730
CUSTAV EGLOFF, f . SHERMAN, AND R . E. DVLL
(3) GROffffINs: Unit Processes i n Organic Synthesis, p. 630. McGraw-Hill Book Company, New York (1938). (4) Reference 3, pp. 631-2. U. S.patents 1,950,359(1934)and 1,844,710(1932). (5) JENKINSAND NORRIS: AND KENNEDY: U. S. patent 1,735,327(1929). (6) LLOYD (7) LLOYDAND KENNEDY: U. S. patent 1,849,844 (1932). (8) RITTLER: u. s. patent 1,936,567 (1933). AND ZELLMAN: U. S. patent 1,961,834(1931). (9) STEINOROENER (10) TISHCHENKO, GUTNER, FAERMAN, AND SHCHIGELSHAYA:J . Applied Chem. (U. S. S.R . ) 8, 685-94 (1935).
BOILING POINT RELATIONSHIPS AMONG ALIPHATIC HYDROCARBONS' GUSTAV E G L O F F , J . SHERMAN,
AND
R. B. DULL
Research Laboratories, Universal oil Products Company, Chicago, Illinois Received October 9, 193'9 INTRODUCTION
The boiling points of the paraffin, olefin, and acetylene hydrocarbons have recently been collated (3)* and evaluated critically. A correlation of the data, as dependent upon molecular structure, becomes important in order that its consistency may be checked and that boiling points for those compounds where data are lacking may be calculated with the same order of accuracy as the experimental data. I n 1842 Kopp ( 5 ) announced that in any homologous series the boiling point rises 18' for the addition of each methylene group to the molecule, but he soon recognized that the increase in boiling point became less with increasing size of the molecule; since then many attempts have been made t o correlate the data. Each of these efforts need not be individually considered here. However, in order to show the diverse forms of boiling point equations used, a representative list is given in table 1. Each of the equations given in table 1 has certain disadvantages which need not be considered in detail. I n general, it may be said that the early workers frequently expressed the boiling point as a function only of the molecular weight, and consequently all isomers yould have the same calculated boiling point. The data of this early period were too limited and 1 Presented before the Division of Physical and Inorganic Chemistry at the Ninety-eighth Meeting of the American Chemical Society, held in Boston, Massachusetts, September 11-15, 1939. * The boiling point data in this paper are taken from reference 3.
unreliable to justify more elaborate formulae to calculate the boiling points of organic compounds. Burnop (2) and Kinney (4)have calculated the boiling point of a compound in a manner analogous to the calculation of the molecular weight from the atomic weights,-i.e., they assign certain “boiling point numbers” to the different atoms such that the boiling point is a function of this additive variable. Unfortunately, the boiling points are not sensitive functions of the “boiling point numbers.” I n the present study of thirty-one aliphatic series, a set of equations has been found which reproduce the data to within their experimental limits. TABLE 1 Boiling point equations AUTHOB
EPUA’FION’
A = 18’. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T = A M s . .................................
T=AdTn+t
............................
144.86 - Tm = ..................... Tk0148
+ c ) + 70/2n.. . . . . . . . . . . . . . Quantity M loglo T + 8.0 dB is additive.. T
= a log (bn
T=2 3 0 . 1 4 m - 543, where N is additive.
,
I
YEAR
KOPP ( 5 ) Walker (8) Boggio-Lera (1)
1842 1894
Young (9)
1905
Plummer (6) Burnop (2) Kinney (4)
1916 1938 1938
1899
~
* M = molecular weight; n = number of carbon atoms; T = boiling point in “K.; A = difference in boiling point between two successive compounds in an homologous series; a, A , b, B , c, N = empirical constants. THE EMPIRICAL EQUATION
It has been pointed out by Wakeman (7) a d others that the curves showing the dependence of boiling point upon the number of carbon atoms are very nearly parallel for various homologous series. If an equation for any one series can be found, then a satisfactory equation for any other will differ from this one only by an additive constant. The equation to use will be derived from the boiling point data of the normal paraffins, since these are the most reliable and include more compounds than any other series. A plot of the boiling points against the number of carbon atoms of linear, logarithmic, and other scales suggests that an equation3 of the following form will represent the dependence of T on n: T = a log (n b ) k (1)
+ +
* T i s the boiling point and n the number of carbon atoms in the molecule. a, b, and k are the empirical constants to be evaluated. In this study T is expressed in
$32
GUSTAV EGLOFF, J. SHERMAN, AND H. I(. DULL
For convenience, ordinary Briggsian logarithms will be used. Equation 1 may be expressed in several equivalent forms. The constant k can bc incorporated into the logarithmic term, so that T = a’ log (b’n k’) (2)
+
the old constants being related to the new by the equations a = a’
(24
b = k‘/b‘ k = a’ log b’
(2b)
(2c) The boiling point may also be expressed as a function of the molecular weight, rather than as a function of the number of carbon atoms, as shown by equation 3. T = a” log ( M b”) k” (3)
+
Af
= the molecular weight.
+
For paraffins
+
+
M = nC (2n 2)H whcre C and H represent the atomic weights of carbon and hydrogen, respectively. a = at’
k = a” log (C
+ 2H) + k”
b = - “’ + 2H for paraffins C 2H
+
=
b’’/(C
+ 2H) for olefins with one double bond, and
b” - 2H - -___ for monoacetylenes, etc.
C
+ 2H
In the present study equation 1 is used in preference to equations 2 and 3, because the parameters a and b can be kept constant for all of the thirtyone homologous series, only k varying from series to series. EVALUATION OF THE CONSTANTS
The constants a, b, and k in equation 1 were evaluated by the method of least squares from the boiling points of the normal alkanes from ethane to nonadecane inclusive. The resulting equation 4 is T = 745.42 log ( n 4.4) - 416.31 (4) The agreement between the calculated and observed values is shown in table 2. hlethane, the first member of the series, is inserted to indicate
+
degrees Kelvin. A shift t o the Centigrade scale would merely change the constant k by 273.1”.
733
BOILING P O I N T RELATIONSHIPS AMONG HYDROCARBONS
that its calculated boiling point is in marked disagreement with thc experimental value. The remarkably close agreement between the observed and calculated boiling points indicates the consistency of the data. The average deviation between the calculated and observed boiling points for the eighteen compounds from ethane through nonadecane (ClgH4a) is 0.40". From butane to dodecane the mean deviation is only 0.05". This is even smaller TABLE 2 Normal alkanes T = 745.42 log (n 4 ~ 4 ) 416.31
+
NUMBER O F ARBON ATOM6
NAME O F COMPOUND
AT
~~
"K.
"K.
3 4 5
(111.55) 184.6 230.9 272.6 309.08
(129.63) 184.6 231.6 272.7 309.08
Hexane. , . . . . . . . . . . . . . . . , . . , . , . Heptane. . . . . . . . . . . . . . . . . . . , . . . Octane. . . . . . . . . . . . . . . . . . . . . . . Nonane . . , . . , . . , . , . . , . . . . . . . . , Decane. . . . . , , . . , . . . . . . . . . . . . . .
6 7 8 9 10
341.88 371.53 398.88 423.83 447.1
341.80 371.52 398.75 423.85 447.2
4-0.08
Undecane . . . . . . . . . . . . . . . . . . . . . Dodecane . . . . . .. . . . . ....... Tridecane . , . . . . . . . . . . . . . Tetradecane. . . . . . . . . , . . . . . . ' Pentadecane . . , , , . . . . . . . .
11 12 13 14 15
468.9 489.3 507 524 543.6
468.0 489.3 508.4 526.5 543.6
0.0 0.0 -1.4 -2.5 0.0
16 17
560.6 576 590.0 603.1
559.9 575.4 590.2 604.3
+0.7 +0.6 -0.2 -1.2
(Methane). . . . . . . . . . . . . . . . . . . . , Ethane . . . . . . . . . . . . . . . . . . . . ... Propane, . . . . . . . , . . , , . . . . . . . . . . Butane. . , . . . . . . . . . . . . . . , . . . . . Pentane. . . . . . , . , . . . . . . . . . . . .
(1) 2
.I
'K. (- 18.08)
0.0 -0.7 -0.1 0.0
+O.Ol +O. 13 -0.02 -0.1
I
Hexadecane . . . . . . . . . . . . . , Heptadecane . . . . . . . . . . . . . . . . Octadecane. . . . . . . ........ . Nonadecane . . . . . . . . . . . . . . .
18
19
~
than the probable error of the data, and may therefore be fortuitous to some extent. The constants 745.42 and 4.4 for a and b, respectively, in equation 1 are used in all the equations covering the other thirty homologous series of the aliphatic hydrocarbons, Le., equation 5 is used where k is a constant to be determined for each series. T = 745.42 log ( n 4.1) 12 (5) The detailed data of the thirty other homologous series are shown in tables 3 to 32, inclusive. In many tables the first entry is given in paren-
+
+
734
QUSTAV EGLOFF, J. SHERMAN, AND R. B. DULL
theses, which signifies that the particular hydrocarbon waa not considered in the evduation of k but waa inserted to show the limits of validity of the formula. TABLE 3
%Met hylalkanes
T
= 746.42 log ( n
+ 4.4)
N U Y B E B OF CABBON ATOYI
NAME OF COYPOUND
- 424.51 T
(OEdEBVED)
1
T
OK.
(2-Methylpropane) . . . . . . . . . . . . . 2-Methylbutane. . . . . . . . . . . . . . . . 2-Methylpentane. . . . . . . . . . . . . . . 2-Methylhexane . . . . . . . . , . , , . . . 2-Methylheptane . . . . . . . . . . . . . . 2-Methyloctane. . . . . . . . . . . . . . . . 2-Methylnonane . . . . . . . . . . . . . . . 2-Methylheptadecane . . . . . . . . . .
(4) 5 6 7 8 9 10 18
586
+
NAME OF COMPOUND
3-Methylpentane . . . , . . . . . . . . , . 3-Methylhexane. . . , . . , . , , . . . . . . 3-Methylheptane , . . . , , . . , . , . . , . 3-Methyloctane. . , . . , . . , . . . . . . . 3-Methylnonane . . , . . . . . . . . . . , .
I ICABBON AZOMI
NuMBEBoF
6 7 8
9 10
+
(4-Methylheptane) . . . , . . . . . . . . . 4-Methyloc tane . . . . . . . . . . . . . . . . 4-Methylnonane . . . . . . . . . . . . . . .
N U M B 1 8 OF CABBON ATOMS
-2.6
- 422.88 T
T
'K. 336.43 364.9 392.18 417.3 440.9
AT
'K. 335.23 364.95 392.18 417.28
'K. +1.20
0.0 0.0 0.0 $0.3
440.68
- 424.69 T
T
(OEdEBVED)
(CALCULATED)
*K.
(8) 9 10
OK.
(-3.6) +0.5 -0.16 -0.09 -0.1 f0.4 +0.9
( O ~ ~ ~ B V E D ()C ~ U L A T E D )
TABLE 5 &Methylalkanes T = 745.42 log ( n 4.4) NAME OF COYPOUND
OK.
(264.5) 300.88 333.59 363.32 390.4 415.7 439.0 588.5
(260.9) 300.93 333.43 363.23 390.3 416.1 439.9
TABLE 4 S-Methylalkanes T = 745.42 log ( n 4.4)
AT
(CAUULA~D)
(381.1) 415.59 438.8
OK.
(390.5) 416.67 438.9
I
AT OK.
(-9.4) +0.02 -0.1
A summary of all the results given in tables 2 to 32, inclusive, is given in table 33. In this table the name of each series is given in column 1, the value of constant k in column 2, the average deviation between calculated and observed boiling points in column 3, and finally the diEerence
735
BOILING POINT RELATIONSHIPS AMONG HYDROCAHBONS
TABLE 6 T
-
#-Ethylalkanes 745.42log ( n 4.4) - 423.01
+
T
N U Y B B B OF CARBON A T O M
NAME OF COILPOUND
(OE8ERYZD)
'K.
3-Ethylpentane . . . . . . . . . . . . . . . 3-Ethylhexane.. . . . . . . . . . . . . . . 3-Ethylheptane.. . . . . . . . . . . . . . 3-Ethyloctadecane . . . . . . . . . . . .
366.4 392.0
7 8
364.8 392.0 417.2 611.2
1 I
T
T
(OBIJmRPED)
(CAWaAl'ID)
!
~
0.0 -1.0
4-3
TABLE 7 9 ,#-Dimethylalkanes
T = 745.42log ( n + 4.4) - 435.34 NUMBIB OF
NAME OF COMPOUND
CABBON A T O M
1 1
(5) 6 7 8
OK.
(282.58) 322.83 352.43 I 380.1 ~
1
~
'IC. 1 (290.05)
1
322.77 352.49 379.72
I ,
1
'* OK.
(-7.47) +0.06
-0.06 +0.4
TABLE 8 8 ,$-Dimethylalkanes
T = 745.42log ( n + 4.4)- 425.88 NAME OF COMPOUND
2,3-Dimethylbutane. . . . . . . . . 2,3-Dimethylpentane. . . . . . . 2,3-Dimethylhexane. . . . . . . . .
(2,4-Dimethylpentane). ........ '2,4-Dimethylhexane ........... 2,4-Dimethylheptane. . . . . . . . . .
"BEE OF CARBON ATOM
6
7 8
(7) 8 9
Ii
1
T (OBSERVED)
'K.
331.18 362.93 388.93
332.23 389.18 414.28
-1.05
1
-0.25 -0.6
'K.
*K.
'K.
(353.6) 384 408.9
(356.5) 383.8 408.9
(-2.9) $0.2 0.0
736
QUSTAV EGLOFF, J. SHERMAN, AND R. B. DULL
NAME OF COMPOUND
2,5-Dimethylhexane. .......... 2,5-Dimethylheptane. ......... 2,5-Dimethyloctane. ...........
8 9
'K.
'K.
382.4 408.9 429
383.2 408.3 431.5
-0.8 +0.6
"K.
'K.
'K.
'K.
-2
2,6-Dimethylheptane 2,6-Dimethyloctane
'
TABLE 12
3,S-Dimethylalkanes
T = 745 log (n + 4.4)- 430.10 NAME OF COMPOUND
.........I
3,3-Dimethylpentane. . . . . . . . . .' 3,3-Dimethylhexane.. 3,3-Dimethylheptane. . . . . . . . .[
NUMBEROF CARBON ATOMS
7 8 9
1 1
T (OBSERVED)
~
~
'K.
359.1 384 410.6
:
'K.
'K.
357.7 384.9
+1.4 -1
'K.
'K.
TABLE 13 Miscellaneous dimethylalkanes
2,7-Dimethyloctane 3,6-Dimethyloctane 7,s-Dimethyltetradecnne
I
1 10
'K.
I
432.79 0
The mean deviation between the observed and calculated boiling points for the one hundred forty-three hydrocarbons hbulated in the thirty-one tables is 0.7'. This is the magnitude of the probable error of the data,
737
POINT RELATIONSHIPS AMONG HYDROCARBONS
BOILING
and so the correlation of the boiling points with structure presented here may be considered to be satisfactory. From equation 5 , the difference in boiling points between two successive members of an homologous series is given by the equation
T
TABLE 14 1-Alkene series = 745.42 log (n 4.4)
+
- 421.91 T
AT
(cA LC UL A T E D)
'K.
(Ethene). . . . . . . . . . . . . . . . . . . , 1-Propene , . . . . . . . . . . . . . . . . . . . i 1-Butene. , , . . . . . . . . . . . . . . . . . . , 1-Pentene . . . . . , . . . . . . , . , , . , , . 1-Hexene . . , , , . . , , . . . . . . . . . . . . . 1-Heptene.. . , . . . . . . . . . . I-Octene . , . . . . . . . . . . , . . . . , 1-Nonene. . . . . . . . . . . . . , . . , 1-Decene.... . . . , . . . . . . . , . I-Dodecene.. , . , . . . , . . , , . . . . . . ~
.I
T
(170.7) 226.1 267.0 303.3 336.48 366.2 393.5 418.4 443.5 486
(2) 3 4 6
12
cis-2-Pen tene . . . . . , . . . . . . . . . cis-2-Hexene. . . , . , . . . . . . , ,. cis-2-Heptene . . . . . . . . . . , . . . . . . cis-2-Oc tene . . . . . . . . . . . . . .. cis-2-Nonene . . . . . . . . . . . . . . . . ,
'K.
(-8.3) +o. 1 -0.1 -0.1 +o .28 +0.3 +0.3 +o. 1 +1.9 +1
TABLE 15 cis-&Alkene series = 745.42 log (n 4.4) - 416.31
+
'K.
,
"K.
(179.0) 226.0 267.1 303.4 336.2% 365.9 393.2 418.3 441.6 484.7
5 6 7 8 9
(276.86) 309.6 342 372.1 398.6 421.6
'K. (272.67) 309.1 341.8 371.5 398.7 423.9
'K.
1
(+4.19) +0.5 f0.2
+0.6 -0.1 -2.3
This difference is dependent only upon n, the number of carbon atoms per molecule of the lowest boiling compound, and is independent of the particular series considered. The dependence of the boiling points upon the structure of molecules containing a given number of carbon atoms is shown in the right-hand column of table 33, where the values of the constant k are given relative to k for the normal alkanes. These relative values of k signify the differ-
738
GUSTAV RQLOFF, J. SHERMAN, AND 8. 8. DULL
ence in boiling point between a given compound and the corresponding normal paraffin.
T
TABLE 16 trans-&Alkene series = 745.42 log (n 4.4) - 416.61
+
T
N M B E B OF CABBON A T O M ' (OBBEBVED)
NAME OF COMPOUND
trans-2-Pentene . . . . . . . . , . . . . . . .
T (CALCULATED)
AT
'K.
OK.
OK.
308.98
308.78 341.5 371.2
+0.2 -0.3 +0.1
T
T
(OBB'EBMD)
(CALCULAT'ED)
AT
TABLE 17 8-Methyl-f -alkene series T = 745.42 log (n 4.4) - 422.81
+
NAME OF COMPOUND ~
NUXBEB OF CARBON ATOYB
2-Methyl-l-propene, . . . . . . . . . . . 2-Methyl-l-butene . . . . , , , , . , . . . 2-Methyl-1-pentene , . . . . . . . . . . . 2-Methyl-l-hexene . . . . . , . . . . . . . 2-Methyl-l-heptene . . . . . , . . . . , , 2-Methyl-1-octene . . . . . . . . . . . , , i
3-Methyl-1-butene . . . . . . . . . . . . . 3-Methyl-1-pentene . . . . . . . . . . . . 3-Methyl-1-hexene . _ . . . . . . . . . . . 3-Methyl-1-heptene . . . . . . . . . . . . 3-Methyl-1-octene . . . . . . . , . . . . .
4
8 9
5
6 7 8
9
'K.
OK.
266.5 304 334.9 364 392.4 416
266.2 302.6 335.3 365.0 392.3 417.4
294.3 328.7 357.0 384.1 409.7
294.4 327.0 356.8 383.2 409.1
*K. +0.3 +1 -0.4 -1 +0.1 -1
-0.1 -0.3 +0.2 +0.9 +0.6
Of the four alkane series listed in table 33 in which there is only one branched chain-namely, the 2-methyl-, 3-methyl-, 4-methyl-, and 3ethyl-alkanes-it may be noted that the boiling point lowering relative to the normal alkanes is of the same order of magnitude in each case, ranging from 0.57" for the 3-methylalkane to 8.28" for the 4-methylalkanes.
739
BOILINQ POINT BEIATIONSHIPS AMONG HYDROCARBONS
TABLE 19 4-Methyl-1-alkene series T = 745.42 log ( n 4.4) - 428.21
+
T
N M B E B OF
NAME OF COMPOUND
T
-
&Methyl-1-pentene.. . . . . . . . . . .!
6
OK.
329.9
(OBsEBVED)
*K.
2-Methyl-2-bu tene . . . . . . . . . . . . . 2-Methyl-2-pentene . . . . . . . . . . . . 2-Methyl-2-hexene. . . . . . . . . . . . 2-Methyl-2-heptene. . . . . . . . . . . 2-Methyl-2-octene. . . . . . . . . . . . . .
.I. I
NAME O F COMPOUND
2,3-Dimethyl-l-butene. . . . . . . . . 2,3-Dimethyl-l-pentene. 2,3-Dimethyl-l-hexene. . . . . . . . .
.......
NAME
or COMPOUND
2,CDimethyl-1-pentene. . . . . . . . 2,4-Dimethyl-l-hexene. . . . . . . . .
5 6 7 8 9
1 ~
T
NUYBEB OF CABBON A T O M
NAME OF COMPOUND
'K.
328.4
I ~
308 339.1 368.2 395.7 419.3
AT
(CALCULATED)
~
'K.
-1.5
OK.
OK.
306.2 338.9 368.6 395.9 422.0
+2 +0.2 -0.4 -0.2 -2.7
NVYBEB OF
T
T
CARBON A T O M
(OMEBVED)
(CALCULATED)
AT
OK.
'K.
OK.
6 7 8
i ~
I
327.1 357.0 383.6
+o. 1
327.0 356.7 384.0
f0.3
-0.4
NUMBEB OB
T
T
CARBON ATOMS
(OMEBVED)
(CALCWLAI'ED)
AT
'K.
'K.
354.2 384.2
356.2 383.5
'K. -2.0
7 8
1
+0.7
The boiling points of paraffins containing two methyl side chains in the molecule which are not attached t o the same carbon atom in the penultimate position dong the main chain or to adjacent carbon atoms is inde-
740
GUSTAV EGLOFF, J. SHERMAN, AND R. B. DULL
TABLE 23 2,B-Dimethyl-%-alkene series T = 745.42log (n 4.4) 427.86
+
NAME OF COMPOUND
NUMBEROF CARBON ATOYI)
2,6-Dimethyl-P-heptene. ..... .. 2,6-Dimethyl-2-octene. ........
9 10
-
1
T (OBSERVED)
'K.
'K.
412.0 436
412.3 435.6
TABLE 24 8,3-Dimethyl-l-alkene series T = 745.42log (n 4.4) 437.71
+
NUMBER OF CARBON ATOMS
NAME OF COMPOUND
T
T
(OBBDBVED)
(CALCULATED)
OK.
'K.
3,3-Dimethyl-l-pentene. ....,, . 3,3-Dimethyl-l-hexene. ... . . . . . 3,3-Dimethyl-1-heptene. ......,
7
350 378.0 401.9
8
9
350.1 377.4 402.6
AT 'K.
0 +0.6
-0.6
TABLE 25 4,4-Dimethyl-l-alkene series T = 745.42log (n 4.4) - 435.41 NAME OF COMPOUND
'I
+
T
T
NUMBlROF CABDON A T o m
( o ~ ~ R V E D ) (CALCWTED)
'K.
OK.
(352.42) 379.7 404.8
(-6.94) +0.6 -0.6
T
T
(OBUERVDD)
(CALCULATED)
AT
TABLE 26 2,S-Dimethyl-2-alkene series T = 745.42log (n 4.4)- 422.11
+
NAME OF COMPOUND
NUMBEROF CABBON ATOMS
1
'K.
2,3-Dimethyl-2-pentene. .. ..... 2,3-Dimethyld-hexene. ., . . , ,.. 2,3-Dimethyl-2-heptene. ... , ..
7 8
9
365.1 393.3 418.6
'K.
365.7 393.0 418.1
*K.
-0.6
+0.3 +0.5
pendent of the relative position of these methyls, as is evidenced by IC remaining approximately constant for these series. For 2 ,a-dimethylalkanes the boiling points are about 4" lower than for the corresponding members of the other dimethylalkanes.
741
BOILING POINT RELATIONSHIPS AMONG HYDROCARBONS
TABLE 27 d,Q-Dimethyl-%alkene series
T
= 745.42log ( n
2,4-Dimethyl-2-pentene , . . . .. . 2,4-Dimethyl-2-hexene. . , .., , .,
+ 4.4) - 432
7 8
I
NUMBEROF CARBON A T O W
N A M l OF COMPOUND
-
I
356 383
I
I
T
~
(OBSERVED)
~
385.4 , 411 1 435
8 9 10
0 0
T
"
(CALCULATED)
"K.
2,5-Dimethyl-2-hexene. ........ 2,5-Dimethyl-2-heptene. . ...... 2,5-Dimethyl-2-octene. ..... . ..
356
~
'K.
~
41: 0.0
385.4 410.6 433.9
+1.1
TABLE 29 Miscellaneous dimethylalkenes
i
N A M E O F COMPOUND
NUMBEROF CARBON ATOM0
''
T (OBBERVED)
"K.
2,5-Dimethyl-l-hexene. , .. . . ... 2,6-Dimethyl-l-heptene. . ..... 3,4-Dimethyl-l-hexene. ..,., ., . 3,5-Dimethyl-l-hexene. ...., ,.. 3,7-Dimethyl-l-octene , ,,,.....
8
NUMBEROF CARBON A T O M
NAME OF COMPOUND
1
?'
~
(OBYi,VED)
Propadiene .................... 1,2-Butadiene. . .. .. . . . . , , . , . , , 1,2-Pentadiene. . . . . . . , . . , . . . . . 1,a-Hexadiene. . , , , . , , , . . . . . 1,a-Heptadiene, . . . . . . . . .. . . . . . ,
,
3 4 5 6 7
OK.
384.7 408.4 378 378.5 427
Z2:9
317.8 351.5 378
384.7 408.4 378.0 378.5 427.0
i j
OK.
0.0 0.0 0
1
I j
' ~
*K.
OK.
240.19 281.7 317.6 350.4 380.1
-1.40
+1.7 +0.2 +1.1
-2
742
GUSTAV EGLOFF, J. SHERMAN, AND R. B . DULL
The introduction of a double bond in the molecule affects the boiling point quite markedly. I n the straight-chain molecules, a double bond in the terminal position lowers the boiling point (relative to the normal alkane) by 5" to 6". A double bond in the 2-position (cis- and trans-2alkenes) lowers the boiling point less than 0.5". TABLE 31 Gp=C-(C)I-cCC series T = 745.42 log ( n 4.4) - 424.89
+
NAYS OF COMPOUND
NUMBER OF CABBON ATOYI)
1,ZPropadiene . . . . . . . . . . . . . . . 1,3-Buta&ene. . . . . . . . . . . . . . . . lt4-Pentadiene . . . . . . . . . . . . . . . 1,bHexadiene. . . . . . . . . . . . . . . . 1,7-0ctadiene,. . . . . . . . . . . . . . . . 1,SNonadiene . . . . . . . . . . . . . . . . . 1,g-Decadiene . . . . . . . . . . . . . . . . 1,ll-Dodecadiene . . . . . . . . . . . . .
3 4 5 6 8 9 10 12
T
T
(OBBmBVSD)
:CALCULATSD
OK.
OK.
238.79 268.38 302.6 332.70 390.6 415.9 443 480
223.05 264.09 300.5 333.22 390.2 415.3 438.6 480.7
+15.74 4-4.29 +2.1 -0.52 +0.4 +0.6 +4 -0.7
T
AT
TABLE 32 I-Alkyne series T = 745.42 log ( n 4.4)
+
OK.
2 3
OK.
- 413.81 (CALCULATED)
Ethyne. . . . . . . . . . . . . . . . . . . . . . . . 1-Propyne . . . . . . . . . . . . . . . . . . . . .
AT
189.5 245.6 281.0 312.4 344.0 373 400.9
424 473
OK.
187.1 234.1 275.2 311.6 344.3 374.0 401.3 426.4 472.0
'K. +2.4 +11.5 $5.8
+0.8 -0.3 -1 -0.4 -2 +l
For molecules containing one side chain, the difference between the boiling points of the olefin and the corresponding parafIin depends upon the relative positions of the double bond and the side chain. If the side chain is attached to one of the carbons forming the double bond, the boiling point of the olefin is higher than that of the paraffin. The 2methyl-1-alkenes boil approximately 1.7' higher than the 2-methylalkanes, and the 2-methyl-2-alkenes boil about 5.3' higher than the 2-methylalkanes. On the other hand, if the side chain is attached to a carbon atom
TABLE 33 Values of the constant k for varioua hydrocarbon series
Alkane ............................ %Methylalkane . . . . . . . . . . . . . . . . . . . 3-Methylalkane. . . . . . . . . . . . . . . . . . . &Methylalkane . . . . . . . . . . . . . . . . . . . %Ethylalkane .....................
-416.31 -424.51 -422.88 -424.59 -423.01
0.40 0.36 0.30
-6.57
0.06
-8.28
0.50
-6.70
2,%Dimethylalkane . . . . . . . , . . . . . . . 2,3.Dimethylalkane . . . . . . . . . . . . . . . 2,4-Dimethylalkane . . . . . . . . . . . . , , . 2,&Dimethylalkane . . . . . . . . . . . . , . . 2,&Dimethylalkane . . . . . . . . . . . . . . . 2,7.Dimethylalkane . . . . . . . . . . . . . . .
-435.34 -425.88 -431.30 -431.90 -431.11 -430.67
0.17 0.72 0.98 1.13 1.25
-19.03 -9.57 -15.00 -15.60 -14.80 -14.38
3,3.Dimethylalkane . . . . . . . . . . . . . . . 3,B-Dimethylalkane. . . . . . . . . . . . . . . 7,8-Dimethylalkane. . . . . . . . . . . . . . .
-430.10 -430.46 -434.62
0.97
-13.79 -14.15 -18.31
1.Alkene . . . . . . . . . . . . . . . . . . . . . . . . . .
0.46
2-Methyl-1-alkene. . . . . . . . . . . . . . . . . 3.Methyl.l.alkene ..... 4-Methyl-l-alkene . . . . . . . . . . . . . . . . . %Methyl-Zal kene . . . . . . . . . . . . . . . . .
-421.91 -416.31 -416.61 -422.81 -431.07 -428.21 -419.21
-5.60 0.00 -0.30 -6.50 -14.76 -11.90 -2.92
2,%Dimethyl-1-alkene ............. 2,4.Dimethyl.l.alkene 2,5-Dimethyl.1.alkene ............. 2,6-Dimethyl.l.alkene . . . . . . . . . . . . . 3,3.Dimethyl.l.alkene ............. 3,4-DimethyI.l.alkene . . . . . . . . . . . . . 3,kDimethyl-l-alkene . . . . . . . . . . . . . 3,7.Dimethyl. 1.alkene .....
-431.11 -431.64 -430.40 -431.80 -437.71 -428.76 -436.56 -436.46
0.27 0.90
4.4.Dimethyl. 1 . d kene . . . . . . . . . . . . . 2,3-Dimethyl.2.alkene . . . . . . . . . . . . . 2,4.Dimethyl. 2.alkene 2,&Dimethyl-%alkene . . . . . . . . . . . . . 2,6-Dimethyl.2.alkene . 1 ,%Alkadiene .....................
-435.41 -422.11 . 432 -429.66 -427.86 -407.75 -424.89
0.60 0.50 1 .0 0.33
-19.10 -5.80 . 16 -13.35 -11.55
1.28 1.7
+8.M -8.54
clc--(C).--Clc. . . . . . . . . . . . . . . .
0.0 -8.20
0.70
0.20 1.30 0.42 1.00 1.10
-14.80 -15.33 -14.09 -15.49 -21.40 -12.45 -20.25 -20.15
0.40
Alkyne 1-Alkyne..........................
I
-413.81 743
I
1.7
1
4-2.60
744
'
GUSTAV EGLOFF, J. SHERMAN, AND R . B . DULL
at least one removed from the double bond, the boiling point of the olefin is less than that of the corresponding paraffin. For example, the 3-methyl1-alkenes boil 8.2' lower than the 3-methylalkanes, and the 4-methyl-lalkenes boil about 3.8' lover than the corresponding alkanes. I n the 2 ,a-dimethyl-a-alkene series, where both side chains are attached to the carbon atoms forming the double bond, the boiling point is 3.8' higher than that of the corresponding alkane, whereas in the 2,3-dimethyl1-alkenes, where one of the side chains is attached to a carbon atom one removed from the double bond, the boiling point is 5.2" lower than that of the corresponding paraffin. When the double bond is in the 1-position and a methyl group is attached to a double-bonded carbon atom, i.e., in the 2-position, the boiling point is independent of the position of the other methyl group except when that group is in the 3-position, and is the same as that of the corresponding dimethylalkane. Thus, isomers of the n,n'dimethylalkane series (n 1 # n' and n' = 2) and of the 2,n'-dimethyl-1alkene series have the same boiling points within experimental error. I n the case of the 3 ,n'-dimethyl-1-alkene group (n' > 3) the boiling point is independent of n' and all isomers boil at the same temperature, except members of the 3,4-dimethyl-l-alkene series. This exception is identical with that for the dimethylalkane series. The above rule does not apply to the dimethyl-m-alkene series with m > 1. The effect of two adjacent double bonds in the molecule is shown by the boiling points of the 1,2-alkadienes being 8.6' higher than for the normal alkanes, and furthermore in table 31. In this table i t may be noted that the difference between observed and calculated boiling points is large in the case of 1,2-propadiene and gradually decreases as the distance between double bonds increases. For 1,5-hexadiene and higher members of the series the difference is negligible. The large deviation between the observed and the calculated boiling points of 1,g-decadiene is probably due to experimental error. The presence of a triple bond in the terminal position raises the boiling point relative to the normal alkanes about 2.5'. The boiling point can be correlated with other physical properties, such as the molal volume and the mole refraction. Studies along this line are being made and will be reported at a later date.
+
SUMMARY
The boiling points of thirty-one homologous series of aliphatic hydrocarbons have been correlated by means of the equation T = a log ( n b) k
+ +
the mean deviation between calculated and observed values being only 0.7' for the one hundred forty-three hydrocarbons considered.
LIGHT SCATTERING IN DENTINE
7-16
I n this equation k varies from series to series while a and b remain constant. The constants a and b were evaluated from the data of normal alkanes, the values being 745.42 and 4.4, respectively. The values for k were calculated for each series and the results reported. Generalizations are given concerning the effect of the structures of the hydrocarbons of the different series on their boiling points. REFERENCES (1) BOWIO-LERA, E . : Gam. chim. ital. 29, I, 441 (1899). (2) BURNOP, V. C. E.: J. Chem. SOC.1938,826. (3) EGLOFF,G . : The Physical Constants of Hydrocarbons. Volume 1 . Parafins, Olefins, and Acetylenes. Reinhold Publishing Corporation, Xeiv York (1939).
(4) KINNEY, C. R.: J. Am. Chem. SOC.80, 3032 (1938). (5) KOPP,H.: Ann. 41, 79, 86, 169 (1842). (6) PLUMMER, H. C . : Phil. Mag. [6] 32, 371 (1916). (7) WAKEMAN, R. L.: Rec. trav. chim. 63, 832 (1934). (8) WALKER, J . : J. Chem. SOC.66, 193 (1894). (9) YOUNG,S.: Phil. Mag. 9, 1 (1905).
LIGHT SCATTERING I N NORMAL HUMAN DENTINE'
THECALCULATION OF ABSORPTION AND SCATTERING CONSTANTS RICHARD S. MANLY,' JOHN F. BONNER,
AND
HAROLD C. HODGE
Department of Biochemistry and Pharmacology, School of Medicine and Dentistry, University of Rochester, Rochester, New York Received June 90, 19N INTRODUCTION
I n the transmission of light by opal glass and gelatin suspensions, the relatively coarse particles cause considerable light scattering in comparison with the absorption. Bloch and Renwick (1) found that the data are described empirically by an equation of the form 1
log 2 = atb
I
where IO and I represent the intensities of the original and transmitted beam, respectively, a is the absorption coefficient, t is the thickness in This work was supported in part by a grant from the Carnegie Foundation of Xew York. * Present address: Chemical Division, Procter and Gamble Company, Ivorydale, Ohio.
