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Excess molar enthalpies for (n-hexane + n-hexadecane) and for three- and four-component alkane mixtures simulating this binary mixture
M-1670 .I. C’hm
Tlwrmo&numics
1984,
16, 1933799
Excess molar enthalpies (n- hexane + n-hexadecane) three- and four-component mixtures simulating this mixture R. C. MILLER”
and
for and for alkane binary
A. G. WILLIAMSON
Department of Chemical Engineering, University of Canterbury, Christchurch,
New Zenland
(Received 19 December 1983; in revised form
13 Murch
1984,
Excess molar enthalpies HL are reported at 0.1 MPa for {.YC,H,,+(I -x)C,,H,,[ at 298.15 and 303.15 K and for three- and four-component mixtures of n-alkanes, simulating the binary mixture, at 303.15 K. Isothermal dilution calorimetry was employed, using initial liquids which were either pure or binary mixtures with average carbon numbers of 6 and 16. The results for the multicomponent mixtures are compared with those for the binary mixtures via the principle of congruence which is found to be capable of correlating the results for all mixtures within 4 per cent of Hi(max.). Values of Hz(max.) for the multicomponent systems are slightly less than for the binary mixture and appear to decrease as the number of components increases.
1. Introduction The principle of congruence, first proposed by Bronsted and Koefoed”’ to describe the excess Gibbs energy of binary n-alkane mixtures, asserts that the composition dependence of thermodynamic properties of mixtures of n-alkanes at given T, p is determined by a single index (in this case the average carbon number) of the mixture. We may thus write X(T,
P, ~1,
-x2>.
. ., n,, n2,. .I = X(T, P,xi xini),
where xi and ni are the mole fraction and carbon number of component i. This concept has been extended to the enthalpies of mixingC2’ and volumes of mixing ‘3) of binary liquid mixtures of alkanes and other homologous seriesC4’and to the (p, V,, T) properties of binary gaseous mixtures of n-alkanes”’ and other homologous series.(6’ Only a small amount of work has been done on mixtures containing more than two components. There have been studies of the solubility of s-tetraphenyl butane in binary ester mixtures”’ (which is really a test of the application of congruence to binary solvent mixtures) and the work of Woycicki”’ ’ On leave from U.S.A. oO?l-9614/84/080793
Department
of Chemical
+ 07 rSO2.00/0
Engineering,
University
‘(
of Wyoming,
1984 Academic
Laramie.
Press Inc. (London)
Wyoming.
Limited
794
R. C. MILLER TABLE
1. Compositions
AND
of liquids
A. G. WILLIAMSON
of average
(n>
carbon
number
(n> = 6 or (In:) = 16
Liquid
6 6
C&l4 “C,H,,(S/lO)” C,,H,, “C,,H,,(8/18)”
16 16
= (0.8OOC,H,,+0.2OOC,,H,,) = (0.2OOCsH,,+0.8OOC,,H,,)
on excess molar enthalpies of mixtures of non-homologues (in which the same number of groups are distributed differently among the component molecules). Recently Lim and Williamson reported measurements”’ of the excess molar volumes at 298.15 K of several multicomponent n-alkane mixtures made from binary mixtures, all initially of average carbon numbers 6 and 16, but made up in different ways. These compared very well with the excess molar volumes of (n-hexane + n-hexadecane). The present paper reports excess molar enthalpies of a similar range of mixtures involving two, three, and four components.
2. Experimental Excess molar enthalpies were measured with an isothermal dilution calorimeter of the type described by Costigan et al.(lo) A glass calorimeter vessel was used of volume (63.06kO.06) cm3. Mercury was displaced from this vessel into a pipette of (32.61 fO.01) cm3 volume. The pipette level was adjusted so that there was always a positive pressure on the calorimeter vessel of about 2.7 kPa above atmospheric pressure. Injections were driven by a motorized burette with an estimated uncertainty of fO.O1 cm3 per injection. The 108.03 R calorimeter heater was operated manually in an on/off mode to compensate the positive enthalpies of mixing. Energy dissipated by the heater was calculated from potential difference (directly measured), current (from measured potential difference across a standard resistor), and accumulated time during which the heater was on. No corrections were necessary for uncompensated mixing effects or net temperature imbalances during a mixing. Stirring corrections were made, and were on average about 1 per cent of the energy dissipation of the heater for the experiments of this study. Calorimeter water-bath temperatures were monitored with a large mercury-inglass thermometer readable to 0.01 K. This thermometer was calibrated against two TABLE
X
0.038 0.067 0.126 0.179 0.230
2. Excess molar H:
x
J.mol-’ 15.3 25.4 47.6 64.9 78.8
enthalpies f&t?
GFX 0.310 0.369 0.423 0.478 0.523
95.8 104.8 110.2 112.6 112.3
0.562 0.594 0.622 0.647 0.681
Hi of {xC,H,,+(l
-x)C,,H,,j
Lx
~-EL
J,mol-’
J.mol-’
110.7 108.3 105.2 102.4 95.9
0.687 0.694 0.701 0.732 0.773
at 298.15 K and 0.1 MPa
x
96.1 93.2 93.6 85.6 75.4
Hfi,
H.k
J.mol-’ 0.820 0.872 0.895 0.919 0.945
62.4 45.7 38.0 29.5 20.2
J.mol-’ 0.958 0.972 0.986
15.3 10.3 5.1
PRINCIPLE
795
OF CONGRUENCE
independently calibrated instruments: a platinum resistance thermometer and a quartz thermometer. Temperatures in the calorimeter vessel were reproducible to better than 0.01 K, and reported temperatures are believed accurate to better than 0.05 K. All components were Koch-Light “puriss” grade (99 moles per cent minimum purity) and were dried over molecular sieve 4A. The mixtures used as initial liquids for the calorimetry were prepared by weighing degassed components from hypodermic syringes into “beehive vessels”(9) over mercury, where they were mixed and stored until required. The compositions of the initial liquids are listed in table 1. Mole-fraction compositions for these liquids are believed to be accurate to 0.001 as reported. Since the primary interest in this study involved relative Hz measurements for different mixtures, no effort was expended to test the absolute accuracy of HE values with the standard mixture (n-hexane + cyclohexane) at 298.15 K using highly purified components. Instead, the materials and operating technique were evaluated by measurements of the excess molar enthalpy of {xC6H,, + (I-x)C~~H~~} at 298.15 K, results for which are listed in table 2. These results agree with those of
TABLE
Y
3. Excess molar
en J.mol-
.y ’
enthalpies
L J.mol-’
Hz of {.&H,,+(l x
2% J,mol-’
-x)C,,H,,)
-
x
AJ.mol-’
at 303.15 K and 0.1 MPa .y
Hi
Lx J,mol-’
J.mol-’
xC,H,,+(l-xK,,H,, 0.066 0.126 0.178 0.225 0.304
22.9 41.8 56.0 66.7 81.3
0.368 0.42 1 0.477 0.522 0.561
X9.6 93.x 95.9 95.7 94.0
0.593 0.646 0.680 0.686 0.694
91.7 86.5 Xl.5 80.8 79.4
x 6‘C,H,,WO) 0.066 0. I26 0. I 7x 0.225 0.304
22.7 41.3 55.2 65.6 80. I
0.36X 0.42 I 0.477 0.522 0.561
88.2 92.4 94.4 94.0 92.3
0.593 0.646 0.680 0.686 0.694
0.066 0. I25 0.178 0.223 0.302
22.2 40.5 54.9 65.0 79 5
0.366 0.419 0.520 0.559
87.8 92.4 94.6 92.8
0.59 1 0.644 0.678 0.685
0.066 0.125 0.171 0.224 0.702
22.2 40.3 54. I 64.1 7X.4
0.366 0.420 0.475 0.521 0.559
86.0 90.0 91.7 91.1 X9.3
90.0 84.5 78.0 78.9 75.X
xC,H,,+(I
0.700 0.731 0.773 0.819 0.872
78.6 72.7 64.1 53.0 3X.7
0.895 0.919 0.945 0.958 0.972
32.1 24.X 17.0 12.9 X.7
0.986
4.3
16.7 69. I 60.4 49.6 36.0
0.895 0.919 0.945 0.958 0.972
29.X 23.0 15.8 12.0 x.2
0.986
4.2
78.6 77.X 72.0 63.4
0.81X 0.871 0.894 0.918
52.5 38.4 31.9 24.7
0.944 0.958 0.972 0.986
17.0 12.9 8.7 4.3
72.3 68.4 60.0 55.0 49.3
0.844 0.871 0.894 0.918 0.944
43.0 35.9 29.7 23.0 15.9
0.958 0.972 0.986
12.1 X.2 4.1
1,+(I -x)C,&u 0.700 0.73 1 0.773 0.819 0.872 --x)“C,,H,,(X/lX)”
90.6 85.4 80.7 79.X
0.692 0.698 0.729 0.771
x“C,H,,(S/IO)“+(l-x)“C,,H,,(X,‘lX)” 0.592 0.644 0.685 0.695 0.699
87.3 X2.2 76.6 74.1 74.4
0.706 0.729 0.771 0.794 0.818
796 TABLE
R. C. MILLER 4. Parameters
h, in the equation
A. G. WILLIAMSON
(1) fit of the experimental standard deviation T
Mixture xC,H,,+(l
AND
K
h, J.moll’
29%. 15 303.15 303.15 303.15 303.15
-xK,,H,,
“ 11 -x G,H,,WW +(I -x)C,&w .~c,H,,+(l-x)“C,,H~,(8/18)” x“C,H,,(S/lO)“+(l -x)“C,,H,,(8/18)”
453.2 385.2 378.7 379.7 367.7
excess molar
hl J.moll’ - 10.2 - 17.4 - 28.4 - 15.2 -28.1
enthalpies.
/I2 J molt
where
s is the
s ’
J.moll’
- 51.3 -41.1 ~ 57.0 -43.9 - 44.0
0.6 0.4 0.6 0.4 0.4
Larkin et al.“” within 1 J.mol-’ near x = 0.5, though the present results are about 2 J. mol-’ lower than those of Larkin et al. near x = 0.3 and x = 0.7. Measurements for this mixture at 303.15 K are given in table 3. These results are within about 1 J. mol- r of the earlier work of McGlashan and Morcom.” 2’ An indication of the precision of the current experiment can be obtained by comparing measured Hfi, values in the composition-overlap region for the two sets of measurements required to span the entire binary composition range. Discrepancies of around 1 J. mol- ’ were noted for most mixtures studied.
3. Results Experimental results for all Hfi, measurements at 303.15 K are listed in table 3. For each pair of initial liquids mixed, parameters were determined by a least-squares fit
I
c
6 FIGURE 1. Excess molar enthalpy H: for (xC,H,,+(I -x)C,,H,,j at 303.15 K and 0.1 MPa against average carbon number (n) of mixture. 0, This work; A, McGlashan and Morcom;” equation (1) with parameters from table 4.
plotted -.
PRINCIPLE
6
797
OF CONGRUENCE
16
FIGURE 2. Excess molar enthalpy Hk for {.x”C,H,,(S/lO)“+(I plotted against average carbon number (n) of mixture. parameters from table 4; - ~ -. curve from figure 1.
0.
-x)C,,H,,} This work;
at 303.15 K and 0.1 MPa
16
FIGURE 3. Excess molar enthalpy Hk for jxC,H,,+(l -.w)“C,,H,,(8/18)“j plotted against average carbon number (n) of mixture. 0, This work: parameters from table 4: - - -. curve from figure I.
equation(1) with
-,
-.
at 303.15 K and 0.1 MPa equation (I) with
R. C. MILLER
798
AND A. G. WILLIAMSON
6
16
FIGURE 4. Excess molar enthalpy Hk for {x“C,H,,(5/10)” + (1 -x)“C,,H,,(8/18)“} 0.1 MPa plotted against average carbon number (n) of mixture. 0, This work: -, parameters from table 4; - - -, curve from figure 1.
of the experimental
Hi’s
at 303.15 K and equation (1) with
to
Ht/(J.mol-‘)
= x(1 -x)
i hi(2x-
1)‘.
i=O
The resulting coefficients are presented in table 4. Also shown are the standard deviations in Hi, which are all less than 1 J .mol- ‘. In each case, the use of three terms in the expansion resulted in optimization of the fit in terms of minimized standard deviation. The experimental Hz values are plotted against average carbon number in figures 1 to 4. In all figures the continuous curves were produced from the equation (1) fits. In figures 2 to 4, the dashed curve is the fit of the results for {.xC6H,, + U -4GJ-L) Ohe continuous curve from figure 1). 4. Discussion The excess molar enthalpies for the ternary mixtures are below those of (xC,H,, + (1 -x)C,,H,,} near x = 0.5 by 1 to 2 J. mol- ‘, which is of the same magnitude as the experimental uncertainty. For the four-component mixture, this negative deviation is slightly larger at about 4 J. mol-’ (or 4 per cent) but still not great. In general, these comparisons confirm the accuracy of the principle of congruence when applied to Hfi, values for normal-alkane mixtures with carbon numbers of 5 or above. The trends described above for excess molar enthalpies were not seen in recent studies’9’ of excess molar volumes of a similar series of mixtures at the same
PRINCIPLE
OF CONGRUENC’E
799
temperature; however, scatter in the r’;,E’s was about f4 per cent in the mid-range of compositions. In addition, somewhat greater strain might have been placed on the principle of congruence in the present work by using overlapping chain lengths in the four-component mixture, i.e. C,,H,, was employed in the pseudo-C,H,,, while C,H,, was used in the pseudo-C,,H,,. REFERENCES I. 2. 3. 4. 5. 6. 7. 8. 9. IO.
Brernsted, J. N.; Koefoed, J. Kgl. Dansk. b’idenskab. Selskab Mat.-Fys. Medd. 1946, 22, 1. Van der Waals, J. H.; Hermans. J. J. Rec. Tram. Chim. Pays-Bus 1950, 69. 971. Desmyter, A.; van der Waals, J. H. Rec. Truv. Chim. Pays-Bus 1958, 77, 53. Diaz Pefia, M.; Fernandez-Martin, F. An. Real Sot. Espafi. Fis. Quim. Ser. B 1964, 60. 9. Barker, J. A.; Linton, M. J. Chem. Phys. 1963, 38, 1853. Pandya. M. V.; Williamson, A. G. Auf. J. Chem. 1971, 24. 465. Koefoed. J. Disc. Faraday Sot. 1953, 15. 207. Wbycicki. W. Proc. ISI International Conf. on Calorimetry & Thermo&namic,s. Warsaw, 1969, 797. Lim, C. B.; Williamson, A. G. J. Chem. Thermo&namics 1980, 12, 65. Costigan. Marion J.; Hodges, L. J.; Marsh. K. N.: Stokes, R. H.: Tuxford. C. W. AU.FI. J. i‘!ww. 1980. 33, 2103. 1 I. Larkin, J. A.; Fenby, D. V.; Gilman, T. S.; Scott. R. L. J. Phys. Chem. 1966, 70. 1959. 12. McGlashan. M. L.; Morcom, K. W. Trans Furada! Sot. 1961, 57. 581.
Tlwrmo&numics
1984,
16, 1933799
Excess molar enthalpies (n- hexane + n-hexadecane) three- and four-component mixtures simulating this mixture R. C. MILLER”
and
for and for alkane binary
A. G. WILLIAMSON
Department of Chemical Engineering, University of Canterbury, Christchurch,
New Zenland
(Received 19 December 1983; in revised form
13 Murch
1984,
Excess molar enthalpies HL are reported at 0.1 MPa for {.YC,H,,+(I -x)C,,H,,[ at 298.15 and 303.15 K and for three- and four-component mixtures of n-alkanes, simulating the binary mixture, at 303.15 K. Isothermal dilution calorimetry was employed, using initial liquids which were either pure or binary mixtures with average carbon numbers of 6 and 16. The results for the multicomponent mixtures are compared with those for the binary mixtures via the principle of congruence which is found to be capable of correlating the results for all mixtures within 4 per cent of Hi(max.). Values of Hz(max.) for the multicomponent systems are slightly less than for the binary mixture and appear to decrease as the number of components increases.
1. Introduction The principle of congruence, first proposed by Bronsted and Koefoed”’ to describe the excess Gibbs energy of binary n-alkane mixtures, asserts that the composition dependence of thermodynamic properties of mixtures of n-alkanes at given T, p is determined by a single index (in this case the average carbon number) of the mixture. We may thus write X(T,
P, ~1,
-x2>.
. ., n,, n2,. .I = X(T, P,xi xini),
where xi and ni are the mole fraction and carbon number of component i. This concept has been extended to the enthalpies of mixingC2’ and volumes of mixing ‘3) of binary liquid mixtures of alkanes and other homologous seriesC4’and to the (p, V,, T) properties of binary gaseous mixtures of n-alkanes”’ and other homologous series.(6’ Only a small amount of work has been done on mixtures containing more than two components. There have been studies of the solubility of s-tetraphenyl butane in binary ester mixtures”’ (which is really a test of the application of congruence to binary solvent mixtures) and the work of Woycicki”’ ’ On leave from U.S.A. oO?l-9614/84/080793
Department
of Chemical
+ 07 rSO2.00/0
Engineering,
University
‘(
of Wyoming,
1984 Academic
Laramie.
Press Inc. (London)
Wyoming.
Limited
794
R. C. MILLER TABLE
1. Compositions
AND
of liquids
A. G. WILLIAMSON
of average
(n>
carbon
number
(n> = 6 or (In:) = 16
Liquid
6 6
C&l4 “C,H,,(S/lO)” C,,H,, “C,,H,,(8/18)”
16 16
= (0.8OOC,H,,+0.2OOC,,H,,) = (0.2OOCsH,,+0.8OOC,,H,,)
on excess molar enthalpies of mixtures of non-homologues (in which the same number of groups are distributed differently among the component molecules). Recently Lim and Williamson reported measurements”’ of the excess molar volumes at 298.15 K of several multicomponent n-alkane mixtures made from binary mixtures, all initially of average carbon numbers 6 and 16, but made up in different ways. These compared very well with the excess molar volumes of (n-hexane + n-hexadecane). The present paper reports excess molar enthalpies of a similar range of mixtures involving two, three, and four components.
2. Experimental Excess molar enthalpies were measured with an isothermal dilution calorimeter of the type described by Costigan et al.(lo) A glass calorimeter vessel was used of volume (63.06kO.06) cm3. Mercury was displaced from this vessel into a pipette of (32.61 fO.01) cm3 volume. The pipette level was adjusted so that there was always a positive pressure on the calorimeter vessel of about 2.7 kPa above atmospheric pressure. Injections were driven by a motorized burette with an estimated uncertainty of fO.O1 cm3 per injection. The 108.03 R calorimeter heater was operated manually in an on/off mode to compensate the positive enthalpies of mixing. Energy dissipated by the heater was calculated from potential difference (directly measured), current (from measured potential difference across a standard resistor), and accumulated time during which the heater was on. No corrections were necessary for uncompensated mixing effects or net temperature imbalances during a mixing. Stirring corrections were made, and were on average about 1 per cent of the energy dissipation of the heater for the experiments of this study. Calorimeter water-bath temperatures were monitored with a large mercury-inglass thermometer readable to 0.01 K. This thermometer was calibrated against two TABLE
X
0.038 0.067 0.126 0.179 0.230
2. Excess molar H:
x
J.mol-’ 15.3 25.4 47.6 64.9 78.8
enthalpies f&t?
GFX 0.310 0.369 0.423 0.478 0.523
95.8 104.8 110.2 112.6 112.3
0.562 0.594 0.622 0.647 0.681
Hi of {xC,H,,+(l
-x)C,,H,,j
Lx
~-EL
J,mol-’
J.mol-’
110.7 108.3 105.2 102.4 95.9
0.687 0.694 0.701 0.732 0.773
at 298.15 K and 0.1 MPa
x
96.1 93.2 93.6 85.6 75.4
Hfi,
H.k
J.mol-’ 0.820 0.872 0.895 0.919 0.945
62.4 45.7 38.0 29.5 20.2
J.mol-’ 0.958 0.972 0.986
15.3 10.3 5.1
PRINCIPLE
795
OF CONGRUENCE
independently calibrated instruments: a platinum resistance thermometer and a quartz thermometer. Temperatures in the calorimeter vessel were reproducible to better than 0.01 K, and reported temperatures are believed accurate to better than 0.05 K. All components were Koch-Light “puriss” grade (99 moles per cent minimum purity) and were dried over molecular sieve 4A. The mixtures used as initial liquids for the calorimetry were prepared by weighing degassed components from hypodermic syringes into “beehive vessels”(9) over mercury, where they were mixed and stored until required. The compositions of the initial liquids are listed in table 1. Mole-fraction compositions for these liquids are believed to be accurate to 0.001 as reported. Since the primary interest in this study involved relative Hz measurements for different mixtures, no effort was expended to test the absolute accuracy of HE values with the standard mixture (n-hexane + cyclohexane) at 298.15 K using highly purified components. Instead, the materials and operating technique were evaluated by measurements of the excess molar enthalpy of {xC6H,, + (I-x)C~~H~~} at 298.15 K, results for which are listed in table 2. These results agree with those of
TABLE
Y
3. Excess molar
en J.mol-
.y ’
enthalpies
L J.mol-’
Hz of {.&H,,+(l x
2% J,mol-’
-x)C,,H,,)
-
x
AJ.mol-’
at 303.15 K and 0.1 MPa .y
Hi
Lx J,mol-’
J.mol-’
xC,H,,+(l-xK,,H,, 0.066 0.126 0.178 0.225 0.304
22.9 41.8 56.0 66.7 81.3
0.368 0.42 1 0.477 0.522 0.561
X9.6 93.x 95.9 95.7 94.0
0.593 0.646 0.680 0.686 0.694
91.7 86.5 Xl.5 80.8 79.4
x 6‘C,H,,WO) 0.066 0. I26 0. I 7x 0.225 0.304
22.7 41.3 55.2 65.6 80. I
0.36X 0.42 I 0.477 0.522 0.561
88.2 92.4 94.4 94.0 92.3
0.593 0.646 0.680 0.686 0.694
0.066 0. I25 0.178 0.223 0.302
22.2 40.5 54.9 65.0 79 5
0.366 0.419 0.520 0.559
87.8 92.4 94.6 92.8
0.59 1 0.644 0.678 0.685
0.066 0.125 0.171 0.224 0.702
22.2 40.3 54. I 64.1 7X.4
0.366 0.420 0.475 0.521 0.559
86.0 90.0 91.7 91.1 X9.3
90.0 84.5 78.0 78.9 75.X
xC,H,,+(I
0.700 0.731 0.773 0.819 0.872
78.6 72.7 64.1 53.0 3X.7
0.895 0.919 0.945 0.958 0.972
32.1 24.X 17.0 12.9 X.7
0.986
4.3
16.7 69. I 60.4 49.6 36.0
0.895 0.919 0.945 0.958 0.972
29.X 23.0 15.8 12.0 x.2
0.986
4.2
78.6 77.X 72.0 63.4
0.81X 0.871 0.894 0.918
52.5 38.4 31.9 24.7
0.944 0.958 0.972 0.986
17.0 12.9 8.7 4.3
72.3 68.4 60.0 55.0 49.3
0.844 0.871 0.894 0.918 0.944
43.0 35.9 29.7 23.0 15.9
0.958 0.972 0.986
12.1 X.2 4.1
1,+(I -x)C,&u 0.700 0.73 1 0.773 0.819 0.872 --x)“C,,H,,(X/lX)”
90.6 85.4 80.7 79.X
0.692 0.698 0.729 0.771
x“C,H,,(S/IO)“+(l-x)“C,,H,,(X,‘lX)” 0.592 0.644 0.685 0.695 0.699
87.3 X2.2 76.6 74.1 74.4
0.706 0.729 0.771 0.794 0.818
796 TABLE
R. C. MILLER 4. Parameters
h, in the equation
A. G. WILLIAMSON
(1) fit of the experimental standard deviation T
Mixture xC,H,,+(l
AND
K
h, J.moll’
29%. 15 303.15 303.15 303.15 303.15
-xK,,H,,
“ 11 -x G,H,,WW +(I -x)C,&w .~c,H,,+(l-x)“C,,H~,(8/18)” x“C,H,,(S/lO)“+(l -x)“C,,H,,(8/18)”
453.2 385.2 378.7 379.7 367.7
excess molar
hl J.moll’ - 10.2 - 17.4 - 28.4 - 15.2 -28.1
enthalpies.
/I2 J molt
where
s is the
s ’
J.moll’
- 51.3 -41.1 ~ 57.0 -43.9 - 44.0
0.6 0.4 0.6 0.4 0.4
Larkin et al.“” within 1 J.mol-’ near x = 0.5, though the present results are about 2 J. mol-’ lower than those of Larkin et al. near x = 0.3 and x = 0.7. Measurements for this mixture at 303.15 K are given in table 3. These results are within about 1 J. mol- r of the earlier work of McGlashan and Morcom.” 2’ An indication of the precision of the current experiment can be obtained by comparing measured Hfi, values in the composition-overlap region for the two sets of measurements required to span the entire binary composition range. Discrepancies of around 1 J. mol- ’ were noted for most mixtures studied.
3. Results Experimental results for all Hfi, measurements at 303.15 K are listed in table 3. For each pair of initial liquids mixed, parameters were determined by a least-squares fit
I
c
6 FIGURE 1. Excess molar enthalpy H: for (xC,H,,+(I -x)C,,H,,j at 303.15 K and 0.1 MPa against average carbon number (n) of mixture. 0, This work; A, McGlashan and Morcom;” equation (1) with parameters from table 4.
plotted -.
PRINCIPLE
6
797
OF CONGRUENCE
16
FIGURE 2. Excess molar enthalpy Hk for {.x”C,H,,(S/lO)“+(I plotted against average carbon number (n) of mixture. parameters from table 4; - ~ -. curve from figure 1.
0.
-x)C,,H,,} This work;
at 303.15 K and 0.1 MPa
16
equation(1) with
-,
-.
at 303.15 K and 0.1 MPa equation (I) with
R. C. MILLER
798
AND A. G. WILLIAMSON
6
16
FIGURE 4. Excess molar enthalpy Hk for {x“C,H,,(5/10)” + (1 -x)“C,,H,,(8/18)“} 0.1 MPa plotted against average carbon number (n) of mixture. 0, This work: -, parameters from table 4; - - -, curve from figure 1.
of the experimental
Hi’s
at 303.15 K and equation (1) with
to
Ht/(J.mol-‘)
= x(1 -x)
i hi(2x-
1)‘.
i=O
The resulting coefficients are presented in table 4. Also shown are the standard deviations in Hi, which are all less than 1 J .mol- ‘. In each case, the use of three terms in the expansion resulted in optimization of the fit in terms of minimized standard deviation. The experimental Hz values are plotted against average carbon number in figures 1 to 4. In all figures the continuous curves were produced from the equation (1) fits. In figures 2 to 4, the dashed curve is the fit of the results for {.xC6H,, + U -4GJ-L) Ohe continuous curve from figure 1). 4. Discussion The excess molar enthalpies for the ternary mixtures are below those of (xC,H,, + (1 -x)C,,H,,} near x = 0.5 by 1 to 2 J. mol- ‘, which is of the same magnitude as the experimental uncertainty. For the four-component mixture, this negative deviation is slightly larger at about 4 J. mol-’ (or 4 per cent) but still not great. In general, these comparisons confirm the accuracy of the principle of congruence when applied to Hfi, values for normal-alkane mixtures with carbon numbers of 5 or above. The trends described above for excess molar enthalpies were not seen in recent studies’9’ of excess molar volumes of a similar series of mixtures at the same
PRINCIPLE
OF CONGRUENC’E
799
temperature; however, scatter in the r’;,E’s was about f4 per cent in the mid-range of compositions. In addition, somewhat greater strain might have been placed on the principle of congruence in the present work by using overlapping chain lengths in the four-component mixture, i.e. C,,H,, was employed in the pseudo-C,H,,, while C,H,, was used in the pseudo-C,,H,,. REFERENCES I. 2. 3. 4. 5. 6. 7. 8. 9. IO.
Brernsted, J. N.; Koefoed, J. Kgl. Dansk. b’idenskab. Selskab Mat.-Fys. Medd. 1946, 22, 1. Van der Waals, J. H.; Hermans. J. J. Rec. Tram. Chim. Pays-Bus 1950, 69. 971. Desmyter, A.; van der Waals, J. H. Rec. Truv. Chim. Pays-Bus 1958, 77, 53. Diaz Pefia, M.; Fernandez-Martin, F. An. Real Sot. Espafi. Fis. Quim. Ser. B 1964, 60. 9. Barker, J. A.; Linton, M. J. Chem. Phys. 1963, 38, 1853. Pandya. M. V.; Williamson, A. G. Auf. J. Chem. 1971, 24. 465. Koefoed. J. Disc. Faraday Sot. 1953, 15. 207. Wbycicki. W. Proc. ISI International Conf. on Calorimetry & Thermo&namic,s. Warsaw, 1969, 797. Lim, C. B.; Williamson, A. G. J. Chem. Thermo&namics 1980, 12, 65. Costigan. Marion J.; Hodges, L. J.; Marsh. K. N.: Stokes, R. H.: Tuxford. C. W. AU.FI. J. i‘!ww. 1980. 33, 2103. 1 I. Larkin, J. A.; Fenby, D. V.; Gilman, T. S.; Scott. R. L. J. Phys. Chem. 1966, 70. 1959. 12. McGlashan. M. L.; Morcom, K. W. Trans Furada! Sot. 1961, 57. 581.