature and pressure.
Keywords: Density, partial molar volume, excess molar volume, isothermal compressibility, isobaric thermal expansivity, internal pressure, n-heptane, n-octane
1. Introduction
n-alkanes form the major components of oil and natural gas. The volumetric properties of n-alkanes and their mixtures are of particular interest in connection with the recovery, production and refining of petroleum. Knowledge about the temperature and pressure dependence of volumetric properties for n-alkanes is important for the modeling, correlating and developing of petrochemical processes. Although these compounds are widely used, there is still a lack of knowledge about their properties. Whilst there are several publications, some of which will be mentioned here, regarding the properties of n-alkanes and their binary and ternary mixtures at atmospheric pres-sure,1–8 data regarding properties under high pressures are relatively scarce.9–14 Only a few researchers have measured the densities of n-heptane, n-octane and their binary mixtures. Data on the experimental densities of n-heptane within temperature range 273.15 to 363.15 K and at atmospheric pressure can be found in Ref. 7. Densities at higher pressures were reported for n-heptane up to 100 MPa13 and up to 400 MPa,9, 11 and n-octane up to 10 MPa.12 This case study concerns binary mixtures of n-heptane and
n-octane in acquiring excess molar volumes at 298.15 K and atmospheric pressure,4 volumetric properties and viscosities at atmospheric pressure,1 and pressures up to
10 MPa.10
We measured the densities of pure n-heptane and n-octane and binary mixtures of n-heptane and n-octane, at 298.15, 323.15 and 348.15 K and within the pressure range 0.1 to 40 MPa, using a vibrating tube densimeter. Furthermore we present the dependence of densities, partial molar volumes, excess molar volumes, isothermal compressibilities, isobaric thermal expansivities and internal pressures, on composition, temperature and pressure.
2. Experimental
2. 1. Materials
Carbon dioxide with a purity of 99.995% and nitrogen with a purity of 99.996% were supplied by Messer Slovenija. n-heptane with stated purity ? 99.5% and n-octane with stated purity ? 99.5% were obtained from Fluka. Water (purified with Mili-Q Plus system, 18.2 Mcm) and
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Acta Chim. Slov. 2007, 54, 538–544
539
all of the chemicals were used without further purification and, prior to use, degassed using an ultrasonic bath.
2. 2. Apparatus and Procedures
Densities were determined using a vibrating tube densimeter. Fig. 1 shows a schematic diagram of this apparatus. The main part of the densimeter is an Anton Paar DMA 512 unit with a vibrating U-tube (4), which is connected to a DMA 60 electronic unit (5). The U-tube was thermostated using an external temperature controlled circulating bath, which regulates temperature within ±5 · 10–3 K (6). The temperature inside the U-tube was measured with an Anton Paar CKT100 platinum resistance thermometer with an uncertainty of 0.01 K. Another thermostat (7) was used for thermostating the interior of the DMA 512 cell. The pressure in the system was regulated by the use of a high pressure Nova Swiss piston pump (3). The pressure was controlled using a Wika pressure gauge. The uncertainty in the pressure measurement is estimated to be 0.05 MPa.
The samples were prepared by weight using an analytical balance with a precision of ±1 · 10–7 kg and, after ultrasonic degassing, introduced into the measurement system using a syringe. At each temperature and pressure the samples were left in the U-tube until the vibration period was almost constant, so that the system reached thermal equilibrium.
After the measuring procedure, the samples were removed and the measurement system was blown through with nitrogen and pressurized a couple of times with carbon dioxide to more than 20 MPa, so that the rest of the sample was removed.
The reference fluids used were water and nitrogen. The reported uncertainty in the density of water was within 0.001% at temperatures up to 423 K and pressures up to 10 MPa, the uncertainties rose at higher temperatures and pressures, but were generally less than 0.1% in density except under extreme conditions.16 The uncertainty in density of nitrogen was within 0.02%.17 Uncertainty in the measured density is estimated to be within 0.7 kg/m3.
3. Results and Discussion
The densities of pure n-heptane and n-octane and binary mixtures of n-heptane and n-octane were measured at 298.15, 323.15 and 348.15 K, and within the pressure range 0.1 to 40 MPa.
The comparisons of some results with literature data for pure n-heptane and n-octane are presented in Table 1. Generally, agreement between experimental and literature data is good.
The experimental values of the densities differ a little from our previously measured densities of n-heptane15 because we used a more precise temperature indicator and, thus, improved temperature control. Moreover, we added thermostating of the exterior part of the measurement system for better temperature stability.
Table 1. Comparison between the experimental and literature values of densities for pure n-heptane and n-octane
Component	T	p	rexp	?lit	Reference
	K	M Pa	kg/m3	kg/m3	
n-heptane	323.15	0.1	657.1	657.4	12
	323.15	20	677.5	677.1	12
	323.15	40	693.7	692.6	12
	298.15	0.1	678.8	679.6	10
n-octane	323.15	0.1	677.4	677.78	11
	323.15	10	687.2	687.51	11
	348.15	0.1	656.3	656.70	11
	348.15	10	668.0	667.96	11
The values of the densities, isothermal compressibilities, isobaric thermal expansivities and internal pressures of pure n-heptane and n-octane are listed in Tables 2 and 3.
The partial molar volumes, excess molar volumes, isothermal compressibilities, isobaric thermal expansivities and internal pressures were calculated from the obtained densities.
Table 4 presents the densities, partial molar volumes, excess molar volumes, isothermal compressibilities, isobaric thermal expansivities and internal pressures of binary mixtures of n-heptane and n-octane.
Figure 1. Schematic diagram of the apparatus: (1) valve, (2) safety valve, (3) high pressure piston pump, (4) DMA 512 cell with U-tube, (5) electronic unit DMA 60, (6) thermostat, (7) thermostat.
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Acta Chim. Slov. 2007, 54, 538–544
Table 2. Densities, isothermal compressibilities, isobaric thermal expansivities and internal pressures for pure n-heptane
p
MPa
P
kg/m3
ICT
104 MPa–1
a
104 K–1
p
int
MPa
T = 298.15 K
0.1	678.7	14.25	12.50	261.5
10	687.8	12.64	11.49	261.0
20	696.1	11.26	10.72	263.9
30	703.5	10.11	10.03	265.7
40	710.4	9.18	9.48	268.0
T = 323.15 K				
0.1	657.1	17.71	13.42	244.7
10	667.9	15.26	12.00	244.0
20	677.4	13.28	11.00	247.7
30	686.0	11.75	10.16	249.6
40	693.7	10.65	9.51	248.6
T = 348.15 K				
0.1	634.7	22.56	14.41	222.3
10	647.8	18.69	12.54	223.6
20	658.8	15.74	11.29	229.7
30	668.7	13.68	10.31	232.3
40	677.4	12.44	9.53	226.8
Table 3. Densities, isothermal compressibilities, isobaric thermal expansivities and internal pressures for pure n-octane
p
MPa
P
kg/m3
104 MPa-1
a
104 K–1
p
int
MPa
T = 298.15 K
0.1 10 20 30 40
697.73 706.17 713.91 720.91 727.38
12.89
11.49
10.29
9.32
8.55
11.46
10.69
10.07
9.41
8.95
264.9 267.4 271.7 271.1
272.2
T = 323.15 K
0.1 10 20 30 40
677.38 687.20 696.01 704.02 711.25
15.48 13.61 12.04 10.77 9.78
12.23
11.10
10.25
9.56
8.99
255.2 253.5 255.0 256.9 257.2
T = 348.15 K
0.1 10 20 30 40
656.31 668.04 678.26 687.26 695.42
19.47 16.43 14.08 12.38 11.32
13.06
11.54
10.43
9.71
9.02
233.4 234.4 238.0 243.1 237.7
The partial molar volumes were calculated using the following equations:
(1)
(2)
where ? is the density, Vm the volume of the mixture, n1 number of moles of n-heptane, n2 number of moles of n-octane, M1 the relative molar mass of n-heptane, M2 the relative molar mass of n-octane, x1 is the mole fraction of n-heptane and x2 is the mole fraction of n-octane.
Partial molar volumes were calculated by fitting densities regarding a third-degree polynomial to the mole fraction and taking derivatives of densities analytically, with respect to the mole fraction at constant temperature and pressure.
It can be seen from Table 4, that the values for the partial molar volumes of n-heptane and n-octane increase with rising temperature and decrease with increasing pressure.
The excess molar volumes under certain experimental conditions (temperature and pressure) were calculated from:
(3)
Table 4. Densities, partial molar volumes, excess molar volumes, isothermal compressibilities, isobaric thermal expansivities and internal pressures for binary mixtures of n-heptane (1) and n-octane (2)
––              E
p        ?        V1      V2        V         ?T       apint
MPa        kg/m3
cm3/mol    cm3/mol       cm3/mol     104 MPa1 104 K 1   MPa
T = 298.15 K
x 1 = 0.104
0.1     696.1     147.2     163.7    -0.0499    12.82   11.69   271.6
10      704.6     145.3     161.8    -0.0277    11.53   10.80   269.4
20      712.3     143.7     160.0    -0.0244   10.38   10.16   271.9
30      719.4     142.2     158.5    -0.0228     9.39     9.51   271.8
40      725.9     140.8     157.0    -0.0203     8.56     9.01   274.1
x 1 = 0.200
0.1     694.6     147.4     163.7    -0.0819    12.88   11.84   273.9
10      703.0     145.5     161.8    -0.0494   11.59   10.90   270.5
20      710.8     143.8     160.0    -0.0454   10.44   10.27   273.3
30      717.9     142.3     158.5    -0.0363     9.45     9.60   272.8
40      724.4     140.9     157.0    -0.0335     8.60     9.09   275.2
x 1 = 0.300
0.1     692.9     147.5     163.6    -0.1025    13.14   11.89   269.6
10      701.5     145.5     161.7    -0.0906    11.71   11.01   270.2
20      709.3     143.8     160.0    -0.0727    10.50   10.27   271.5
30      716.4     142.3     158.4    -0.0692     9.50     9.62   271.8
40      722.9     141.0     157.0    -0.0590     8.71     9.09   271.0
x 1 = 0.400
0.1     691.1     147.5     163.6    -0.1146    13.22   11.95   269.5
10      699.7     145.6     161.7    -0.0938    11.84   11.01   267.4
20      707.6     143.9     159.9    -0.0838    10.62   10.35   270.7
30      714.8     142.4     158.4    -0.0769     9.56     9.68   272.0
40      721.3     141.0     157.0    -0.0628     8.66     9.12   274.1
x 1 = 0.499
0.1     689.2     147.6     163.6    -0.0920   13.44   12.03   266.7
10      697.9     145.7     161.6    -0.0787    11.96   11.14   267.8
20      705.8     143.9     159.9    -0.0665    10.69   10.45   271.5
30      713.0     142.4     158.4    -0.0589     9.64     9.74   271.1
40      719.6     141.0     157.0    -0.0512     8.81     9.21   271.8
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p             P
MPa       kg/m3
cm3/mol    cm3/mol
VE        ?T      apint
cm3/mol      104 MPa–1   104 K–1    MPa
xj = 0.596
0.1      687.3      147.6      163.5     -0.0826    13.49    12.15    268.4
10       696.0      145.7      161.6     -0.0644    12.07    11.21    266.8
20       704.0      143.9      159.9     -0.0550    10.82   10.52   269.7
30       711.3      142.4     158.3     -0.0545      9.75     9.82   270.2
40       717.9      141.1      156.9     -0.0480      8.85     9.25    271.8
xj = 0.700
0.1      685.1      147.6      163.5     -0.0507    13.63    12.20   266.8
10       693.9      145.7      161.6     -0.0395    12.22   11.20   263.2
20       702.0      144.0     159.9     -0.0350    10.96    10.58   267.6
30       709.3      142.4     158.3     -0.0331      9.86     9.87   268.6
40       716.0      141.1      156.9     -0.0291      8.89     9.36   273.9
xj = 0.800
0.1      683.0      147.6      163.5     -0.0396    13.79    12.47   269.7
10       691.9      145.7      161.6     -0.0258    12.33    11.38   265.0
20       700.1      144.0     159.9     -0.0249    11.05    10.63    266.8
30       707.4      142.4     158.3     -0.0221      9.93     9.96   268.9
40       714.1      141.1      156.9     -0.0144      8.97     9.38   271.9
xj = 0.899
0.1      680.9      147.6      163.5     -0.0202    13.99    12.42   264.6
10       689.9      145.7      161.6     -0.0182    12.49    11.40   262.3
20       698.1      144.0     159.9     -0.0159    11.17    10.70   265.4
30       705.5      142.4     158.3     -0.0097    10.06     9.98   266.0
40       712.3      141.1      156.9     -0.0059      9.12     9.44   268.6
T = 323.15 K
x = 0.104
0.1      675.6      152.2     168.6     -0.0239    15.70   12.35    253.9
10       685.5      149.7      166.2     -0.0227    13.76    11.17   252.4
20       694.4      147.7      164.1     -0.0219    12.14   10.30   254.1
30       702.4      145.8      162.3     -0.0180    10.85     9.60   256.0
40       709.7      144.2     160.6     -0.0184      9.87     9.04   256.0
xj = 0.200
0.1      673.8      152.3      168.6     -0.0378    15.92   12.49   253.4
10       683.8      149.8      166.2     -0.0360    13.88    11.27   252.3
20       692.7      147.8      164.1     -0.0286    12.22   10.39   254.6
30       700.8      145.9      162.3     -0.0237    10.94     9.66   255.6
40       708.1      144.3      160.6     -0.0269    10.00     9.08   253.5
xj = 0.300
0.1      672.0      152.4     168.6     -0.0661    16.14   12.62   252.5
10       682.1      149.9      166.2     -0.0674    14.06    11.38   251.5
20       691.1      147.8      164.1     -0.0611    12.36    10.47   253.7
30       699.3      146.0     162.2     -0.0592    11.03     9.75    255.7
40       706.6      144.4     160.6     -0.0592    10.05     9.15    254.1
xj = 0.400
0.1      670.1      152.4     168.6     -0.0856    16.32   12.74   252.0
10       680.3      150.0     166.1     -0.0813    14.19    11.49   251.6
20       689.4      147.9      164.0     -0.0726    12.46    10.56   253.9
30       697.6      146.0     162.2     -0.0670    11.12     9.81    255.1
40       705.0      144.4     160.5     -0.0674    10.15     9.20   253.0
xj = 0.499
0.1      668.1      152.5      168.5     -0.0735    16.44   12.82   252.0
10       678.3      150.0     166.1     -0.0612    14.33    11.55    250.4
20       687.5      147.9      164.0     -0.0512    12.60   10.61    252.3
30       695.7      146.1      162.2     -0.0513    11.23     9.85    253.5
40       703.2      144.4     160.5     -0.0512    10.21      9.24   252.3
p             P
MPa       kg/m3
cm3/mol
V
VE
KT
a
cm3/mol       cm3/mol     104MPa1   104 K 1   MPa
xj = 0.596
0.1      666.0      152.5      168.5     -0.0608    16.68    12.94   250.6
10       676.4      150.0     166.1     -0.0510    14.49    11.63    249.3
20       685.6      147.9      164.0     -0.0377    12.72    10.70   251.8
30       693.9      146.1      162.2     -0.0416    11.35     9.92   252.5
40       701.4      144.5      160.5     -0.0349    10.37     9.30   249.8
xj = 0.700
0.1      663.8      152.5      168.5     -0.0360    16.97    13.09   249.0
10       674.3      150.0     166.1     -0.0345    14.70    11.73    247.9
20       683.5      147.9      164.0     -0.0237    12.85    10.75    250.4
30       691.9      146.1      162.1     -0.0253    11.41      9.97   252.5
40       699.4      144.5      160.5     -0.0197    10.36     9.35    251.7
xj = 0.800
0.1      661.6      152.5      168.5     -0.0206    17.40    13.18   244.6
10       672.2      150.0     166.1     -0.0143    14.94    11.80   245.2
20       681.5      147.9      164.0     -0.0133    12.99    10.81    248.9
30       690.0      146.1      162.1     -0.0112    11.52    10.03    251.4
40       697.6      144.5      160.5     -0.0127    10.52     9.39   248.6
xj = 0.899
0.1      659.4      152.5      168.5     -0.0125    17.45    13.30   246.2
10       670.1      150.0     166.1     -0.0067    15.06    11.88   245.0
20       679.5      147.9      164.0     -0.0098    13.13    10.90   248.2
30       688.0      146.1      162.2     -0.0056    11.66    10.09   249.8
40       695.6      144.5      160.5     -0.0023    10.61      9.47   248.3
T = 348.15 K
xj = 0.104
0.1      654.4      157.6      174.0     -0.0524    19.64    13.06   231.3
10       666.3      154.4     171.0     -0.0391    16.63    11.57   232.2
20       676.6      151.8      168.4     -0.0415    14.24    10.44   235.2
30       685.7      149.6      166.2     -0.0355    12.46     9.70   241.0
40       693.8      147.7      164.3     -0.0209    11.26     9.06   240.2
xj = 0.200
0.1      652.5      157.7      174.0     -0.0575    19.97    13.18   229.7
10       664.5      154.5      171.0     -0.0497    16.82    11.66   231.2
20       674.9      151.9      168.4     -0.0449    14.38    10.51    234.5
30       684.0      149.7      166.2     -0.0443    12.61      9.73    238.8
40       692.3      147.8      164.3     -0.0377    11.47     9.07   235.3
xj = 0.300
0.1      650.5      157.8      174.0     -0.0634    20.44    13.40   228.2
10       662.6      154.6      171.0     -0.0609    17.05    11.77   230.3
20       673.1      152.0     168.4     -0.0598    14.48    10.67   236.6
30       682.3      149.8      166.2     -0.0542    12.70     9.89   241.2
40       690.6      147.8      164.2     -0.0481    11.65     9.21    235.4
xj = 0.400
0.1      648.4      157.8      174.0     -0.0728    20.45    13.59   231.1
10       660.7      154.6      170.9     -0.0668    17.27    11.99   231.8
20       671.2      152.0     168.4     -0.0627    14.75    10.78   234.4
30       680.5      149.8      166.2     -0.0569    12.87     9.94   238.8
40       688.9      147.9      164.2     -0.0535    11.58     9.28   239.0
xj = 0.499
0.1      646.3      157.8      174.0     -0.0717    20.89    13.69   228.1
10       658.7      154.7      170.9     -0.0633    17.47    11.98   228.8
20       669.3      152.1      168.3     -0.0603    14.85    10.78   232.9
30       678.7      149.8      166.1     -0.0558    12.98     9.97   237.3
40       687.1      147.9      164.2     -0.0540    11.83     9.26   232.3
2
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Acta Chim. Slov. 2007, 54, 538–544
p
MPa
p
kg/m3
VE
?    ap
12                                        T                            int
cm3/mol    cm3/mol       cm3/mol     104 MPa–1 104 K–1   MPa
x 1 = 0.596
0.1     644.2     157.9     173.9    -0.0660   21.14   13.79   227.0
10      656.7     154.7     170.9    -0.0563    17.67   12.08   228.0
20      667.4     152.1     168.3    -0.0550   15.00   10.88   232.5
30      676.8     149.8     166.1     -0.0460   13.12   10.02   236.0
40      685.3     147.9     164.2    -0.0414   11.96     9.34   232.0
x 1 = 0.700
0.1     641.8     157.9     173.9    -0.0600   21.57   14.04   226.5
10      654.5     154.7     170.9    -0.0538    18.04   12.30   227.3
20      665.3     152.1     168.3    -0.0483    15.28   10.93   229.2
30      674.9     149.8     166.1     -0.0481    13.25   10.08   234.9
40      683.3     147.9     164.2    -0.0260   11.90     9.34   233.2
x = 0.800
0.1     639.4     157.9     173.9    -0.0272   21.94   13.95   221.3
10      652.3     154.7     170.8    -0.0282   18.23   12.25   224.0
20      663.2     152.1     168.3    -0.0269    15.38   11.00   228.9
30      672.8     149.9     166.1     -0.0259    13.35   10.10   233.6
40      681.4     147.9     164.2    -0.0177    12.08     9.40   230.9
x 1 = 0.899
0.1     637.1      157.9     173.9    -0.0169   22.32   14.26   222.3
10      650.1      154.7     170.8    -0.0158    18.48   12.40   223.6
20      661.0     152.1     168.3    -0.0135    15.55   11.11   228.7
30      670.8     149.9     166.1     -0.0126    13.49   10.21   233.5
40      679.4     147.9     164.2    -0.0079    12.23     9.50   230.2
where i = 1, 2, ?m mixture density, ?i the densities of pure n-heptane (1) and n-octane (2) respectively.
The Redlich-Kister type equation was used for the correlation of experimental values of excess molar volumes:
(4)
where Ai are coefficients.
Standard deviations of experimental, and calculated values of excess molar volumes were calculated from:
(5)
where VeEx pi is the experimental value of excess molar volume, VcEa li the calculated value of excess molar volume, N the number of experimental points, and n the number of coefficients Ai.
Because small differences in density can contribute to large differences in excess molar volumes, we can observe discrepancies in the obtained excess molar volumes by other authors.1, 4, 8, 10 From Figs. 2–4, one can
see that the values for excess molar volumes are negative regarding our experimental conditions. The deviation from ideal mixture is relatively small (maximum value of excess molar volume at 298.15 and 0.1 MPa is less than –0.12 cm3/mol), but is larger than by the before-mentioned authors, in some cases the values are even positive.8 The minima obtained is at x1 = 0.4 similar as in Ref. 10.
Figure 2. Excess molar volumes as a function of mole fraction at 298.15 K (lines – calculated from Redlich-Kister Eq. 4 with coefficients from Table 5)
Figure 3. Excess molar volumes as a function of mole fraction at 323.15 K (lines – calculated from Redlich-Kister Eq. 4 with coefficients from Table 5)
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Figure 4. Excess molar volumes as a function of mole fraction at 348.15 K (lines – calculated from Redlich-Kister Eq. 4 with coefficients from Table 5)
Table 5. Coefficients of the Redlich-Kister equation (4) and standard deviations of experimental and calculated values of excess molar volumes
p	A0	A1	A2	8(VE)
MPa	cm3/mol	cm3/mol	cm3/mol	cm3/mol
T =	298.15 K			
0.1	0.3853	0.2233	0.0138	4.98 · 10–05
10	0.3217	0.1196	0.1406	1.32 · 10–04
20	0.2761	0.1007	0.1054	8.18 · 10–05
30	0.2601	0.1044	0.1493	6.51 · 10–05
40	0.2231	0.1096	0.1434	2.59 · 10–05
T =	323.15 K			
0.1	0.2858	0.0989	0.1777	6.80 · 10–05
10	0.2631	0.1267	0.1915	6.60 · 10–05
20	0.2122	0.1083	0.0995	1.15 · 10–04
30	0.2159	0.0989	0.1720	7.84 · 10–05
40	0.2097	0.1221	0.1724	8.27 · 10–05
T =	348.15 K			
0.1	0.2714	0.1786	0.1208	1.04 · 10–04
10	0.2518	0.1252	0.0531	2.80 · 10–05
20	0.2360	0.1395	0.0687	3.97 · 10–05
30	0.2184	0.1187	0.0553	2.81 · 10–05
40	0.1994	0.0991	0.0727	8.29 · 10–06
The isothermal compressibilities ?T can be obtained from densities according to:
(6)
where V is the molar volume. The derivatives of a third-degree polynomial of the densities with respect to pres-
sure at constant temperature, were calculated analytically.
It is obvious from Fig. 5 that isothermal compressibilities increase with increasing temperature and decrease with increasing pressure.
Figure 5. Isothermal compressibilities as a function of pressure (x1 = 0.499)
The isobaric thermal expansivities were calculated from densities using the following equation:
(7)
The derivatives of the densities’quadratic polynomial with respect to temperature at constant pressure were calculated analytically. In Fig. 6 the isobaric thermal expansivities for binary mixture of n-heptane and n-octane are plotted against pressure. The isobaric thermal expansivities increase with increasing temperature and decrease with increasing pressure.
The obtained values for isothermal compressibilities and isobaric thermal expansivities for n-heptane agree within 1.4% and 1.6% with those reported in Ref. 9.
Internal pressures were obtained from:
(8)
Internal pressures decrease with increasing temperature and increase with increasing pressure (Table 4).
The estimated uncertainties of partial molar volumes, excess molar volumes, isothermal compressibilities, isobaric thermal expansivities and internal pressures are 0.2 cm3/mol, 0.1 · 10–3 cm3/mol, 0.02 · 10–4 MPa–1, 0.01 · 10–4 K–1, 0.6 MPa, respectively.
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Figure 6. Isobaric thermal expansivities as a function of pressure (x1 = 0.499)
4. Conclusions
The densities of n-heptane, n-octane and their binary mixtures were measured at 298.15, 323.15 and 348.15 K and within the pressure range 0.1 to 40 MPa using a vibrating tube densimeter. The properties calculated from the obtained densities were compared with available literature data. The present data for isothermal compressibilities and isobaric thermal expansivities are in good agreement with those already published,9 while the values of excess molar volumes could not be directly compared, because of different experimental conditions. Generally our values are more negative, so that the difference between our mixtures and ideal mixture is, in our case, bigger than in those published in Refs. 1, 4, 10. For the comparison of partial molar volumes there are, to the best of our knowledge, no available data in literature.
5. References
1. J. S. Matos, J. L. Trenzado, E. Gonzαlez, R. Alcalde, Fluid Phase Equilib. 2001, 186, 207–234.
2. J. S. Matos, J. L. Trenzado, R. Alcalde, Fluid Phase Equilib. 2002, 202, 133–152.
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6. M. I. Aralaguppi, C. V. Jadar, T. M. Aminabhavi, J. Chem. Eng. Data 1999, 44, 435–440.
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8. A. Aucejo, M. C. Burguet, R. Munoz, J. L. Marques, J. Chem. Eng. Data 1995, 40, 141–147.
9. R. Malhotra, L. A. Woolf, J. Chem. Thermody. 1991, 23, 49–57.
10. I. M. Abdulagatov, N. D. Azizov, J. Chem. Thermody. 2006, 38, 1402–1415.
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Povzetek
S pomo~jo gostotomera z nihajo~o U-cevko smo izmerili gostote heptana, oktana in njunih binarnih me{anic pri 298,15, 323,15 in 348,15 K ter v obmo~ju tlakov od 0,1 do 40 MPa. Zanesljivost te tehnike je bila preverjena v na{ih prej{njih delih. Iz dobljenih gostot smo izra~unali parcialne molske prostornine, prese`ne molske prostornine, izotermne stisljivosti, prostorninski razteznostni koeficienti in notranji tlak. Nadalje smo predstavili, kako se gostote, parcialne molske prostornine, prese`ne molske prostornine, izotermna stisljivost, prostorninski razteznostni koeficient ter notranji tlak spreminjajo s sestavo, temperaturo in tlakom.
Pe~ar and Dole~ek:   Temperature and Pressure Dependence of Volumetric Properties for Binary Mixtures ...