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Molar volumes in the homologous series of normal alkanes at two temperatures
Fluid Phase Equilibria, 21 (1985) 165-170 Elsevier Science Publishers B.V., Amsterdam
165 -
Printed
in The Netherlands
MOLAR VOLUMES IN THE HOMOLOGOUS ALKANES AT TWO TEMPERATURES RICHARD
S. HUTCHINGS
Chemistry (U.S.A.) (Received
Department,
and W. ALEXANDER
University
June 5, 1984; accepted
SERIES OF NORMAL
VAN HOOK
of Tennessee at Knoxville, in final form September
Knoxville,
Tennessee
37996
6, 1984)
ABSTRACT Hutchings, R.S. and Van Hook, W.A., 1985. Molar volumes in the homologous normal alkanes at two temperatures. Fluid Phase Equilibria, 21: 165-170.
series of
Molar volumes of the n-alkanes C, through C,s, as obtained by vibrating tube densitometry, are reported at 288.15 and 298.15 K. The trend with carbon number is discussed.
INTRODUCTION
The variation of molecular properties with chain length in homologous series of related molecules has attracted the attention of many authors commencing with Kopp (1839). Over the years many different schemes correlating properties, including molar volumes, using parametric relations based on group contributions have been suggested (Partington, 1951). Recent theories, such as those of Flory et al. (1964) and Orwell and Flory (1967), employ a corresponding states approach. The n-alkane homologous series is a particularly attractive one to employ in testing theoretical ideas because of its chemical simplicity. Our interest in this problem resulted from a study (Van Hook, 1985) on deviations of mixtures of n-alkanes from the Bronsted-Koefed principle of congruence (Bronsted and Koefed, 1946). That principle describes the properties of mixtures of n-alkanes in terms of their average carbon number. Many modern theories, such as that of Flory, are in fact congruent theories. Real solutions, on the other hand, are almost, but not quite, congruent (Hijmans, 1958; Holleman, 1963; Van Hook, 1985). In the development of a simple formula to describe deviation from congruence as a function of carbon number and concentration it is obviously important to establish the base-line carbon number dependence of the pure n-alkanes with maximum precision and accuracy. 0378-3812/85/$03.30
0 1985 Elsevier Science Publishers
B.V.
166 EXPERIMENTAL
Densities of pure n-alkanes from C, to Cl5 (except for Cl2 and C,,) were measured at 288.15 and 298.15 K using a Mettler-Paar DMA 601 HT vibrating densitometer. Our experimental techniques have been described previously, and we have also discussed the calibration problems which can result from possible nonlinearities in instrument response (Dessauges et al., 1980). The data obtained in the present series are reported in Table 1. Precision for replicate measurements on the same sample was better than + 2 X lop3 kg me3 in accord with our experience of several years with the DMA 601 HT on a variety of aqueous and nonaqueous samples. The figure quantifies the precision of the instrument response plus the reliability of our sample handling and sample transfer techniques. The precision for measurements on different samples (i.e., obtained from different sources and separately purified) is about f2 or 3 x 10e2 kg rnm3, also in accord with previous experience. Examination of the literature shows that inter-laboratory agreement for density measurements is rarely, if ever, better than a few per hundred thousand (Dessauges et al., 1980). In Table 1 we compare our results at 298.15 K with selected high-precision measurements from other laboratories. For 6 < n < 15 the rms agreement is &-6 x 10e2 kg rnm3, within the expected range. The inter-laboratory differences might be due to systematic differences in calibration or technique, but are most likely connected with sample impurities or similar problems.
TABLE 1 Measured densities and molar volumes obtained from them for some n-aIkanes at two temperatures T(K)
T(K) 288.15 (This work) n 5 6 7 8 9 10 11 13 15
298.15 (This work)
298.15 a
621.99 655.33 679.50 698.76 713.98 726.22 736.52 753.15 765.07
298.15 (This work)
Molar volume (lo6 I’, m3 mol- ‘)
Density (p, kg mm3) 631.40 663.45 687.53 70640 721.35 733.38 743.55 760.22 771.80
288.15 (This work)
621.40 ’ 655.32 b 679.49 a 698.66 a 713.94 a 726.11’ 736.49 = 753.11 c 765.00 =
114.270 129.892 145.744 161.707 177.807 194.011 210.222 242.514 275.223
115.999 131.501 147.467 163.475 179.637 195.924 212.229 244.791 277.645
a Goateset al., 1981; Ott et al., 1981; b Trszczanowicz et al, 1981; ’ Van and Patterson, 1982.
167
Reagent-grade hydrocarbons were purchased from Aldrich, dried using a molecular sieve, and vacuum distilled, rejecting generally the first and last thirds. The purified samples were stored over sodium and analyzed by gas chromatography. We judge the samples to be at least 0.9995 fraction, as labelled, with the most likely impurity being branched isomers of very nearly the same density. DISCUSSION
Van Hook (1985) pointed out that at a given temperature the reduced molar volumes of the n-alkanes can be described in terms of an empirical expansion in reciprocal powers of the carbon number, n ln(v/n)-A(O)+A(-l)/n+A(-2)/n*+
...
(1)
The effect of thermal expansion was treated by taking the A(i) parameters as functions of temperature: A(i) = a,(O) + a,(l)T+ a,(2)T* + . . . . Using a six-parameter fit, A(0) = ~~(0) + a,(l)r+ a,(3)T3 and A( - 1) = a_,(O) + a_,(l)T+u_,(3)T3, Van Hook fit the n-alkane data, C, to C20, -20 to 120°C summarized by Zwolinski et al. (1966-78), with a standard deviation of 0.0013 ln( v/n) units. The four-parameter fit with A(0) = u,(O) + u,(2)T2 and A( - 1) = a_ i(0) + a_ ,(2)T2 gave u = 0.0016. Examination of the original data, compiled from many sources (Zwolinski et al., 1966-78) and supplemented with other more modern studies, showed that the statistical errors in the fits to eqn. (1) accurately reflect the experimental disagreement, laboratory to laboratory. The density of a typical n-alkane is in the range 600-800 kg rne3, consequently the experimental uncertainty, (I = 0.0013 ln( v/n) unit, corresponds to almost 1 kg rne3. If attention is restricted to a narrow range around room temperature, the inter-laboratory agreement is a little better (- 0.6-0.8 kg me3). We regard this situation as unsatisfactory. Even with old-fashioned pycnometric methods, experimental precision and accuracy of at least 0.1 kg me3 should be obtainable. We have already pointed out that with vibrating densitometry inter-laboratory agreement typically lies in the range 1I2-8 X lo-* kg m-3 (different samples, different laboratories, different methods of purification). Apparently, this is representative of modem work of quality. Least squares fits of the present data (Table 1) to eqn. (1) are reported in Table 2. Both two- and three-parameter representations are given, but use of the F test at the 90% confidence level indicates no statistical basis for selecting the three-parameter fit in preference to the two-parameter at either 288.15 or 298.15 K. Standard deviations of the two-parameter fits, _+3 and + 5 x lop4 ln( v/n) units (equivalent to about +0.2 and 0.35 kg mb3), show an improvement of about a factor of five compared with our analysis
168
of older data from many laboratories (Marsh et al., 1980; Goates et al., 1981; Ott et al., 1981; Trszczanowicz et al., 1981; Van and Patterson, 1982; Van Hook, 1985). Even so this is still about a factor of five larger than the standard deviation expected from replicate analyses on different samples by different laboratories as discussed above. Deviation plots of the differences, ln( V/n) (observed - calculated), are shown in Fig. 1 for both the two- and three-parameter fits. The differences between expected and observed standard deviations are most likely due to either an inappropriate choice of smoothing relation, a
TABLE 2 Least squares fits of molar volume data to eqn. (1) ln(V/n,cm3mol-‘)=A(O)+A(-l)/n+A(-2)/n’+...
4’)
Two-parameter 288.15 298.15 Three-parameter 288.15 298.15
fits a 2.80005 2.80564 fits 2.79646 2.80477
a Estimated
5
A(-2)
AC-l)
T(K)
+ 0.0005 f 0.0003
1.64852 f 0.004 1.69234 f 0.002
f 0.0009 f 0.0010
1.70924 * 0.015 1.70701+ 0.016
errors obtained
9
from diagonal
elements
10s a* 25 9
- 0.23016 f 0.055 - 0.05565 f 0.060
7 9
of least squares error matrix.
n 13
’
6
t
Fig. 1. Deviation plots (Y(obs)- Y(calc) versus carbon number; Y = ln(V/n)) reported in Table 2. Two-parameter fits ( x); three-parameter fits (+).
for the fits
169
systematic error arising from calibration, or unexpected impurities in one or more of the samples. The present empirical relation gives the best fit of a large number of different forms we have tried. In addition, it is of the form predicted by a semi-empirical application of a cell model to the liquid state in the pseudo-harmonic approximation (Slater, 1939). Nonlinearities in vibrating tube densitometer response were discussed by Van Hook and co-workers (Dessauges et al., 1980; Dutta-Choudhury and Van Hook, 1980) in considerable detail. Over the present range of densities (Ad(max) = 150 kg rnp3) it is not likely that an error in calibration can contribute an effect of more than + 2 or 3 x lo-* kg mm3. The present individual data points, C, to through Cii, are in average agreement with other modern determinations better than kO.07 kg rnp3 (Marsh et al., 1980; Goates et al., 1981; Ott et al., 1981; Trszczanowicz et al., 1981; Van and Patterson, 1982). Even so, purification becomes more difficult as chain length increases. We conclude that the most likely reason that the least squares standard deviation is in excess of that expected from replicate analyses arises from problems with sample purity, especially for the longer molecules. CONCLUSION
The molar volume of the n-alkanes is described by eqn. (1) with a precision of about k4 x 10e4 ln( V/n) units. This is almost a factor of five better than is obtained upon statistical analysis of extant literature data, but remains a factor of five to ten worse than would be anticipated from experimental precision judged by replicate analyses of different samples (of the same carbon number). ACKNOWLEDGEMENT
This research was supported grant CHE-81-12965.
by the National
Science Foundation
under
REFERENCES Brsnsted, J.N., 1946. The Thermodynamic Properties of Paraffin Mixtures. K. Dan. Vidensk. Selsk. Mat. Fys. Medd., 22: l-32. Dessauges, G., Miljevic, N. and Van Hook, W.A., 1980. Isotope Effects in Aqueous Systems. 9. Partial Molar Volumes of NaCl/HOH and NaCl/DOD Solutions at 1530 and 45 C. J. Phys. Chem., 84: 2587-2595. Dutta-Choudhury, M.K. and Van Hook, W.A., 1980. Isotope Effects in Aqueous Systems. 11. Excess Volumes in HOH/DOD Mixtures. The Apparent Molar Volume of NaCl in an HOH/DOD Mixture. J. Phys. Chem., 84: 2735-2740.
170 Flory, P.J., Orwoll, R.A. and Vrij, A., 1964. Statistical Thermodynamics of Chain Molecule Liquids. I. An Equation of State for Normal Paraffin Liquids. II. Liquid Mixtures of Normal Paraffin Hydrocarbons. J. Am. Chem. Sot., 86: 3507-3514; 86: 3515-3520. Goates, J.R., Ott, J.B. and Grigg, R.B., 1981. Excess Volumes of n-Hexane + n-Heptane, +n-Octane, +n-Nonane, and +n-Decane at 283.15, 298.15 and 313.15 K. J. Chem. Thermodyn., 13: 907-913. Hijmans, J., 1958. Molar Volumes of Some n-Alkane Mixtures. Mol. Phys. 1: 307-309. Holleman, Th., 1963. Application of the Principle of Corresponding States to the Excess Volumes of Liquid Binary Normal Alkane Mixtures. Physica, 29: 585-599. Kopp, - 1839. Ann. Phys., 47: 133; 1855, Ann., 96: 303 (quoted from Partington 1951). Marsh, K.N., Ott, J.B. and Richards, A.E., 1980. Excess Enthalpies, Excess Volumes, and Excess Free Energies for (n-Hexane+n-Undecane) at 298.15 and 308.15 K. J. Chem. Thermodyn., 12: 897-902. Orwoll, R.A. and Flory, P.J., 1967. Equation of State Parameters for Normal Alkanes. Correlation with Chain Length. J. Am. Chem. Sot., 89: 6814-6821. Thermodynamic Properties of Binary Mixtures of n-Alkanes. J. Am. Chem. Sot., 89: 6821-6829. Ott, J.B., Marsh, K.N. and Stokes, R.H., 1981. Excess Enthalpies, Excess Volumes, and Excess Gibbs Free Energies for (n-Hexane+n-Dodecane) at 298.15 and 308.15 K. J. Chem. Thermodyn., 13: 371-376. Partington, J.R., 1951. Advanced Treatise on Physical Chemistry. Vol II, pp. l-35. Slater, J.C., 1939. Introduction to Chemical Physics. McGraw-Hill, New York, pp. 199-269. Treszczanowicz, A. J., Kiyohara, 0. and Benson, G.C., 1981. Excess Volumes for n-Alkanols + n-Alkanes. Binary Mixtures of Decan-1-ol+ n-Pentane, + n-Hexane, + n-Octane, + nDecane, + n-Hexadecane. J. Chem. Thermodyn., 13: 253-260. Van, H.T. and Patterson, D. 1982. Volumes of Mixing and the P* Effect: Part I. Hexane Isomers with Normal and Branched Hexadecane. J. Solution Chem., 11: 793-805. Van Hook, W.A., 1985. Correlation of the Molar Volumes of n-Alkanes and their Mixtures. Fluid Phase Equilibria (in press). Zwolinski et al., 1966-78. Selected Values of Properties of Hydrocarbons and Related Compounds. API Research Project 44, Texas A & M University, College Station, Texas.
165 -
Printed
in The Netherlands
MOLAR VOLUMES IN THE HOMOLOGOUS ALKANES AT TWO TEMPERATURES RICHARD
S. HUTCHINGS
Chemistry (U.S.A.) (Received
Department,
and W. ALEXANDER
University
June 5, 1984; accepted
SERIES OF NORMAL
VAN HOOK
of Tennessee at Knoxville, in final form September
Knoxville,
Tennessee
37996
6, 1984)
ABSTRACT Hutchings, R.S. and Van Hook, W.A., 1985. Molar volumes in the homologous normal alkanes at two temperatures. Fluid Phase Equilibria, 21: 165-170.
series of
Molar volumes of the n-alkanes C, through C,s, as obtained by vibrating tube densitometry, are reported at 288.15 and 298.15 K. The trend with carbon number is discussed.
INTRODUCTION
The variation of molecular properties with chain length in homologous series of related molecules has attracted the attention of many authors commencing with Kopp (1839). Over the years many different schemes correlating properties, including molar volumes, using parametric relations based on group contributions have been suggested (Partington, 1951). Recent theories, such as those of Flory et al. (1964) and Orwell and Flory (1967), employ a corresponding states approach. The n-alkane homologous series is a particularly attractive one to employ in testing theoretical ideas because of its chemical simplicity. Our interest in this problem resulted from a study (Van Hook, 1985) on deviations of mixtures of n-alkanes from the Bronsted-Koefed principle of congruence (Bronsted and Koefed, 1946). That principle describes the properties of mixtures of n-alkanes in terms of their average carbon number. Many modern theories, such as that of Flory, are in fact congruent theories. Real solutions, on the other hand, are almost, but not quite, congruent (Hijmans, 1958; Holleman, 1963; Van Hook, 1985). In the development of a simple formula to describe deviation from congruence as a function of carbon number and concentration it is obviously important to establish the base-line carbon number dependence of the pure n-alkanes with maximum precision and accuracy. 0378-3812/85/$03.30
0 1985 Elsevier Science Publishers
B.V.
166 EXPERIMENTAL
Densities of pure n-alkanes from C, to Cl5 (except for Cl2 and C,,) were measured at 288.15 and 298.15 K using a Mettler-Paar DMA 601 HT vibrating densitometer. Our experimental techniques have been described previously, and we have also discussed the calibration problems which can result from possible nonlinearities in instrument response (Dessauges et al., 1980). The data obtained in the present series are reported in Table 1. Precision for replicate measurements on the same sample was better than + 2 X lop3 kg me3 in accord with our experience of several years with the DMA 601 HT on a variety of aqueous and nonaqueous samples. The figure quantifies the precision of the instrument response plus the reliability of our sample handling and sample transfer techniques. The precision for measurements on different samples (i.e., obtained from different sources and separately purified) is about f2 or 3 x 10e2 kg rnm3, also in accord with previous experience. Examination of the literature shows that inter-laboratory agreement for density measurements is rarely, if ever, better than a few per hundred thousand (Dessauges et al., 1980). In Table 1 we compare our results at 298.15 K with selected high-precision measurements from other laboratories. For 6 < n < 15 the rms agreement is &-6 x 10e2 kg rnm3, within the expected range. The inter-laboratory differences might be due to systematic differences in calibration or technique, but are most likely connected with sample impurities or similar problems.
TABLE 1 Measured densities and molar volumes obtained from them for some n-aIkanes at two temperatures T(K)
T(K) 288.15 (This work) n 5 6 7 8 9 10 11 13 15
298.15 (This work)
298.15 a
621.99 655.33 679.50 698.76 713.98 726.22 736.52 753.15 765.07
298.15 (This work)
Molar volume (lo6 I’, m3 mol- ‘)
Density (p, kg mm3) 631.40 663.45 687.53 70640 721.35 733.38 743.55 760.22 771.80
288.15 (This work)
621.40 ’ 655.32 b 679.49 a 698.66 a 713.94 a 726.11’ 736.49 = 753.11 c 765.00 =
114.270 129.892 145.744 161.707 177.807 194.011 210.222 242.514 275.223
115.999 131.501 147.467 163.475 179.637 195.924 212.229 244.791 277.645
a Goateset al., 1981; Ott et al., 1981; b Trszczanowicz et al, 1981; ’ Van and Patterson, 1982.
167
Reagent-grade hydrocarbons were purchased from Aldrich, dried using a molecular sieve, and vacuum distilled, rejecting generally the first and last thirds. The purified samples were stored over sodium and analyzed by gas chromatography. We judge the samples to be at least 0.9995 fraction, as labelled, with the most likely impurity being branched isomers of very nearly the same density. DISCUSSION
Van Hook (1985) pointed out that at a given temperature the reduced molar volumes of the n-alkanes can be described in terms of an empirical expansion in reciprocal powers of the carbon number, n ln(v/n)-A(O)+A(-l)/n+A(-2)/n*+
...
(1)
The effect of thermal expansion was treated by taking the A(i) parameters as functions of temperature: A(i) = a,(O) + a,(l)T+ a,(2)T* + . . . . Using a six-parameter fit, A(0) = ~~(0) + a,(l)r+ a,(3)T3 and A( - 1) = a_,(O) + a_,(l)T+u_,(3)T3, Van Hook fit the n-alkane data, C, to C20, -20 to 120°C summarized by Zwolinski et al. (1966-78), with a standard deviation of 0.0013 ln( v/n) units. The four-parameter fit with A(0) = u,(O) + u,(2)T2 and A( - 1) = a_ i(0) + a_ ,(2)T2 gave u = 0.0016. Examination of the original data, compiled from many sources (Zwolinski et al., 1966-78) and supplemented with other more modern studies, showed that the statistical errors in the fits to eqn. (1) accurately reflect the experimental disagreement, laboratory to laboratory. The density of a typical n-alkane is in the range 600-800 kg rne3, consequently the experimental uncertainty, (I = 0.0013 ln( v/n) unit, corresponds to almost 1 kg rne3. If attention is restricted to a narrow range around room temperature, the inter-laboratory agreement is a little better (- 0.6-0.8 kg me3). We regard this situation as unsatisfactory. Even with old-fashioned pycnometric methods, experimental precision and accuracy of at least 0.1 kg me3 should be obtainable. We have already pointed out that with vibrating densitometry inter-laboratory agreement typically lies in the range 1I2-8 X lo-* kg m-3 (different samples, different laboratories, different methods of purification). Apparently, this is representative of modem work of quality. Least squares fits of the present data (Table 1) to eqn. (1) are reported in Table 2. Both two- and three-parameter representations are given, but use of the F test at the 90% confidence level indicates no statistical basis for selecting the three-parameter fit in preference to the two-parameter at either 288.15 or 298.15 K. Standard deviations of the two-parameter fits, _+3 and + 5 x lop4 ln( v/n) units (equivalent to about +0.2 and 0.35 kg mb3), show an improvement of about a factor of five compared with our analysis
168
of older data from many laboratories (Marsh et al., 1980; Goates et al., 1981; Ott et al., 1981; Trszczanowicz et al., 1981; Van and Patterson, 1982; Van Hook, 1985). Even so this is still about a factor of five larger than the standard deviation expected from replicate analyses on different samples by different laboratories as discussed above. Deviation plots of the differences, ln( V/n) (observed - calculated), are shown in Fig. 1 for both the two- and three-parameter fits. The differences between expected and observed standard deviations are most likely due to either an inappropriate choice of smoothing relation, a
TABLE 2 Least squares fits of molar volume data to eqn. (1) ln(V/n,cm3mol-‘)=A(O)+A(-l)/n+A(-2)/n’+...
4’)
Two-parameter 288.15 298.15 Three-parameter 288.15 298.15
fits a 2.80005 2.80564 fits 2.79646 2.80477
a Estimated
5
A(-2)
AC-l)
T(K)
+ 0.0005 f 0.0003
1.64852 f 0.004 1.69234 f 0.002
f 0.0009 f 0.0010
1.70924 * 0.015 1.70701+ 0.016
errors obtained
9
from diagonal
elements
10s a* 25 9
- 0.23016 f 0.055 - 0.05565 f 0.060
7 9
of least squares error matrix.
n 13
’
6
t
Fig. 1. Deviation plots (Y(obs)- Y(calc) versus carbon number; Y = ln(V/n)) reported in Table 2. Two-parameter fits ( x); three-parameter fits (+).
for the fits
169
systematic error arising from calibration, or unexpected impurities in one or more of the samples. The present empirical relation gives the best fit of a large number of different forms we have tried. In addition, it is of the form predicted by a semi-empirical application of a cell model to the liquid state in the pseudo-harmonic approximation (Slater, 1939). Nonlinearities in vibrating tube densitometer response were discussed by Van Hook and co-workers (Dessauges et al., 1980; Dutta-Choudhury and Van Hook, 1980) in considerable detail. Over the present range of densities (Ad(max) = 150 kg rnp3) it is not likely that an error in calibration can contribute an effect of more than + 2 or 3 x lo-* kg mm3. The present individual data points, C, to through Cii, are in average agreement with other modern determinations better than kO.07 kg rnp3 (Marsh et al., 1980; Goates et al., 1981; Ott et al., 1981; Trszczanowicz et al., 1981; Van and Patterson, 1982). Even so, purification becomes more difficult as chain length increases. We conclude that the most likely reason that the least squares standard deviation is in excess of that expected from replicate analyses arises from problems with sample purity, especially for the longer molecules. CONCLUSION
The molar volume of the n-alkanes is described by eqn. (1) with a precision of about k4 x 10e4 ln( V/n) units. This is almost a factor of five better than is obtained upon statistical analysis of extant literature data, but remains a factor of five to ten worse than would be anticipated from experimental precision judged by replicate analyses of different samples (of the same carbon number). ACKNOWLEDGEMENT
This research was supported grant CHE-81-12965.
by the National
Science Foundation
under
REFERENCES Brsnsted, J.N., 1946. The Thermodynamic Properties of Paraffin Mixtures. K. Dan. Vidensk. Selsk. Mat. Fys. Medd., 22: l-32. Dessauges, G., Miljevic, N. and Van Hook, W.A., 1980. Isotope Effects in Aqueous Systems. 9. Partial Molar Volumes of NaCl/HOH and NaCl/DOD Solutions at 1530 and 45 C. J. Phys. Chem., 84: 2587-2595. Dutta-Choudhury, M.K. and Van Hook, W.A., 1980. Isotope Effects in Aqueous Systems. 11. Excess Volumes in HOH/DOD Mixtures. The Apparent Molar Volume of NaCl in an HOH/DOD Mixture. J. Phys. Chem., 84: 2735-2740.
170 Flory, P.J., Orwoll, R.A. and Vrij, A., 1964. Statistical Thermodynamics of Chain Molecule Liquids. I. An Equation of State for Normal Paraffin Liquids. II. Liquid Mixtures of Normal Paraffin Hydrocarbons. J. Am. Chem. Sot., 86: 3507-3514; 86: 3515-3520. Goates, J.R., Ott, J.B. and Grigg, R.B., 1981. Excess Volumes of n-Hexane + n-Heptane, +n-Octane, +n-Nonane, and +n-Decane at 283.15, 298.15 and 313.15 K. J. Chem. Thermodyn., 13: 907-913. Hijmans, J., 1958. Molar Volumes of Some n-Alkane Mixtures. Mol. Phys. 1: 307-309. Holleman, Th., 1963. Application of the Principle of Corresponding States to the Excess Volumes of Liquid Binary Normal Alkane Mixtures. Physica, 29: 585-599. Kopp, - 1839. Ann. Phys., 47: 133; 1855, Ann., 96: 303 (quoted from Partington 1951). Marsh, K.N., Ott, J.B. and Richards, A.E., 1980. Excess Enthalpies, Excess Volumes, and Excess Free Energies for (n-Hexane+n-Undecane) at 298.15 and 308.15 K. J. Chem. Thermodyn., 12: 897-902. Orwoll, R.A. and Flory, P.J., 1967. Equation of State Parameters for Normal Alkanes. Correlation with Chain Length. J. Am. Chem. Sot., 89: 6814-6821. Thermodynamic Properties of Binary Mixtures of n-Alkanes. J. Am. Chem. Sot., 89: 6821-6829. Ott, J.B., Marsh, K.N. and Stokes, R.H., 1981. Excess Enthalpies, Excess Volumes, and Excess Gibbs Free Energies for (n-Hexane+n-Dodecane) at 298.15 and 308.15 K. J. Chem. Thermodyn., 13: 371-376. Partington, J.R., 1951. Advanced Treatise on Physical Chemistry. Vol II, pp. l-35. Slater, J.C., 1939. Introduction to Chemical Physics. McGraw-Hill, New York, pp. 199-269. Treszczanowicz, A. J., Kiyohara, 0. and Benson, G.C., 1981. Excess Volumes for n-Alkanols + n-Alkanes. Binary Mixtures of Decan-1-ol+ n-Pentane, + n-Hexane, + n-Octane, + nDecane, + n-Hexadecane. J. Chem. Thermodyn., 13: 253-260. Van, H.T. and Patterson, D. 1982. Volumes of Mixing and the P* Effect: Part I. Hexane Isomers with Normal and Branched Hexadecane. J. Solution Chem., 11: 793-805. Van Hook, W.A., 1985. Correlation of the Molar Volumes of n-Alkanes and their Mixtures. Fluid Phase Equilibria (in press). Zwolinski et al., 1966-78. Selected Values of Properties of Hydrocarbons and Related Compounds. API Research Project 44, Texas A & M University, College Station, Texas.