296
GUSTAV EGLOFF AND ROBERT C. KUDER
T H E MOLAL VOLUMES OF ALIPHATIC HYDROCARBONS AT THEIR MELTING POINTS' GUSTAV EGLOFF AND ROBERT C. KUDER Research Laboratories, Universal Oil Products Company, Chicago, Illinois
Received August 2 2 , 2041 I . INTRODUCTION
Although the molal volume of homologous aliphatic hydrocarbons at 20°C. or a t the boiling point is not a strictly additive function (1,3,i ) , the molal volume a t the melting point may be expressed as a linear function of the molecular weight or the number of carbon atoms. Krafft (4),from the melting-point and density data available in 1882 on seventeen normal alkanes of eleven or more carbon atoms, obtained the value 17.83 ml. per mole for the volume increment due to the addition of a CH* group to the molecule. Later Le Bas (5) proposed linear equations relating the molal volume a t the melting point to the number of carbon atoms for alkanes, alkenes, and alkynes of higher molecular weight, each equation with a slope of 17.82 ml. per mole. The effect of the alternating factor was also noticed by Le Bas (6). He observed that members of a series having an odd number of carbon atoms possessed relatively low melting points and molal volumes, while those members with an even number of carbon atoms had higher melting points and molal volumes. Pauly (S), in discussing the oscillation of physical constants in homologous series, maintained that the geometrical conditions resulting from the addition of successive carbon atoms to the chain a t the tetrahedral angle could account for the oscillation in molal volume and therefore in melting point. Enough data are now available on aliphatic hydrocarbons to warrant a reinvestigation and an extension of the work on molal volumes in the liquid state a t the melting points. The present paper will show how the alternating melting points affect the densities and molal volumes, necessitating separate molal volume equations for the even and odd series, and it will show that a single value (e.g., 17.82) for the slope of these equations cannot be used to represent homologous series of the aliphatic hydrocarbons. 11. DISCUSSION OF THE D.4TA
The melting point possesses two advantages as a temperature for comparison of molal volumes. ( a ) The melting point (at least for the higher members of an homologous series) is approximately the same fraction of the critical temperature for members of a given series, thus permitting comparisons to be made under approximately corresponding states. ( b ) The normal alkanes constitute an exceptionally long series of compounds for which the densities a t the melting points are either known or can be estimated with reasonable accuracy. It was Presented before the Division of Physical and Inorganic Chemistry at the lOlst meeting of the American Chemical Society, which was held in St. Louis, Missouri, April, 1941.
297
MOLAL VOLUMES O F HYDROCARBONS
found possible to determine from the literature the densities at the melting points of thirty-four of the first thirty-six normal alkanes; in contrast. twelve of the TABLE 1 Normal alkanes comwutm
i
YELTISO POINT
Methane . . . . . . . . . . . .i -182.6 Ethane . . . . . . . . . . . . . . -172.0 Propane . . . . . . . . . . . . . - 187.1 Butane . . . . . . . . . . . . . I -135.0 Pentane . . . . . . . . . . . . - 129.7 Hexane . . . . . . . . . Heptane . . . . . . . . . . . Octane . . . . . . . . . . . . . . . 1 -56.8 Xonane . . . . . . . . . . -53.69 Decane . . . . . . . . . . . . . -29.72 -25.61 Cndecane . . . . . . . . Dodecane . . . . . . . . . . -9.65 Tridecane . . . . . . . . . . . . . -6 Tetradecane . . . . . . . . . . . 5.5 Pentadecane . . . . . . . . . . . 10 Hexadecane . . . . . . . . . . 18.1 22.0 Heptadecane . . . . . . . . . ., Octadecane . . . . . . . . . 28.0
1 ~
: : 1:; ~
.I ' ~
DESSITY A T MELTING POINT
ll ' 11
YELTING POINI
COypoUND
SC
11
0.4547 Sonadecane . . . . . . . . . . Eicosane . . . . . . . . . . . . . 0.6546 0.7492 ~; Heneicosane . . . . . . . . Docosane . . . . . . . . . . . 0.7595 Tricosane . . . . . . . . . . . . 0.7566 Tetracosane . . . . . . . . . 0.7737 Pentacosane ...... 0.7633 .......... 0.7755 ....... 0.7684 Octacoaane . . . . . . . . . . . 0.7745 Konacosane . . . . . . . . . . 0.7712 1 Triacontane . . . . . . . . . . 0.7753 Hentriacontane . . . . 0.7738 Dotriacontane'. . . . . 0.7758 Tritriacontane . . . . . . . 0.7754 1; Tetratriacontane., . . Pentatriacontane. . 0.7767 0 . 7767 I~ Hexatriacontane . . . . .
li
i;
IENSITY AT YELIING WIN1
.
32 36.4 40.4 44.4 47.4 51.1 53.3 57 60 61.6 64 66 68.4 70.3 71.6 73 74.6 76
0.7777 0.7778 0.7782 0.7778 0.7797 0.7786 0.7787 0.7792 0.7792 0.7796 0.7797 0.7803 0.7808 0.7802 0.7806 0.7814 0.7813
* The calculated "best" density values (2) for these compounds were so far out of line that the esperimental values given here were used instead . TABLE 2 1-Alkenes couwcm
I
MELTING POINT
1
DENSITY A I YELTINO POINI
"C
Ethene . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Propene. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Butene-1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Dodocene-1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
-169 44 . 185 -190' -31 . 13 . 12 -3 40 11 2 18 21.7
i I i I
0.6588 0.7830 0.8220 0.7954 0.7953 0.7936 0.7952 0.7917 0.7950 0.7910 0.7940
normal alkanes are liquid at 20°C. and atmospheric pressure. and the boiling points of only the first nineteen are known a t 760 mm . The melting points and the corresponding densities of the hydrocarbons con-
298
GUSTAV EGLOFF AND ROBERT C. KUDER
sidered are listed in tables 1 to 5. For the greater part, the data were obtained from those collected in Physical Constunis of Hydrocarbons (2) ; those obtained elsewhere are noted. In the case of compounds for which the density has not been determined experimentally a t the melting point, extrapolations were made, TABLE 3 I-Alkynes
1
COMPOUND
MELTINGPOINT
I
DENSITY AT MELTING POINT
*C.
Ethyne.. . . . . . . . , . . . . . . . , , , , , , , , . . , , , , , , , , , , ,
-81.8 -101.5 -122.5 -98 - 124 -80 -79 15 28
..................... ..................... Octyne-1.. . . . . . . . . , . . . . , , , . . , , . , . . . , . , , , , , , .
.......................
Octadecyne-1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
0.6179 0.7640 0.8342 0.8595 0.8206 0.8380 0.7999 0.7969
TABLE 4 ,%Alkynes
I
COMPOmm
MELTING POXNI
I
DENSITY AT MELTING POW1
%.
Butyne-2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Pentyne-2, , , . . , , . , , . . . . . . . . . . . . . . . . . . . . . . . , . Hexyne-2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . , . , . . . . Dodecyne-2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Tetradecyne-2. . . , . . . . . . . . . . . . . . . . . . . . . . . . . . . Hexadecyne-2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Octadecyne-2. . . , . . . . . . . . . . . . . . . . . . . . . , . . . . .
.I
-32.5
- 101
-92
-9 6.5 20
30
0.7593 0.8325
0.8365 0.8097 0.8064
0.8039 0.8016
' TABLE 5 1 ,Z'-Alkadiynes DENSITY A I MELTING POINT BC.
Butadiyne-1 ,3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Hexadiyne-l,5. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Nonadiyne-l,8. . . , . . . , . , . , . . . . . . . . . . . . . . . . . . Undecadiyne-1, 10. . . . . . . . . . . . . . . . . . . . . . . . . . . Tridecadiyne-1 ,12. . . . . . . . . . . . . . . . . . . . . . . . . .
-36.4 -6 -21 - 17 -2
0,9271 0.8121 0.8579 0.8562 0.8492
either graphically or by means of the calculated temperature coefficients (2). The data can be extrapolated to the melting points with reasonable confidence, since the density-temperature curves are practically linear a t low temperatures. The effect of the alternating factor is clearly revealed by a study of these first five tables. Conversion of the densities a t 20°C., a t which temperature
299
MOLAL VOLUMES OF HYDROCARBONS
they form a smooth series, to densities a t alternating melting points results in an alternating density series, and consequently an oscillating molal volume series. Hence it appears that the oscillation in molal volumes a t the melting points may be attributed, a t least partly, to the melting points themselves, rathei than entirely to the reverse relationship suggested by Pauly (8). Sufficient data are not known to correlate effectively the densities of branchedchain aliphatic hydrocarbons a t their melting points. The profound effect of branching on the melting point undoubtedly has a marked effect on the molal volume a t the melting point. 111. THE MOLAL VOLUME EQUATIONS
Each homologous series was divided into an even and an odd series and the molal volume data fitted by the method of least squares to equations of the type
V=a+bn where V is the molal volume (milliliters per mole) a t the melting point, number of carbon atoms in the molecule, and a and b are constants.
TL
is the
TABLE 6 V=a+bn
I SEXIES
n-Alkanes . . . . , . . . . . , , 1-Alkenes.. ....... . . . . 1-Alkynes... . . . . . . . . , 2-Alkynes.. , . . _ ,. . . , . 1 , l ‘-A1kadiynes . . . . . .
1
EVEN N M B E P OF CAPBON ATOMS
Standnrdl deviation
0.19 0.06 0.23 0.04
I
ODD N M B E P OF CAPBON ATOM8
/StandardlStandvd/ error of b deviation
6.72 -3.48 -14.21 -8.89
17.842 17.927 18.254 17.850
0.005 0.006
0.39 0.10
0.023
Standard
/error of 6
4.98 -1.20 -7.20
17.900 0.010 17.72’2 0.023 17.77
0.005 0.34
-12.05
16.88
0.12
It was not found possible to use the same value of b for all series as Le Bas had done ( 5 ) . Not only are slightly different slopes required for each homologous series, but also separate slopes are required for the even and the odd subsets of each homologous series. Thus the volume effect of adding CH2 groups differs in each series, and the volume difference due to unsaturation does not remain constant, as Le Bas stated, but varies linearly with the number of carbon atoms in the molecule. For example, the volumes of the alkanes having an even number of carbon atoms are represented by VI = 6.72 17.842~~ and the volumes of the 1-alkenes having an even number of carbon atoms by Vz = -3.48 17.927~~ The difference of the two equations, V i - Vz = 10.20 - 0 . 0 8 5 ~ ~ gives the diminution in volume due to removing two hydrogen atoms from the 1,%position in a straight-chain alkane of given carbon content.
+
+
300
GUBTAV EQLOFF AND ROBERT C
. KUDER
For most of the series an “end-effect” is shown. in that the first one or two members fail to line up with the remainder of the series. These inconsistent values were not used in calculating the constants a and b . TABLE 7 n-Alkanes with an even number o j carbon atoms V = 6.72 17.842n
+
V W.
I
6. . . . . . . . . . . . . . . . . . . .
Vdod
113.89
.
113.77 149.46 185.14 220.82 256.51 292.19 327.88 363.56 399.24 434.93 470.61 506.30 541.98 577.66 613.35 649.03
AV
-0.12 -0.18 -0.02 -0.04 0.14 0.17 0.23 0.31 -0.08 0.00 -0.23 -0.30 -0.27 0.24 -0.15 0.17
TABLE 8 n-Alkanes m‘th an odd number of carbon atoms V = 4.98 17.9OOn
+
.
1)
3. . . . . . . . . . . . . . . . . . . .
i
‘
7.................... 9. . . . . . . . . . . . . . . . . . . . 1 11 . . . . . . . . . . . . . . . . . . . . 13. . . . . . . . . . . . . . . . . . . . 15. . . . . . . . . . . . . . . . . . . . 17. . . . . . . . . . . . . . . . . . . . 19. . . . . . . . . . . . . . . . . . 21 . . . . . . . . . . . . . . . . . . . . 1 23 . . . . . . . . . . . . . . . . . . . . 25 . . . . . . . . . . . . . . . . . . .1 27. . . . . . . . . . . . . . . . . . . . j 29 . . . . . . . . . . . . . . . . . . . . 31 . . . . . . . . . . . . . . . . . . . . ! 33. . . . . . . . . . . . . . . . . . . . 35. . . . . . . . . . . . . . . . . . . .
,.I
1 ’
1
VOtUl.
58.85 94.99 129.50 165.38 237.78 273.79 345.26 381.09 416.33 488.60 524.33 559.81 595.a3 630.82
AV
58.68 94.48 130.28 166.08 201.88 237.68 273.48 309.28 345.08 380.88 416.68 452.48 488.28 524.08 559.88 595.68 631.48
-0.17 -0.51 0.78 0.70 0.09 -0.10 -0.31 -0.31 -0.18 -0.21 0.35
-0.32 -0.25
0.07 -0.15 0.60
In table 6 are shown the values of the constants for the several even and odd series. together with the standard deviations of the calculated from the observed molal volumes and the standard errors of the slopes. For the 1-alkynes with
301
MOLAL VOLUMES OF HYDROCARBONS
an odd number of carbon atoms the line is based upon two points only, the resulting equation therefore being of doubtful validity. For the remainder of the hydrocarbons the fit is close, the standard deviation being only 0.26 ml. per mole for the fifty-three compounds. The equivalent mean deviation is 0.20 ml. per TABLE 9 1-Alkenes with an even number of carbon atoms V = -3.48 17.927n
+
I
m
4. . . . . . . . . . . .. , , , . , ., 6. . . . . . . . , . . . . . , . . . . . 8.. . . . . . . , . . . . . . . . . . . 10,. . . . . . . . . . , . , , . . . . , 12. . . . . . . . . . . . . . , . . . . . 14. . . . . . . . , . . . . , , . , . , . 16. . . . . . . . . . . . . . . , . . . . 18. . . . . . . . . . . . . . . . . . . .
V O W .
Valcd
68.23 104.08 139.94 175.79 211.64 247.60 283.35 319.21
68.25
211.61 247.43 283.46 319.18
AV
-0.02
0.03 0.07 -0.11 0.03
TABLE 10 1-Alkenes with a n odd number o j cqrbon atoms V = -1.20 17.722n
+
13. . . . . . . . . . . . . . . . . . . . 15. . . . . . . . . . . . . , , , , , , . 17. . . . . . . . . . . . . . . . . . . . 19. . . . . . . . . . . . . . , , . , , ,
335.63
m
VOW.
4. . . . . . . . . . . . . . . . . . . . 6. . . , . . . . . . . . . . . . . . . . 8.. . . . . . . . ., . . . . . , .. . 10. . . . . . . . . . . . . . . . . . . . 12. . . . . . . . . . . . . . . . . . . . 14.................... 16. . . . . . . . . . . . . . . . . . . . 18....................
229.27 284.57 299.93
95.57 131.49
229.19
264.63 300.07 335.52
Vulcd.
58.81 95.31 131.82 168.33
-0.08 0.06 0.14 -0.11
AV
-0.26 0.33
204.84
278.03 314.28
241.35 277.85 314.36
-0.17 0.08
mole and the average fractional deviation is 0.09 per cent. In tables 7 to 14 are given the calculated and observed molal volumes and the individual deviations for all the hydrocarbons considered. The use of non-parallel lines for the even and odd subsets of each series of course results in a point of intersection of the two lines. For the normal alkanes
302
GUSTAV EGLOFF .4ND ROBERT C. KUDER
this point is a t n = 30. Thus the calculated lines give the members having an even number of carbon atoms densities less than those of the members having an odd number of carbon atoms below n = 30 and greater above n = 30. A direct examination of the data (see table 1) shows that there are hardly enough experimental values to confirm this effect as real. There seems to be no physical reason why the sign of the density alternations should change a t this point; TABLE 12 i-Alkynes with an odd number of carbon atoms V = -7.20 17.770n n
i
5 7 9 11 13
Vobad.
+ i
81 65 117 19
Vcalcd.
I
81.65
,
AV
223.8 TABLE 13 $-Alkynes with an even number of carbon atoms V = -8.89 17.850n
+
fl
I
Vabld.
I
Vdod.
I
AV
~
6 . . . . . . . . . . . . . . . . . . .1 8. . . . . . . . . . . . . . . . . . . . . 10 . . . . . . . . . . . . . . . . . . . . ' 12 . . . . . . . . . . . . . . . . . . . . . 14 . . . . . . . . . . . . . . . . . . . . i 16. . . . . . . . . . . . . . . . . . . . 18.. . . . . . . . . . . . . . . . . .;.
98.19
98.21 133.91 169.61 205.31 241.01 276.71 312.41
205.38 241.01 276.65 312.44
0.02 -0.07 0.00 0.06 -0.03
TABLE 14 i,i'-Alkadiynes with an odd number of carbon atoms V = -12.05 16.878n fl ~~
~
Vobad.
I
5 . .. . . . . . . . . . . . . . . . . 7. . . . . . . . . . . . . . . . . . 9. . . . . . . . . . . . . . . . . . . 11. . . . . . . . . . . . . . . . . . 13.. . . . . . . . . . . . . . . . . .I.
i
140.09 173.13 207.60
,
I
+
Vealed
72.34 106.10 139.85 173.61 207.36
I
AV
-0.24
0.48 -0.24
a more reasonable situation would be that in which the densities of the two series approached a common curve for the higher members. In terms of molal volumes such a situation can be represented by an equation of the type
V = a'
+ b'n =tn
Tn this equation a' and b' have the same values for the odd members aa for the even members, and the new constant c has the same absolute value for each sub-
303
MOLAL VOLUMES O F HYDROCARBONS
set, but the positive sign is used for the even members and the negative sign for the odd members. While this type of an equation does not preserve the simple physical significance of strict additivity possessed by the straight line, it does give the same
V
=
TABLE 15 Normal alkanes 5.86 17.871n 3.61/n
+
*
n
..................... .....................
58.85
..................... 6. . . . . . . . . . . . . . . . . . . 7. , . . . . . . . . . . . . . . . . . 8 . . . . . . . . . . . . . . . . .. . ..................... 10 . . . . , . . . , . . . . . . . . . . 11. . . . . . . . . . . . . . . . . . . 12. . . . . . . . . . . . . . . . . . . . 13. . . . . . . . . . . . . . . . . . . 14 . . . . . . . . . . . . . . . . . . . . 15. . . . . . . . . . . . . . . . . 16 . . . . . . . . . . . . . . . . . 17. . . . . . , . . , . . . , 18. . . . . . . . . . . . . . . . . 19. . . . . . . . , . . . . . . . . . 20. . . . . . . . . . . . . . . . . . 21. . . . . . . . . . . . . . . . . 22 . . . . . . . . . . . . . . . . . . . 23 . . . . . . . . . . . . . . . . . . . 24 . . . . . . . . . . . . . . . . . 25 . . . . . . . . . . . . . . . . . . , 26. . . ............ 27. . . . . . . . . . . . . . . . . . 28. . . . . . . . . . . . . . . . . 29. . . . . . . . . . , 30 31 32 33 34 35 36 ,
,
,
,
,
,
__
94.99 113.89 129.50 149.64 165.38 185.16 201.81 220.86 237.78 256.37 273.79 292.02 309,59 327.65 345.26 363.25 381.09 399,32 416.33 434.93 470.84 488.60 506.60 524.33 542.25 559.81 577.42 595.83 613.50 630.82 648.86
58.27 78.25 94,49 113.69 130.44 149.28 166.30 184.93 202.11 220.61 237.91 256.31 273.68 292.02 309.45 327.74 345.22 363.46 380.98 399.18 416.74 434.92 452.78 470.64 488.24 506.38 524.00 542.11 559.75 577.84 595.49 613.58 631.24 649.32
-0.58
-0.50 -0.20 0.94 -0.36 0.92 -0.23 0.30 -0.25 0.13 -0.06 -0.11 0.00 -0.14 0.09 -0.04 0.21 -0.11 -0.14 0.41 -0.01 -0.20 -0.36 -0.22 -0.33 -0.14 -0.06 0.42 -0.34 0.08 0.42 0.46
iimiting line for the higher members For series other than the normal alkanes the data are not sufficient to warrant fitting a three-constant curve; for the normal alkanes a’ = 5.86, b’ = 17.871, and c = 3.61. The fit as measured by the standard deviation using these parameters is between that of the even and the odd straight lines. The agreement of the individual hydrocarbons is shown in table 15; the standard deviation for the thirty-two hydrocarbons is 0.36 ml.
304
GUSTAV EGLOFF AND ROBERT C. KUDER
per mole, corresponding to a mean deviation of 0.27 ml. per mole and an average percentage deviation of 0.14 per cent. IV. SUMMARY
The molal volumes of straight-chain aliphatic hydrocarbons in the liquid st.ate at their respective melting points can be expressed accurately (average percentage deviation of 0.09 per cent) by equations of the type:
V=a+bn The data are such as to justify different values of b for series differing in degree or position of unsaturation and for the even and odd sub-sets of each series. I n the case of normal alkanes the same limiting line for each sub-set is given by
V = a'
+ b'n cn
where the plus sign is used for the even members and the minus sign for the odd members. The authors wish to thank L. S. Kassel and R. B. Ewe11 for helpful suggestions. REFERENCES
G.,BEATTY,H. A , , KUDER,R . C., AND THOMPSON, G. W.: Ind. Eng. (1) CALINGAERT, Chem. 33, 103-6 (1941). G.:Physzcal Constants of Nydrocarbons, Vol. I. Reinhold Publishing Cor(2) EGLOFF, poration, New York (1939). (3) EGLOFF, G.,AND KUDER,R. C.: J . Phys. Chem. 46, 836-45 (1941). (4) KRAFFT, F . : Ber. 15, 1711-27 (1882). (5) LE BAS,G.: J . Chem. SOC.91, 112-15 (1907); Phil. Mag. [el 16, 60-92 (1908). (6) LE BAS,G.: Proc. Chem. SOC.27, 196-7 (1911). (7) LE BAS,G.: The Molecular Volumes of Liquid Chemical Compounds, p . 240. Longmans, Green and Company, London (1915). (8) PAULY,H.: Z. anorg. allgem. Chem. 119, 271-91 (1921).
