elations between Physical Properties of Paraffin
Hydrocarbons J
ALFRED W. FRANCIS Oil Company, Inc., Paulsboro, N. J.
Socony-Vacuum
Boiling, melting, and aniline points, density, index of refraction, and octane number are given for paraffin hydrocarbons, through the decanes. Equations are derived reproducing directly and probably within experimental uncertainty the densities, indices of refraction, and boiling points of the normal and most of the simpler types of branched-chain paraffins, each as a function of the number of carbon atoms. For each group of isomeric paraffin hydrocarbons : (a)Aniline point is nearly a linear function of density or index of refracECENT compilations ( l a , 1 4 ) of the physical properties of paraffin hydrocarbons, together with still more recent and reliable determinations for some of them, permit the discovery of nearly quantitative relations between the properties which are useful in evaluating the data themselves and also in predicting missing data. They are of interest to the petroleum industry, especially in so far as they relate to octane numbers, since it is difficultto synthesize or to isolate some of the octanes, nonanes, and decanes in amounts sufficient for accurate octane number determinations. The relations established by Lovell, Campbell, and Boyd (SO) between structure and antiknock value are very useful, b u t they would not apply directly to paraffinic mixtures of unknown structure. Edgar and Calingaert ( I S ) showed ordinal regularities for many different properties of the isomeric heptanes, and for a few properties of hexanes, octanes, nonanes, and decanes. Calingaert and Hladky (IO)published a graphical method of evaluating and predicting properties. Xinney (24) published a boiling point relation for all aliphatic hydrocarbons, which, however, fails by an average of over 3" C. even in the case of paraffins. I n Table I are assembled some properties of all isomeric paraffin hydrocarbons (except optical isomers) up to the OCtanes, inclusive; the nineteen known and two of the sixteen unpublished nonanes; and the twenty-two known and five of the fifty-three unpublished decanes. The properties of the unknown isomers and the unknown properties of the known isomers (except melting point) are estimated by the relations discussed below, and are identified by brackets. I n a few cases where the accuracy of the literature values is suspected because of failure t o conform to these relations, the estimated values arc given in addition.
- R
tion. ( b ) Octane number is nearly a linear function of 1000 times the density minus twice the boiling point; qualitatively, the higher the density and the lower the boiling point, the higher the octane number. ( c ) Octane number is nearly a linear function of boiling point plus aniline point. These relations are used to detect errors in the literature, to suggest possible revisions in values, to estimate all the unknown properties except melting point among those listed above, and to predict the properties of seven isomers unknown in the literature. Khere necessary, corrections of density and index of refraction to 20" C. (not over 5" range except for neopentane and TLD of propane and isobutane), and of boiling point t o 760 mm. (not over 26 mm. range) were made with the following coefficients, for uniformity and because they hold with considerable accuracy for the known data: dd,/dt = 0.0019 (1.13- dzo) dnD/dt = 0.0011 (1.13- d:O) dtb/dp = 0.05"/mm.
Each value taken from the literature was considered critically; in most cases the original literature references given by Egloff ( 1 0 , by Doss (II), and in the more recent papers were consulted. This permitted the detection of several slight errors. Most of the values are weighted means of what seem t o be the most reliable determinations. In assigning weights to values, preference was given to those of more recent determinations (especially by the same author), those of the National Bureau of Standards, those accompanied by determinations of freezing point or by estimates of uncertainty, those by authors who have made several other reliable determinations, those made on larger amounts of material, and those more consistent with regularities known to exist among related hydrocarbons. For simplicity not all the references are given, but only those too recent for Egloff's book ( 1 4 ) or those to which greater weight should be given in selecting the most probable values. An entry is not necessarily that from the new reference, the earlier determinations also being given some weight. A few values were checked experimentally by the author, and some original entries are included (17 ) . The index of refraction of n-butane was found equal t o that of water a t 19 * 0.5" C. because a t that temperature the in-
TABLE I. Paraffin Hydrocarbon Methane Ethane Propane n-Butane 2-Methylpropane (isobutane)
B. P., * C. 161.58
-
PROPERTIES OF PARAFFIN
M. P., -182.6
Literature Citation
C.
Aniline Pointb
Oatane No. Publishedb E8td.c
0.424 (-162’C.) 0.341 (40) 0.5042 (30)
1:2957
-159.42
0.5789 0.5593
1.3324 (17) 1.3233 (17)
84 1 (17 Si) 94d lOO’(17, i l ) 100 [lo’&4
- 88.63 (88) - 183.2 (67) - 42.17 (80) -187.1 - 138.29 -0.50 -11.72
HYDROCARBONS”
....
None None None (17)
n-Pentane 2-Methylbutane (isopentanel 2,2-Dimethylpropane (neopentane)
36.08 27.95 9.45
-129.7 160.0 (37) 16.63
--
0.6262 (61) 0.6197 0.593
1.3577 1.3539 1.339
n-Hexane 2-Methylpentane 3-Methylpentane 2 2-Dimethylbutane (neohexane) 2:3-Dimethylbutane (diisopropyl)
68.74 60.27 (66) 63.23 (62) 49.73 58.00
-118 98,2 -129.0
0.6594 0.6532 0.6642 0.6490 0.6616
1.3750 1.3716 1.3765 1.3689 1.3750
69.1 74.3 69.3 (61) 81.0 (61) 72.0
32 66 75 94.6 (1) 95
n-Heptane 2-Methylhexane 3-Methylhexane 3-Ethylpentane 2 2-Dimethylpentane 2’3-Dimethylpentane 2’4-Dimethylpentane 3’3-Dimethylpentane 2:2,3-Trimethylbutane (triptane)
98.424 90.10 91.9 93.47 79.21 (68) 89.8 80.70 (17)
Glass -118.65 -124.0 Glass -119.1 -135.0 25.06
0.68368 0.6787 0.6865 0.6982 0.6739 0.6950 0,6730 0.6930 0.6900
1.38764 1.3850 1.3882 1.3934 1.3824 1.3920 1.3820 1.3910 1.3895
70.0 (61) 73.8 70.6 66.3 78.0 68.1 78.8 69.7 61)
‘g0 (1)
0.7028 0.6976 0.7057 0.7042
1.3976 1.3954 1.3986 1.3980
72.0 (61) 74 72.2 71.6 [74]
-19 23.8 (1) 35 (1) 39 (1)
0.7128 0.6947 0.7125 0.7002 0.6940 0.7107 0.7194 0.7191 0.7274 0.7162 0.6919 0.7253 0.7188 0.7219 ext. liquih)
1.4021 1.3930 1.4017 1.3958 1.3929 1.4008 1.4044 1.4046 1.4079 1.4029 1.3916 1.4072 1.4044
68.7 [71]
52.4 (1)
[%I. 6 76.0 (17) 78.0
78.9 (1) 69.9 ( I ) 55.7 (I)
0.7178 0.7134 0.7210 0.7199 0.7266 0.7407 10.7261 0.7105
1.4056 1.4030 1,4065 1.4061 1.4090 1.4156 [1.409] 1,4035 [1.40111 1.4095 1.4023 1.4033 1.4008 1.4087
86.0
125.63 (68) 117.65 119.05 117.5
3-Ethylhexane 2 2-Dimethylhexane 2:3-Dimethylhexane 2 4-Dimethylhexane 2’5-Dimethylhexane 3’3-Dimethylhexane 3’4-Dimethylhexane 2lMethyl-3-ethylpentane 3-Methyl-3-ethylpentane 2 2 3-Trimethylpentane 2’2’4-Trimethylpentane (isooctane) 2,’3,’3-Trimethylpentane 2,3,4-Trimethylpentane 2,2.3,3-Tetramethylbutane (hexamethylethane)
118.7 106.2 115.7 109.8 109.25 112.0 117.85 115.7 118.4 109.84 99.23 115.1 113.5
n-Nonane 2-Methyloctane 3-Methyloctane 4-Methyloctane 3-Ethylheptane 4-Ethylheptane
150.74 (68) 143.2 (68) 144.18 142.46 143.1 138.5
- 2 3-Dimethylheptane
Glass (I) Glass Glass Glass ( 1 ) 90.1
- ....
Glass -114.5 ( 1 ) 90.9 -112.32 -107.37 -119.1 -109.19 (I)
-
104 (18)
133 135.21 (6$) 135.21 137.2
3,3-Diethylpentane
139.2
2,3-Dimethyl-3-ethylpentane
[:;:I6
2 2 3 3-Tetramethylpentane
2:2:4:4-Tetramethylpentane
133 122.28
n-Decane 2-Methylnonane
174.04 166.8
3-Methylnonane 4-Methylnonane
167.8 165.7
.I:::‘
.... ....
,102.95
.... .... ....
- 106.35
....
- 41.0 .... .... .... .... 66.6
-- 29.72 74.69 84.83 - 101.62 - 86.80 .... .... .... .... ....
1 153.2
[E?!
Glass
-129.5
....
0
2 6-Dimethyloctane 2:7-Dimethyloctane
158.54 (67) 160
3,3-Dimethyloctane
[:;:I2
3 4-Dimethylootanee 3:6-Dimethyloctane 4 5-Dimethyloctane 4IPropylheptane 3-Methyl-3-ethylheptane
I;[
3’3’5-Trimethylheptane 3:Zi:Diethvlhexanee 3;4-Dieth$lhexane
.... ....
....
124.1 130
2 4 6-Trimethylheptane
-113.3 Glass
I:%! 65
2 2 5-Trimethylhexane 2:3:5-Trimethylhexane
2 2 3-Trimethylheptanee 2:2:6-Trimethylheptane?
- 53.69 - 80.3 -108.0
I4 :[
\:El 126.5
2.5-Dimethyloctane
- 56.84 (1)
106.5
2’4-Dimethylheptane 2’5-Dimethylheptane 2’6-Dimethylheptane 3’3-Dimethylheptane 3’4-Dimethylhe tanw 2:2.3-Trimethyl~exanec 2,2,4-Trimethylhexane?
5-Methylnonane 3-Ethyloctanes 2 2-Dimethyloctane 2’3-Dimethyloctanea 2:4-Dimethyloctane
--118.2 90.60
-
80.88
n-Octane 2-Methylheptane 3-Methylheptane 4-Methylheptane
2,2-Dimethylheptane
--153.7 95.3 (37)
....
-49.2
.... .... .... .... .... ....
161 161.7 156.3 I1621
....
[:E193
-10i:il
143.7 159.1 [:;I5
%25 136.2 2’2’5’5-Tetramethylhexane 162 3:3:4:4-Tetramethylhexane a Figures in brackets [ ] indicate estimated properties. b Citation (16)unless another h given in parentheses. e Estimated from Figure 3. 2 2 3 4-Tetramethylhexane
.
.... .... .... .... ....
.... .... ....
0.7270 0.7140 (44) 0.7147 0.7089 0.7254
:10.7048 77%1
[0.7141 0.7076 0.7159 10.7191 0.7522 IO. 7481 0.7294 [O .744] 0.742 0.7196
71.5 (61)
is 77
[107’ [loo
... ... ...
36
i:ii+5
...
...
77.5 80.3
1.4125 1.4123
78.2 78.3
0.7325 [O.73801 0.7245 [0.7384] 0.7246
1.4117 [1.4154] 1.4082 [1.4157] 1 ,4090
0: i3k9 [0.7320] 0.7291 0.7226
1.4128 1.4107 1.4082
0.7390 0 73761 f0:744] 0.7365 [0.744] 0.736 0.7460
1,4165 [1.4151] [1.417] 1.4145 [1.418] 1.414 1.4179
10.741I 0.7229 [O.7204 0.7198 0.7553 L0.7571 0.744
L1.4161 1.4077 [1.4064] 1.4057 1.4230 [1.425] 1.4184
555
-39 :50 ,73 .83, 82 ;73 97
...
1.4120 1.4099
6
lo:
,
... ... ... ... ... ...
[i:iiil
....
....
[77] [lo5 [gal
- 34
.... .... 1.4197
....
E641 [QOI [1121
...
130
0.7299 0.7280 IO. 72601 0.7334 0.7323
d
98
None
1.4068
o:i5is 10.7181 0.770
so
ai17 I ) 88.1 [ f ) 90.5 105 100 99.1 (8) 97 (1, 6)
1.3996 1.4051
....
68 80 82 (17)
[%IO 67.2 65.8 70.8 (61) 80.1 (61) 67.0 68.3
1.4031
....
(921 I99 I
63 90 116
... ... ... 92.1 ... 91.2 ... ... ... ... ...
I:[
... .. .. ..
125 125 125
$ij
79 (18)
78 I501 [74 761 1731
... - 53 ...
[-52
... ...
[41
... ...
..
25
... [I51 ...
...
...
52
... ... ... ...
... ... ...
[441
M I
Kl
la
f401 70 1
78.7
1.4224 1.do49 [1.431] The following figures in this column are plotted in Figures 3 and 4. Unpublished data.
I N D U S T R I A L A N D E N G I N E E R I N G CHEMISTRY
556
Vol. 33, No. 4
value for the first member fails to agree with the observed T . ~ B L11. E EQUATIONS FOR DEKSITY AND INDEX OF REFRACTION value, as was expected. The density of propane also shows a OF PARAFFIN HYDROCARBOXS slight disparity. These values are enclosed in parentheses and di0 % . - b/n + 0.00062n + 0.4S/n' are not considered significant. A majority of the others agree nso = A - B/n 4- 0.00027n + 0.27/nS within 0.0002, and all of them may agree within the experiSystem a b A B B'b mental uncertainty. Those observed values differing by more Sormal 0.8339 1.15 1.4675 0.61 0.530 2-Methyl 0.8330 1.18 1.4668 0.625 0.530 than 0.0009 from the calculated are marked with a question mark as possibly in error. The discrepancies in the accurately 4-Methyl 3-Methyl tz 1,4670 ::!:: 0.57 0,533 3-Ethyl 0,8340 1.07 determined properties of 2,2,6-trimethylheptane raise doubts 2 2-Dimethyl 0.8348 1.22 1.4679 0.65 0.633 2'3-Dimethyl 0.8364 1.09 1.4703 0.60 0.550 as to the identity of the sample, for which the authors (6) 2'4-Dimethyl 0.55 0.529 0.8178 1.04 1.4580 2'6-Dimethyl 0.8790 1.58 1,4900 0.83 0.525 'lad no direct evidence* 2' &Dimethyl 0.8924 1.75 1.4950 0.90 0,514 2,3-Dimethylbutane has values between those calculated 0.66 0.528 2'2'-Dimethyl 0.8371 1.25 1.4688 3'3-Dimethyl 0.8386 1.12 1.4707 0.61 0,545 for it as a 2,3-dimethyl isomer, and as a 2,2'-dimethyl isomer, 2:2,2'-Trimethy1 E4 1.20 Eo0.63 0.525 to both of which types it belongs. Of the other hydrocarbons Mean 0,83515 1.46780 0.530 with a similar dual nature, 2,4-dimethylpentane fails t o con3 4-Dimethyl 0.8357 1.03 1.4680 0.56 0.543 form in the 2,4- classification, where it is the first member; 3.3-Diethyl 2:2,3-Trimethy1 ': :E ~:~~~~ but its properties agree well in the 2,2'- group in which it is the second member. 2,5-Dimethylhexane and 2,6-dimethylExcluding 2,4-, 2,5-, and 2,6-dimethyl systems. heptane show good agreement in both groups. The constants for the last three systems in Table I1 are calculated from the properties of a single member each. Since there is no separation between the side chains, the a and terface between the two liquids in a sealed tube disappeared, A values are taken approximately equal to the means, adboth in sodium light and in daylight. The corresponding justed slightly s~ as to round off the b and B t o two decimals. extinction for isobutane was a t 3" C. The indices of the butanes in Table I were extrapolations from these observations. The aniline points of the butanes were observed prior to Ludeman's paper (31) and checked his values within 1". TABLE111. DENSITIESOF PARAFFIN HYDROCARBONS (EQUAPropane was shown to lack an aniline point because its TIONS OF TABLE 11) critical temperature is reached without mixing with aniline. n Calcd. 0bsvd.a n Calcd. 0bsvd.o The same is true obviously of ethane and methane. Hexa7h -o -m r a-l c 2,2-Dimethyl----? .methylethane lacks an aniline point because it cannot be 6 (0.6131) 0.593 2 (0.38014) 0.341 supercooled sufficiently below its melting point. 3 (0.50576) 0,5042 6 0.6485 0.6490 4 0.57858 0.6789 7 0.6747 0.6739 2,2,3,3-Tetramethylpentanewas made in 5 per cent yield 5 0.62620 0.6262 8 0.6948 0.6947 from tert-butyl magnesium chloride and tert-amyl iodide and 6 0.66928 0.6594 9 0,7108 0,7105 7 0.68375 0,68368 10 0.7238 0.7245 chloride by the method of Marker and Oakwood (34), and 8 0.70261 0.7028 9 0.71763 0.7178 2,3-Dimethy1 gave by-products of hexamethylethane (melting point 100O C.) 10 0.72990 0.7299 6 (0.6718) 0.6616 and 3,3,4,4-tetramethylhexane. Since the small yields pre11 0.74014 0.7402 7 0.6948 0.6980 12 0.74884 0.7486 8 0.7126 0.7126 vented high purification of the nonane and decane, only ap13 0,75634 0,7568 9 0.7268 0.7270 proximate boiling points and densities are recorded for them. 14 0.76289 0,7636 .... 15 0,76867 0.7688 lo 0'7384 Although melting points are listed in Table 1: no relation to 16 0.77382 0.7739 2,4-Dimethyl 17 0.77845 0.77836 other properties is apparent except the well-known one that 18 0.78263 0.782Ob 7 (0.6834) 0.6730 for isomers, the more symmetrical the molecule, the higher 8 0.7003 0.7002 2-Methyl 9 0.7138 0.7140 is the melting point. 0.7246
-
g: ::::
t:!:
g:iit
g::;
g:;:
(1
.
45 6
Density and Index of Refraction Huggins (32)showed correlations of the structures of paraffin isomers with their molal volumes and molal refractions. The present treatment is more empirical, but also much more oonvenient and fully as accurate'. Table I1 presents equations yielding calculated values for ,density and index of refraction for sixteen different series ,of corresponding homologs as functions of the number of carbon atoms, n. The form of the two equations and the signs of their corresponding terms are the same, and in each case two of the four constants apply to all the paraffins, the ather two depending upon the configuration. Of these the a and A constants also are nearly uniform except for three systems with separated side chains. And the ratios of all the respective b and B constants in the last column are nearly uniform, especially for simpler derivatives. The calculated and observed values for thirteen systems .are compared in Tables 111and IV. In several of the series, especially those containing 2-methyl groups, the calculated Since thin paper was accepted, Calingaert, Beatty, Kuder, and Thorn[IND.ENQ. CHEW.,33, 103 (1941)l published another correlation of struoture with molecular volumes. Five of the discrepancies in their Table IV a r e nearly paralleled in the present paper. The other five are reconciled with calculations. 1
'son
7 8 9 10 18 20 6
7 8 9 10 12 8 9 10 11
(0,67048) 0.61980 0.65339 0,67857 0.69796 0.71340 0.72600 0.78009 0.78760
3-Methyl (0.6616) 0.6865 0.7057 0.7210 0.7335 0.7528 4-Methyl 0.7047 0.7197 0.7320 0.7422
0.5598 0.6197 0.6532
0.6787 0,6976 0.7134 0.72801 0.7806 0.78641
0.6866
0.7057 0.7210 0.7334 0.7527 0,7042 0.7199 0.7323 0.7422
3-Ethyl (0.6953) 0.6982 0.7127 0.7128 0.7266 0.7266 10 0.7380 16 0.7789 0.7784 20 0.7941 0.7949 a Table I up to decanes; citation ( 1 4 ) for others except n-undecane (40 n-dodecane (82). n-tridecane (68).n1 (10~).
~
b Extrapolated, liquid..
9 10 11 12
2,6-Dimethyl 0.7095 0.7284 0.7441 0.7573
0.7089 0.7291 0.7440 0.7575
2,2'-Dimethyl (0.6458) 0.6727 0.6933 0.7097 0.7231 0.7589 0.7949
0.6616 0.6730 0.6940 0.7089 0.7226 0.76911 0.7953b
3,a-Dimethyl 0.6927 0.7111 0.7257 0.7376 0.7475 0.7559
0.6930 0.7107 0.7254 0.73901 0.7474 0.75421
6
7 8 9
~
10 11 12
8 9
0.6642
~
0.734
0'7248 0'7340 2,j-Dimethyl 0.6940 0.7149 0,7320 0,7461 0.7581
lo l1
7 8 9 10 14 22 7
8 9
10 11
12
0.6940 0.7147 0.73491 0.7421 0,7431
2,2,2'-Trimethyl 9 10
(:);:;: ~
0.7076 0.7204
0.6919 ~ 0'6900 0.7076 0.72291
INDUSTRIAL AND ENGINEERING CHEMISTRY
April, 1941
557
have fewer constants but are not more convenient to use, OF REFRACTION OF PARAFFIN HYDROCAR- and each fails to reproduce the data by an average of a t least TABLE IV. INDICES BONS (EQUATIONS O F TABLE 11) 1.3" C. over the C1 to C1*range. That of Cox (11): n
c-
3 4
5 6
7 8 9 10 11 12 13 14 15 16 17 18
Calcd. -Normal 1.29498 1.33296 1.35765 1.37495 1.38776 1.39763 1.40548 1.41190 1.41725 1.42178 1.42569 1.42909 1.43208 1.43475 1.43714 1.43930
0bsvd.a
1.2957 1.3324 1.3577 1.3750 1.38764 1.3976 1.4056 1.4120 1.4173 1.4217 1.42701
....
1.4330 1.4347 1.43766 1 ,43950
5 6 7 8 9 10 18 20
2-Methyl (1.32850) 1.35395 ' 1.37175 1.38491 1.39505 1.40312 1.40970 1.43777 1.44163
6 7 8 9 10 12
3-Methyl (1.3755) 1.3883 1.3984 1.4064 1.4129 1.4230
1.3765 1.3882 1.3986 1.4065 1.4125 1.4236
9 10 11
4-Methyl 1.3981 1.4060 1.4124 1.4177
1.3980 1.4061 1.4123 1.4177
7 8 9 10 16 20
3-Ethyl 1.3930 1.4021 1.4094 1.4154 1.4368 1.4446
4
8
n
Calod. -2,2-Dimethyl(1 ,3500) 1.3687 1.3824 1.3930 1.4014 1.4083
0bsvd.o
log T
7-
1.3233 1.3539 1.3716 1.3850 1.3954 1,4030 1.4099 1.4377 1.4416
5 6 7 8 9 10
2,3-Dimethyl (1.3794) 1.3920 1.4017 1.4094 1.4157
1.3750 1.3920 1.4017 1.4095
7 8 9 10
(1.3868) 1.3956 1.4026 1.4084
1.3820 1.3958 1,4023 1.4090
8 9 10
2,5-Dimethyl 1.3926 1.3929 1,4035 1.4033 1.4124 1.4128
....
1.4368 1,4447
10 11
12
2,6-Dimethyl 1,4008 1.4104 1.4184 1.4251
1.07575
....
-= 745.42 log (n
+ 4.4) - 416.31
holds for butane to dodecane nearly as well as the above Francis equation, the maximum deviation being about 0.1' C.; but their value for propane fails by 0.7" C.
TABLE V. BOILING POINTS OF NORMAL PARAFFIN HYDROCARBONS n -B, Calcd. P., Obsvd. C . 7 Source n -B. Calcd.P., Obsvd. * C.Source
--88.63 161.68
(-95.03) -88.66 -42.19 0.53 36.07 68.76 98.42 125.61 150.72
-42.17 0.50 36.08 68.74 98.42 125.63 150.74
-
1.4008 1.4107 1.4176 1.4243
+ 0.949128log (14n+ 2) - 0.101 log2 (14% + 2)
holds well for the range butane t o decane, but not beyond, and is extremely awkward to calculate. The still more recent equation of Egloff, Sherman, and Dull (16),
T
6 7 8 9 10
9
1.3934 1.4021 1.4090
1.339 1.3689 1.3824 1.3930 1.40357 1.4082
-
Table Table Table Table Table 'Fable Table Table Table
I
I
I I I
I I I I
174.06 174.04 195.85 195.84 216.28 216.26 235.52 234 253.71 252.5 270.98 270.5 287.47 287.5 303.20 303 318.55 317
10 11 12 13 14 15 16 17 18
2,2'-Dimethyl 6 7 8 9 10 14 7 8 9 10 11 12
3.3-Dimethyl 1.3910 1.4008 1.4087 1.4151 1,4205 1,4250
1.3910 1.4008 1,4087 1.4165? 1.4206 1.42261
2,2,2'-Trimethyl 7 (1.3814) 1.3895 1.3916 1.3916 8 1.3998 1.3996 9 1.4064 1.40771 10 Table I up t o decanes; citation 14) for others except n-undecane 41) n-dodeoane (%.a), n-tridecane (33). n-hexadecane ( 6 1 ) , 4-methyldecane 148)1 and 3.3-dimethyl nonane and decane ( 1 0 A ) . b Extrapolated, liquid.
Similar equations could be derived for other groups of corresponding homologs, as with density; but in most cases the number of homologs available would not justify so many constants. The boiling points of the branched-chain isomers can be calculated more accurately by relating them to the normal paraffins from which they are derived-i. e., with the same length of longest chain. Table VI shows these differences in boiling points and also the equations used, which are similar in form but have three constants each, except in two systems.
(i
I n two cases the isomer used is the first member; but the discrepancy should be slight, since there is no 2-methyl group. The second member of the 2,2,3-trimethyl series is used. The other systems represented in Table I by members up to nonanes do not permit these extrapolations.
Boiling Points The most accurate observed boiling points of the normal paraffin hydrocarbons from ethane to dodecane and also hexadecane can be duplicated within 0.03" C. by the following equation of the form used with density and index of refraction, but with two additional terms containing n2 and na (tin " C.): t = -76.4
+ 36.4~1- 1.047~~~ + O.OlSn8 - 270/n + 216/n*
Table V compares the calculated and observed values. Those for tridecane to octadecane also agree within the probable errors of observation; but that of methane disagrees greatly. The recent equations of Aten (4),Burnop (9),Kinney @4), and Merckel (36) for the same purpose, Aten: T = 420,500n - 7200 B m o p : M log T - 8 1 / M = 21.8 45.03% Kinney: t = 2 3 0 . 1 4 G m - 543 Merckel: log T = 0.212 log[(%- l)2 - (n - 1)
+
+ 11 + 2.2546
TABLEVI.
INCREMENTS IN BOILING POINTS OF PARAFFIN HY-
DROCARBONS (REFERRED TO THE PARENT NORMALPARAFFINS) n At Calcd. A: 0bavd.a n At Calcd. At 0bsvd.a 2-Methyl 2,Z-Dimethyl At 51.52 2.8% 576/nz At = 20.7 0.75n -!-288/nP 4 (35.70) 30.45 , (60.16) 51.62 50.24 60.23 5 28.47 28.45 7 43.12 43.13 6 24.20 24.19 7 21.33 21.36 8 37.48 37.46 9 32.71 31. 98T 8 19.20 19.23 9 17.51 17.57 10 28.48 10 16.08 16.06 2,a-Dimathyl 18 8.09 8 At E 24.6 1428/nB 3-Methyl 6 (64.27) 58.50 At 17.55 0.5n 450/n' 7 53.74 53.72 8 46.91 46.96 6 27.05 27.15 9 42.23 42.23 7 23.23 23.16 10 38.88 ... 8 20.58 20.63 9 18.61 18.55 2,5-Dimethyl 10 17. 05 17.06 At 58.0 2.75n 288/nz 4-Methyl 8 40.50 40.51 At 8.45 680/nz 9 36.81 36.79 8 19.08 19.08 10 33.38 33.37 9 16.85 16.83 15.25 14.967 2,2'-Dimethyl At 58.0 2.75n 288/nz 11 lo 14.07 14.06 6 (49.5) 58.50 3-Ethyl 7 44.63 44.62 At = 32.45 O.6n 1428/n* 8 40.50 40.51 9 36.81 36.79 7 57.39 57.39 10 33.38 34.377 8 49.96 49.96 9 44.68 44.68 3,3-Dimethyl 10 40.73 At 19.52 0.18n 1428/n* 20 24.02 24 7 49.92 49.92 8 43.27 43.26 a Table I u t o decanes. citation 9 38.77 38.78 (48) for 4-metbdecane, ( i 4 ) for the 10 35.60 86.57 other two.
-
2
-
-
+
...
-
-
+
+
-
-
+
-
+
-
-
-
+
-
+
+
+
...
558
Vol. 33, No. 4
INDUSTRIAL AND ENGINEERING CHEMISTRY
The method of Egloff, Sherman, and Dull (15)for calculating boiling points of branched-chain paraffins by subtracting a constant for each type from the boiling points of the normal isomers is not sufficiently accurate to detect possible errors in observed values or to give more than approximate estimates on unknown boiling points. The observed values for this "constant" for 2-methyl isomers, for example, are 11.22", 8.13', 8.47", 8.32", 7.98", 7.54", and 7.24" C. for butanes to decanes, inclusive. Omitting the first member, there is a distinct rise followed by a gradual fall of 1.23" c.
1.31
1.1
INDEX OF REFRACTION, x l , [ ~ C l ~ , ,
L
l
~
DECANES
82 HEXANES OCTANES OX
80
ox
for density and index of refraction are 39.2 and 38.3 per
cent, respectively. Thus the boiling point could have been estimated from the other properties within about 0.03 " C. The first-member discrepancies are reasonably parallel with those in Tables I11 and IV (except for slight disparities in the 3alkyl systems of the latter). One degree in boiling point is roughly equivalent to 0.002 in density and 0.001 in index of refraction. It will be shown later that the effects of such increments upon calculated octane numbers also are about equivalent. They are roughly parallel with experimental uncertainties in determination. The densities, indices of refraction, and boiling points of two unknown decanes in Table I are estimated in Tables 111,IV, and VI. For the other unknown paraffins the first two properties were calculated by the equations at the bottom of Table 11; and the boiling points were estimated by the method of Egloff, Sherman, and Dull (16), although they did not compute the constants for these systems. The equations of Tables I1 and VI can be used to calculate the properties of homologs higher than decanes also with considerable accuracy.
Aniline Point
.61
.63
.65
.67 .69 DENSITY, o
.71
.73
FIGUREI Some of the groups included in Tables I11 and IV are omitted from Table VI because the small number of members available (excluding the first as unreliable) does not justify calculation of a three-term equation, whereas in Tables I11 and IV only two characteristic constants were required. In three of the four systems containing a 3-alkyl group, the last term in the equation is identical. A similar coincidence occurs in three of the systems containing a 2-methyl group. The whole equations for the 2,5- and 2,2'-dimethyl systems are the same. The calculated boilinn uoint of the first member fails t o agree-with the observed 140 value in four of the series containing the 2methyl group. All but three of the other 100 points agree with the calculations within CT 0.1" C. The boiling point listed for 2,7W m dimethyloctane may be about 1" high. The 5z 60 other discrepancies are 0.29" for 4-methylnonane and 0.73" for 2,2-dimethylheptane. W z The boiling point of 2-methylheptane agrees a 20 L only because it is the mean of two apparently 0 excellent but discrepant determinations. -20 The boiling point of 2,3-dimethylbutane is between those calculated for i t as a 2,3-60 dimethyl isomer and as a 2,2'-dimethyl 380 isomer. It is nearer the former, being 39 per cent of the way from the former to the latter. The corresponding percentages
The critical solution temperature of a hydrocarbon with aniline is designated in this paper by "aniline point" for convenience, although the latter strictly is the solution temperature for equal volumes of the two liquids. When the aniline points of paraffins are plotted against the values for density or index of refraction, the points fall near a straight line for each group of isomers, higher densities or indices corresponding to lower aniline points. Figure 1 illustrates this relation, and also the refractivity intercept relation of Kurtz and Ward (ZG),TZ - d / 2 = 1.0461, by the proximity of the circles (density) and crosses (index of refraction). Their relation is used, as are those in this paper, in detecting discrepancies in properties, and in estimating undetermined ones. The points for the normal and 2-methyl derivatives seem t o be a little low, about 2" C. in aniline point. The other discrepancies include three of the octanes whose aniline points were observed only by Maman (33). Since in five other cases other authors have found aniline points higher than he did, it is possible that these three values are too low. The other points are within the probable error of the lines, which are used t o estimate the undetermined aniline points in Table I. &4naniline point, which for individual paraffins is thus shown not to be an independent criterion of identity, is nevertheless useful for a paraffinic mixture in indicating mean molecular weight by the position of the plot of aniline point vs. density
400
420
440
460 480 500 1000 d$- 2 B P.
FIGVRE 2
520
540
56
INDUSTRIAL AND ENGINEERING CHEMISTRY
April, 1941
-20
N D
NONANES DECANES
-40
1000 d$O-
2 B.P. + C
FIGURE 3
among the lines of Figure 1. Such plots for narrow cuts of a commercial paraffinic mixture distilled by the author have checked consistently within 0.1' C. of a nearly straight line (even though with rising boiling temperature the points went back and forth along this line), as long as the distillate remained uniform in molecular weight.
Octane Number No relation appears between octane number and any other single physical property. It is well known that increased branching increases octane number. To some extent also it lowers the boiling point and increases the density; but neither of the latter two properties is a consistent function of the degree of branching. The lowest boiling octane is not 2,2,3,3tetramethylbutane as might be expected, but 2,2,4-trimethylpentane (isooctane). The latter, though highly branched and one of the isomers highest in octane number, is not one of the highest in density but actually is the lowest of the eighteen isomers. It seemed possible, however, that a combination of these two properties-namely, a correction to the density proportional to the boiling point-might provide a function which has a relatively high value for isooctane and which has a simple relation to the octane number. The function chosen after many trials is 1000 times the density minus twice the centigrade boiling point. I n Figure 2 are plotted the values for this function against all available octane numbers of pure paraffins from butanes to decanes, whether by research or motor method, or by blending value. The points for each group of isomers fall near a straight line. Discrepant values are connected by thin vertical lines. These uncertainties in determination seem to be greater than the departures from the lines. Excessively high values for nhexane and 2,3-dimethylbutane, and excessively low values for tetramethylbutane and neopentane are probably in error. It is recognized that there is no general agreement in octane ratings above 100. The very high ones in Table I are blending values, which (unfortunately) are receiving diminished em-
559
phasis probably because the base fuels used were not pure. A logical method of rating is to determine the percentage of n-heptane which the hydrocarbon-e. g., triptanewould tolerate to match pure isooctane in antiknock quality. If 10 per cent, a rating of 111.1 would be assumed. In this way the heptane-isooctane scale, so useful for interpolation, can be used also for extrapolation. Since the lines of Figure 2 seem to be parallel and the higher ones evenly spaced, they can be superposed by adding a parameter to the above mentioned function, depending upon the number of carbon atoms. The parameters are 142 for butanes, 157 for pentanes, 178 for hexanes, and 29n for higher paraffins. With this modification all the paraffin hydrocarbons above propane for which octane numbers have been reported are plotted in Figure 3. To avoid confusion only one value is plotted for each hydrocarbon-the one in the next to the last column in Table I, which is the mean of determinations in fair agreement, or the determination nearest the curve in the case of widely discrepant values. The best line near all these points now shows a slight curvature. The average departure of the points from the curve is a little over 2 octane numbers, if we omit two of the decanes and 3-methylhexane, whose values may be in error. The agreement is now so good that the curve is used to estimate octane numbers for all the paraffins (above propane) of Table I ; these estimates are given in the last column. For two of the nonanes, 4-ethylheptane and diethylpentane, this method would give absurdly high octane numbers. Since other considerations (e. g., citations 16 and 86) also suggested that the values for boiling point are too low and for density too high, revised estimates of the properties are made using reasonable figures (estimated by the relations of citation SO) for octane numbers. For the same reasons revisions are suggested in one property each of 2,2,4trimethylhexane, 2,3-dimethyl-3-ethylpentane, 2,4-dimethyloctane, 3-methyl-3ethylheptane, and 3,4-diethylhexane. This reversed method was employed also in estimating the properties of 4,5-dimethyloctane, of which the boiling point is the only property published. An error of 14.5' C. in its boiling point in both books (1.2, 14) was detected by the relations in this paper. The error was due to a misprint in Chemisches Zentralblatt (16).
The boiling point of 2,3,3,4-tetramethylpentane is reported in a t least two publications (94, 86) without original reference. By correspondence with the author of one of them (24) and consulting the original reference (&), it was ascertained that the name of the hydrocarbon was given incorrectly in the third edition of Beilstein (dA), and that this hydrocarbon is still unknown in the literature.
1401
I
IO0
a
%
60
8
eo
4z
50
- 20 -60 100
120
140 160 IS0 200 220 BOILING POINT PLUS ANILINE POINT
FIGURE 4
240
260
INDUSTRIAL AND ENGINEERING CHEMISTRY
560
The octane number of a paraffinic mixture of narrow boiling range may be estimated from Figure 3, using the mean boiling point even if the molecular weight is not uniform, by interpolating the parameter according to the mean molecuhr weight as found from Figure 1. This expedites research in which narrow cutsmay be inadequate in amountfor engine tests. Relations similar to those in Figure 2 result when index of refraction is used instead of density-that is, when 1000 times the index of refraction minus the boiling point is plotted against octane number. But the agreement is not quite so good as with density. Another simple function is plotted against octane number in Figure 4-namely, the sum of boiling point and aniline point. Again the points fall near a straight line for each group of isomers. The agreement seems slightly better than that in Figure 2. However, the steepness Gf the lines and the less general availability of accurate aniline points make this method as yet less satisfactory than the previous one for predicting unknown octane numbers. These lines can be nearly superposed by subtracting 25n from the above function, n being the number of carbon atoms.
Literature Cited (1) Am. Petroleum Inst., Hydrocarbon Project, 2nd Ann. Rept., 1940. (2) Aaton, J. G., Kennedy, R. M., and Schumann, 9. C., J . Am. Chem. Soc., 62, 2061 (1940). (3) Aston, J. G., and Messerly, G. H., Ibid., 62, 1919 (1940). (4) Aten, A. H. W., Jr., J . Chem. Phys., 5, 260 (1937). (4A) Beilstein, F. K., Handbuch der organischen Chemie, 3rd ed., Vol. I, p. 105 (1893). (5) Boord, C. E., and Henne, A. L., Div. of Petroleum Chem., A. C. S., Detroit, Sept., 1940. (6) Brooks. D . B.. Cleaton. R. B.. and Carter, F. R . , J . Research Natl.Bur. Standards, 19, 331, 333 (1937). (7) Brooks, D. B., Howard, F. L., and Crafton, H. C., Jr., Ibid., 23, 641 (1939). (8) Zbid;, 24, 44 (1940). (9) Burnop, V. C. E . , J . Chem. Soc., 1938, 826. (10) Calingaert, G., and Hladky, J. W., J . Am. Chem. Soc., 58, 153 (1936). (10A) Campbell, K. N., and Eby, L. T., Ibid., 62, 1800 (1940). (11) Cox, E. R., IND. ENG. CHEM.,27, 1423 (1935). (12) Doss, M. P., "Physical Constants of the Principal Hydrocarbons", Texas Co., 1939. (13) Edgar, G., and Calingaert, G . , J . Am. Chem. Soc., 51, 1540 (1929). (14) Egloff, G., "Physical Constants of Hydrocarbons", Vol. I, New York, Reinhold Pub. Co., 1939. (15) Egloff, G., Sherman, J., and Dull, R . B., J . Phys. Chem., 44, 730 (1940). (16) Featrsete, G., Chem. Zentr., 104, I, 45 (1933). \-,
~
Vol. 33, No. 4
(17) Francis, A. W.,unpublished data. (18) Garner, F. H., J. I n s t . Petroleum Tech,, 14, 713 (1928). (19) Glasgow, A. R., Jr., J . Research Natl. B u r . Standards, 24, 528 (1940). (20) Hicks-Bruun, M. M., and Bruun, J. H . , J . Am. Chem. SOC.,58, 810 (1936). (21) Howard, F. L., J . Research Natl. B u r . Standards, 24, 683 (1940). (22) Huggins, M.L., J . Am. Chem. Soc., 63, 116 (1941). (23) Kelso, E . A., and Felsing, W. A., Ibid., 62, 3133 (1940). (24) Kinney, C. R., Ibid., 60, 3032 (1938); IND. ENQ. CHEM.,32, 559 (1940).
gzz," s f ~ , ~ ~ ; . ~ ~ n ~ 6 ~ ~ ~ ~ , o " ( ~ Franklin Inst., 222, 563
(1936); 224, 583, 697 (1937); IND. ENG.CHEM.,Anal. Ed., 10, 559 (1938). (27) Lamb, A. B., and Roper, E . E., J . Am. Chem. Soc., 62, 813 (1940). (28) Leslie, R . T., J . Research Natl. B u r . Standards, 10, 617 (1933). (29) Loomis, A. G., and Walters, J. E., J . Am. Chem. Soc., 48, 2051 11926). (30) L&ell,'W. G., Campbell, J. M., and Boyd, T. A., IND.ENQ. CHEM.,23, 26 (1931). E N G .CHEhf., Anal. Ed., 12, 446 (1940). (31) Ludeman, C. G., IND. (32) Mair, B. J., and Streiff, A. J., J . Research Natl. B u r . Standards, 24, 401 (1940). (33) Maman, A., Compt. rend., 205, 320 (1937). (34) Marker, R . E., and Oakwood, T.S., J . Am. Chem. SOC.,60, 2598 (1938). (35) Merckel, J. H . C., Proc. Acad. Sci. Amsterdam, 40, 164 (1937). (36) Mornan. G. T.,Carter, S. R., and Duck, A. E., J . Chem. Soc.. 127, 1254, 1258 (1925). (37) Rossini, F. D., IND.ENG.CHEM.,News Ed., 17, 389 (1939). (38) Ruhoff, J. R., J . Am. Chem. SOC.,55, 3889 (1933). (39) Sage, B. H., Schaafsma, J. G., and Lttcey, W. N., IND. ENG. CHEM..26. 1220 (1934). (40) Sage, B.'H.; Webster, D. C., and Laeey, W. N., Ibid., 29, 662 (1937). (41) Shepard, A. F., Henne, A. L., and Midgley, T., Jr., J. Am. Chem. Soc., 53, 1948 (1931). (42) Silva, R. D., Ber., 5, 984 (1872). 14.59 Timmermens and Hennaut-Roland. Anales soc. esvafi. . .f i 8 . guim., 27, 460 (1929). (44) Tuot, M., Compt. rend., 197, 1436 (1933) (45) White, J. D., and Glasgow, A. It., Jr., J . Research Nutl. B u r . Standards, 19, 423 (193'7). (46) Ibid., 22, 152 (1939). (47) White, J. D., Rose, F. W., Jr., Calingaert, G., and Soroos, H., Ibid., 22, 317-19 (1939). (48) Whitmore, F. C . , and Orem, H . P., J. Am. Chem. Soc., 60, 2574 (1938). (49) . , Whitmore. F. C . , Popkin, A. H . , and Pfister, J. R., Ibid., 61, 1616 (1939). (50) Whitmore, F. C., and Southgate, H. A,, Ibid., 60, 2573 (1938). (51) Wibaut, J. P., Hoop, H., Langedijk, S. L., Oberhoff, J., and Smittenberg, J., Rec. traw. chim., 58, 358, 373-4 (1939). (52) Wojciechowski, M., Proc. Am. Acad. A r t s Sci., 73, 363, 8 (1940) \--,
~
PRESENTED in part before the Special Research Conference of the Chemistry Section, of the American Association for the Advancement of Soience Gibson Island, Md.
