June, 1941
INDUSTRIAL AND ENGINEERING CHEMISTRY
(66) Radlberger, Oesterr.-ungar. 2. Zuckerind. Landw., 42, 236-9 (1915). (67) Rathke, Ber., 23, 1675 (1890). (68) Rathsburg, Zbid., 54,3183 (1921). (69) Ripper, U. 6.Patent 2,056,142(Sept. 29, 1936). (70) Robinson and Robinson, J . Chem. SOC.,123, 532 (1923). (70A) Rochow, Stafford, Davis, and Miller, IND. ENG. CHEIM.,32, 1187 (1940). (71) Ryan, U. 8.Patent 2,211,912(Aug.20,1940). (72) Sanderson, Paint, Oil, Chem. Em.,102, No. 8, 7-9 (1940). (73) Ibid., 102,No. 12, 12 (1940). 23, 1124 (74) . . Smith, Sabetta, and Steinbach, IND.ENO. CHEIM., (1931). (75) Smoika and Friedreich, Monatsh., 10,86 (1889).
779
(76) Ibid., 11, 179-220 (1890). (77) St&ger, Sohweiz. Arch. angew. Wias. Tech., 5, No. 8, 221-6 11939). (78) St& and Erauch, Ber.,46,2337 (1913). (79) Sward, Natl. Paint, Varnish Lacquer Assoc., Sci. Sect., Circ. . . 510 (1936). Volhard, J . p u k t . Chem., [2]9,29 (1874). Widmer and Fisch, U. 8. Patent 2,170,491(Aug 22, 1939). Ibid., 2,197,357(April 16, 1940). Widmer. Fisch, and Jakl. Ibid., 2,161,940(June 13, 1,939). Wienhaus and Ziehl. Ber..65. 1461 (1932). . . Zirnmermann, Zbid.,’7, 289 (1874).
.
P R E S ~ N before T ~ D t h e Dividon of Paint and Varnish Chemistry a t the 100th Meeting of the American Chemiosl Society, Detroit, Mioh.
Molecular Volume of Saturated
Hvdrocarbons Recently Aranda (2,3) and S. S. KURTZ, JR., AND M. R. LIPKIN TUDIES of the composiKomshilov (22, 28) have pubtion of the high-moSun Oil Company, Marcus Hook, Penna. lished linear equations for the lecular-weight fractions of paraffin homologous series. petroleum (17,31, 88, 41, 4.2, Calingaert (6) and Huggins The molecular volume of saturated hydro@, 64) make it clear that, in (20) independently developed spite of the extensive work of carbons can be calculated with considerable more precise equations which Mikeska (33), still more data accuracy, using the equation: involve a third term, both for are needed for pure compounds V = 16.28 ni 4-13.15 n2 4-9.7 n3 31.2 normal paraffins and certain of Qf high molecular weight, esthe isomers. pecially compounds containing This equation is used to calculate graphs of The present work continues several rings and side chains. density vs. molecular weight for paraffins the study of molecular volume Molecular volume has long of high-molecular-weight comand various classes of naphthenes. There been known as an approxipounds, taking into consideramately additive property (2, is a large difference in density between tion rings containing from 3 to 8, 9, 28-86,29,37,61) ; therenaphthenes of equal molecular weight and 8 carbon atoms of both the confore it seemed possible that equal number of rings per molecule, dedensed and noncondensed information concerning the pending on the number of carbon atoms in types. density of high-molecularBy “condensed” naphthenes weight compounds could be the ring. It is suggested that this differwe mean compounds having obtained if a sufficiently relience can be used to determine the average structure analogous to decaable system of calculating number of carbon atoms per ring. hvdronavhthalene-i. e.. commolecular volumes of such A means of calculating the degree of pounds i n which no carbon compounds could be decyclization in hydrocyclorubber and reatom forms part of more than veloped. two ring structures. Few data The early work on molecular lated compounds is also proposed. are available on naphthenes volume by Kopp (24, 26) and in which one or more carbon L e Bas (29), which was reatoms are common to three-ring structures, and there is little -viewed by Cohen (9),was complicated by the fact that they evidence (27,41, 4.2) that such compounds exist in petroleum. .compared molecular volumes a t the boiling point rather than Therefore, we feel justified in omitting, for the present a t least, .at a oonstant temperature. In spite of this difficulty Le Bas consideration of naphthenes of this more highly condensed (29,page 7 and Chapter 11) recognized the fact that moilecular volume is well adapted to the study of ring structure. type. Richards (87)was interested in molecular volumes but was Molecular Volume of CH2 Group in Paraffins and ’harnnered by a lack of reliable data. Davis and McAllister in Side Chains of Naphthenic Compounds (11) published a chart (similar to our Figure 1) showing a Graphs of molecular volume 8s. number of carbon atoms linear relation between molecular volume and molecular were prepared for paraffins and naphthenes with five and six .weight for paraffins and mono-, di-, and tricyclic naphthenes carbon atoms in the rings. The data used were mainly those in whi& the rings were of the six-carbon (cyclohexane) type. of Ward and Kurtz (60). Where necessary, these were supEach ring structure has its characteristic line on the chart. plemented by data of Mikeska @), Kreulen (26),Eaton ( l a ) , This chart did not, however, take into consideration the fact and Egloff (14). The graph for paraffins and the cyclothat ring structures containing more or less than six carbon hexane, decahydronaphthalene, and higher carbon ring naphatoms Rer ring might be present. The Davis and McAllister thenes is shown in Figure 1. The corresponding graph for ,chart has never been widely used even though it is fairly the five-carbon ring naphthenes is similar except that the accurs,te CerS).
S
+
INDUSTRIAL AND ENGINEERING CHEMISTRY
780
Since the rate of change of the CH; increment above 9 carbon atoms is small, according to the equations of both Calingaert and Huggins, considerable simplicity of treatment in considering the whole field of paraffins and naphthenes can be obtained by assuming as a first approximation that CH; is a constant above 9 carbon atoms, and then introducing a correction factor to take care of the difference between the average CH; obtained in this way and the values predicted by the equations of Calingaert and of Huggins. For example, in the case of average paraffins in the range 9 to 20 carbon atoms the following simple equation is quite accurate:
620 600 -
580 560540 -
520500 -
480460 440-
k
Vol. 33, No. 6
420-
mol. vol. (20’ C.) of av. paraffins = 16.28 n
+ 31.2 = V (1)
j 400-
s 380’ 360_I
0
5
340-
2
320-
$
300-
280
-
260 240
-
220 -
PARAFFINS AND CYCLOHEXANES
{//I:
200 -
Neither Calingaert nor Huggins developed an equation for average paraffins. However, since the average difference in molecular volume between normal paraffins and the corresponding group of isomers is 1.38 cc., we have modified the Calingaert and the Huggins normal paraffin equations to obtain corresponding equations for the average paraffins. This was done simply by subtracting the 1.38-cc. increment from the molecular volume constant in each equation, respectively. Equation 1A is the Calingaert type and Equation 1R the Huggins type for average paraffins obtained in this way: V = 29.012 V = 28.58
PARAFFINS .KURT2 AND WAR0 MKREULEN
180-
160-
CYCLOHEXANES o MONOCYCLIC A DICYCLIC
140 -
b ,b
li
14
20 2‘2 24 26 28 d0 32 34 36 38 I6 NUMBER CARSON ATOMS
+ n f 74.44/n2 + 16.375 16.49 n + 29.0 /n
Kj
The degree of approximation involved in using Equation 1 is shown in Table I, which gives corrections to the molecular volume increment 16.28 cc. per CHf, based on the difference between Equation 1and Equations 1A and lB, respectively.
FIGURE 1. LINEARRELATION BETWEEN MOLECULAR VOLUME AND
NUMBER OF CARBON ATOMS
lines are closer together. The slope of the lines in all these graphs is the same; therefore, there is a n essentially uniform increment of volume associated with the addition of each -CHZgroup to the paraffin, or the side chain of the naphthene. (By CH: we mean the average CH2 group, irrespective of branching. To avoid possible confusion, the alpha will indicate throughout this paper that CH; is used in the sense of an average. Fuithermore, the prefix “chain” or “ring” will be used to indicate the type of structure under discussion.) Considerable evidence is available to show that molecular volume and other physical property increments associated with the CH; groups are far from uniform for the lower members of the normal paraffin homologous series. For example, Rossini (39, 40) showed that only above 5 carbon atoms are the heat of combustion and heat of formation increments associated with the CHI: group constant. I n the case of molecular volume data Calingaert (6) and Huggins (20) showed independently that the volume increment associated with the addition of each CH; is not constant until far up the homologous series. The fact that the thermal increment, as established by Rossini, becomes oonstant above 5 carbon atoms, whereas the volume increments do ‘notbecome constant until much further up the homologous series, is related to the fact that the percentage deviation of the molecular volume from a linear equation is approximately forty-five times as great as the percentage deviation of the thermal data from a linear equation. This statement is based on data for propane and butane for which good thermal data and molecular volume data are available (8, 10, 16, 19, $319
W43,&Ct)~
TABLE I. CORRECTIONS TO AVERAGE CH; VALUEOF 16.28 Cc./ GRAMMOLET O PI’IAKE EQUATION1 AGREEWITH EQUATIONS OF THE CALINGAERT AVD HUGGINS TYPES
6 6
7 8 10 15 20 25 30 35 40 50 70
100 Limiting value 0
1-0.264 1-0.075 0.000 -0.032 -0.049
-0.029 -0,005
f0.246
1-0.078 -0.001
-0.039 -0.062 -0.036
+0.001
+0.012
+0.030 +0.055
+0.041
+0.088
+0.064
10.138 +0.168
+0.024 1-0.034 1-0.053
+0.073 +0.095
+0.073
i-0.109
+O.ZlO
For values between those given, interpqlation is su5ciently acourate.
I n the case of naphthenes the available data indicate t h a t 16.28 cc. per side chain CHZ is & good average value and oan be used without correction.
At both 7 and 20 carbon atoms both Equations 1A and 1B predict an average CHZ increment of 16.28 if the constant term is 31.2 cc. as in Equation 1. The agreement of experimental data for average paraffins with Equations 1, lA, and 1B is shown in Table 11. Data are shown for one hundred three compounds, divided into twelve molecular weight groups, in the range 5-42 carbon atoms, and for seventy compounds divided into eight molecular weight groups, in the range 9-42 carbon atoms. The average deviation for the former groups is 0.8 cc. per gram mole for lineal Equation 1, whereas with equations in the Huggins and Calingaert form the average deviation is 0.6 cc.
INDUSTRIAL AND ENGINEERING CHEMISTRY
lune, 1941
781
per gram mole. The advantage of the equation representing a curved line is not so great in the case of the average paraffin data as in the case of the normal paraffin data.
The equation of Komshilov 23) was developed for average paraffins. When checked against the same data used for the other equations, it shows an average deviation of 1.5 cc. However, above 20 carbon atoms the equation shows a definite and increasing trend to give low molecular volumes. We recommend the simple linear Equation 1 for average TABLE 11. COMPARISON OF MOLECULAR VOLUMES OF AVERAGE PARAFFINS CALCULATED BY LINEAREQUATION 1 AND EQUATIONS p,araffins of any molecular weight, and either the Calingaert or Huggins equations for normal paraffins and homologous 1A AND 1B series of particular isomers such as 2-methyl, 3-methyl, etc., Molecular Volume, Cc. Mol. Wt. No. of Equation Equation Equation up to 20 carbon atoms. 1 1A 1B Range Group6 Although CI-CLP 12'3 0.8 0.6 0.6 Av. deviation (regardTraube's molecuCo-Ce 8" 0.7 0.6 0.6 lesa of sign) 1 4 0 7 lar solution 12 0.0 -0.2 -0.2 CrCe Deviation of av. (con8 +0.2 0.0 0.0 crcu sidering sign) volume for paraf1301 Each group weighted accordin to number of compounda. The 12 611s (9, 48) was groups represent 103 compounds an$ the 8 groups represent 70 compounds. t~ 120 published forty years ago, it ti 110: i agrees well with 0 5 100modern d a t a . The results in Table I1 indicate that the average increment 90Traube reported of 16.28 cc. per CH; group may be used without serious error 3 16.1 cc. per gram for average paraffins. 80mole as the soluSince we are particularly interested in having a system of 0 = 70tion volume of calculations which can be used in the higher molecular weight CH2 a t 0' C., range, there is still another angle to be considered. The 60which compares question may be raised that high-molecular-weight paraffins well w i t h o u r may contain many multiples of a branched-chain unit such value of 16.28 cc. and that the statistical treatment as -(CH& 4 H - , 40 per gram mole at I 20"C. Further1 2 3 4 5 6 7 8 CHa more, Traube's NUMBER OF C ATOMS IN RINQS of the data thus far used may conceal the effect of repeated "molecular cointroduction of side chains. Therefore, we have compared FIGURE 2. LINEAR RELATION BETWEES for no'1the molecular volume increments between compounds of 10, MOLECCLAR VOLCJIEOF RINGS AND aqueous solut ions XCJNBER OF CARBOX ATOMSIN RISQS 20, 30, and 40 carbon atoms for the normal paraffins, and for is approximately a group of compounds in which the added groups are multiples 25 cc., which is of -CH-(CH&-. These data show (Table 111) that as our residual volume a t least of the same order of magnitude I of 3 1 . 2 ~ ~ . CHa the volume of the average CH2 group calculated for the branch-chain compounds is only slightly less than for the Molecular Volume of CH; in Rings normal compounds. The limiting value is certainly not over The average CH: increment (16.28 cc.) used in Equation 16.50 cc. per CHI in either case, Hydrogenated rubber gives 1 was originally derived using data for alkyl derivatives of a value of 16.39. cyclopropane, cyclobutane, cyclopentane, cyclohexane, and More data are needed in this field. At present it is safe to decahydronaphthalene as well as data for paraffins. To obsay that the true value for the average CHs group in hightain information concerning the nature of the ring portion of molecular-weight branched paraffins is close to 16.28 cc. and the molecule in naphthenes with alkyl side chains, the mocertainly not greater than 16.50 cc. lecular volume of the side chain (16.28 X the number of sideThe linear equation of Aranda (B, S), in which molecular chain carbon atoms) was subtracted from the molecular volvolume is calculated from molecular weight, shows a n averume of the naphthene as a whole. These data are shown in age deviation of about 1.5 cc. (generally plus) when tested column 4 of Table IV. The constancy of the effective ring with the same data used in testing Equations 1, lA, and 1B. volume, even when side chains as long as 22 carbon atoms are subtracted. amin indicates that 16.28 is a good average Tncrement for TABLE111. COMPARISON OF CHz INCREMENTSFOR NORMAL the CH: group. This is shown particularly by AND BRANCHED-CHAIN COMPOUNDS WHICHARI ESSENTIALLY the data for cyclohexane derivatives. OF SIMPLE GROUPS MULTIPLES When the molecular volumes of the rings are plotted against the number of carbon atoms in % :spending :& :: Increment of vO1' per $ : NO. the ring, one can draw a good straight line CitaMol. N-ParafC Condensed Formulaa di0 tion Vol. finb Branched mal through these points and a point correspondAtoms CHsRiCHa 0,7247 (14 196.3 194.8 ing to 31.2 cc. for zero carbon atoms per ring 10 0.7887 (141 368.2 358.1 ii:ig ii:i3 20 CHsRaRiRaCHa 522.1 523.0 16.39 16.45 (Figure 2). The slope of this line is 13.15 cc. CHsRzRaRiRzRzCHs 0.8098 30 40 CHsRzRaRaRiRzRzRzCHs 0.8200 686.7 687.8 16.46 16.48 per ring CH;. Therefore we may write: (Ra)z + Ha (hydrogenated rubber0 0.8558 (46) .. . ... 16.39 . . . vol. of naphthene ring = 13.15 nz 31.2 cc. (2) H
/
0
3 ;
ti$
a
R1 = -CH-(CHP)~-CH-;
Ra
-
-CH-(CHa)y;
Rs
-
+
-CHF-D(CHZ)?-.
AH* dHs dH8 dH8 a carefully developed method of correcting densities of normal hydrocarbons to the hypothetical liquid state at 20° C. and on smpothed curve of the best corrected data. c Structure not definitely known but probably as indicated.
where na
=
number of ring CH; groups
b Based on
The same residual volume applies for naphthene rings as for paraffins.
INDUSTRIAL AND ENGINEERING CHEMISTRY
782
TABLEIV. AVERAGEMOLECULAR VOLUMEDATAFOR NAPHTEENE RINGS Mol. Vol. of Ring5 Residual V01.b Formula Cyolopropanes
Cyolobutanes Cyclopentanes
Cyolohexanes
Cyclohe tane yoloooLne
No. of
Isomers
Data
Monocyclic Compounds 3 71.2 CsHio 72.1 1 CeHis 72.9 1 ClH14 2 70.1 CaHia 1 84.6 CaHia 1 82.8 CsHiz 3 84.7 CioHm 1 93.9 CsHio 1 96.1 CaHiz 4 97.1 CrH14 97.3 7 C8H16 96.2 4 CaHia 96.7 3 CisHzo 1 96.3 CiiHw 1 102.0 C12H24 93.7 1 CiaHz6 1 108.0 C6HlZ 110.9 1 C7H14 8 111.8 CaHis 111.2 14 CoHis 109.2 14 CioHzo 110.1 6 CiiHzz 109.1 1 CizHn 105.2 2 CisHm 108.6 1 CnnHis 109.5 2 CzsHsa 110.5 1 CSZH64 1 121.0 C7H14 133.5 1 CaHi6
Av.
+
84.3 96.8
Uncondensed
n-Monoolefins Monocyclic aromatics
110.1
121.0 133.5
CizHzr
1
161.7
161.7
CioHis CisHza CZSHM CazHai CisHz4 CuHe
3 3 1 2 1 1
156.3 153.1 158.2 156.6 189.5 187.4
156.1
No. of Compounds
..
Satd. Compound Mol. Vol. 176.5
Unsatd. Compound 1Llol. Vol. 170.3
A Vol. per Hz 6.2
Av. Deviation 0.6
Max. Deviation 1.0
12
152.5
131.9
6.8
0.4
1.0
TABLE VI. CALCULATIOX OF MOLECULAR VOLUMEOF CH" AT RINGJUNCTIONS FROM DATA FOR DECAHYDRONAPHTHALENE AND DERIVATIVES
Compound trans Decahydronaphthalene Mixed decahydronaphthalenes cis Decahydronaphthalene Tetrahydroselinene Tetrahydrocadinene Tetrahydroeudeamene CioHii-CisH3i CioHir-CzzH4a CioHir-(C4Ho) (CiaHse) Av. mol. vol. C H a at ring junctions
-
Dicyclic Compounds Cyclopentanes (uncondensed) Cyclohexanes Condensed
TABLEV. MOLECULAR VOLUMEINCREMENT FOR HYDROGENATION OF DOUBLE BONDS
Reference
71.2
Vol. 33, No. 6
-
Mol. Vol. of Each Ring Junction C+CH" Group tion
No. C Atoms
Mol. Vol.
10
159.0
11.3
50
10
155.5
9.6
50
.. ..
10 15 15 15 28 32 32
154.3 234.4 235.8 234.3 451.2 513.2 516.5
9.0 8.3 9.0 8.3 10.9 9.3 11.0
50 12 12 12 33 33 33
E-'603 E-602 E-599 M-37 M-38 M-39
Code No.
9.63 cc.
TABLEVII. CALCULATION OF CH" AT RINGJUXCTIONS FROM DATAFOR AROhT.4TICS A N D O L E F I N S , U S I N G INCREMENTB" FOR HYDROGEN TO CONVERT TO MOLECULAR VOLUMEOF SATURATED COMPOUND Mol. Vol. Mol. Vol. Code of Correof Eaoh No. sponding Ring from Satd. Junction Eaton Compound C0mpd.a CHo: Group (18) 12 1 4-Dimethylnaphthalene 187.6 9.3 E-456 12 189.6 1:6-Dimethylnaphthalene 10.3 E-458 12 188.7 2,3-Dimethylna~hthaiene 9.9 E-461 13 205.6 9.9 Irene E-488 221.1 14 E-517 Apocadalene 9.8 236.4 E-544 15 9.3 Cadalene 235.3 E-570 Cadinene 15 8.8 235.3 E-572 a-Selinene 15 8.8 236.7 E-573 p-Selinene 15 9.5 15 237.4 E-593 Dihydrocadinene 9.8 291.3 E-680 12.4 1,4-Diisobutylnaphthalene 18 Average 9 . 8 a 3.4 cc. added for each H required t o hydrogenate aromatic unsaturation 3 . 1 cc. added for each H required t o hydrogenate olefin unsaturation.
No. C Atoms
188.5
0 Calculated on basis of subtracting molecular volume of side chain from whole molecular volume, using 16.28 cc. for each CHPin side chain. 1, Residual volume for paraffins and naphthenes = 31.2 CC.
Molecular Volume of CH" at Junction of Condensed Rings I n order to calculate the molecular volume of condensed dicyclic rings, it was found necessary t o derive a value for the CH" group a t ring junctions. (By "CH" group a t ring junctions" we mean only the CH groups common to two condensed rings, as in decahydronaphthalene.) For example, a mixture of the isomers of decahydronaphthalene has a molecular volume of 155.5 cc. per gram mole and contains eight ring CHY groups whose volume totals 105.2 cc. per gram mole. Subtracting 105.2 and the residual volume, 31.2 cc., leaves 19.1 cc. for the two CH" groups a t the ring junction, or 9.55 cc. each per gram mole as compared with 13.15 cc. each for the other ring CH: groups. Since there was a limited amount of data on decahydronaphthalene derivatives from which an average value for CH a t ring junctions could be derived, it was desirable to use some of the data available on unsaturated compounds corresponding to decahydronaphthalene derivatives. To do this it was necessary to derive molecular volume increments for the hydrogenation of olefin and aromatic double bonds (61). As Table V shows, it was possible to obtain good average increments of this sort, the value for normal olefins being 6.2 cc. and for monocyclic aromatics, 6.8 cc. per gram mole of hydrogen added to the double bond. Six dicyclic aromatics gave an average increment of 6.3 cc. per gram mole of Hz, but the density difference from which these increments are calculated is only about half as large as in the case of the monocyclic aromatics. Until more data
are available, we recommend that the increment 6.8 cc. per gram mole Hz be added to the aromatic double bond for either mono- or dicyclic aromatics. From the naphthene data in Table VI and the corrected data in Table VI1 i t was possible to obtain a good average value for CH" a t ring junctions. This was done as pre\eously illustrated by subtracting the residual volume, the volume of the chain CHf groups, and the volume of the eight ring CH; groups. This gave an average volume of 9.7 cc. per gram mole for each of the two ring junction CH" groups. The volume of CHY in rings and CH" in rings, if subtracted, gives a volume of 3.45 cc. per gram atom for the apparent atomic volume of hydrogen in ring compounds. This is almost equal to the values 3.4 cc. per gram atom of hydrogen for hydrogenation of aromatic rings and 3.1 cc. for hydrogenation of an olefin.
General Equation for Molecular Volume of Saturated Hydrocarbons The informatfon now available makes it possible to write the following equation for the molecular volume of saturated hydrocarbons : mol. vol. (20' C.) = 16.28 nl f 13.15 % 4-9.7 na 31.2 (3)
+
INDUSTRIAL AND ENGINEERING CHEMISTRY
June, 1941
783
molecular volume of the ninety-eight compounds is 398.4 cc., and the average volume calculated from the formula is 397.1. The small difference (+1.3 cc.) shows that the system of calculating must be essentially correct. Average deviation of the The agreement of density data with curves calculated from ninety-eight individual compounds is 4.4 cc. or about 1 per this equation is shown in Figure 3. It is clearly shown that cent. Omitting the ten compounds showing the widest dethe lower members of any homologous series deviate from viation reduces the average deviation to 3.1 cc. the curves. Also, i t is shown that densities for the higher It is particularly gratifying that the agreement obtained members of the series as calculated are usually correct within for groups IIa, IIb, 111, and IV (Table IX) for condensed *0.005 or about *0.6 per cent on the density. The deviaand noncondensed dicyclic naphthenes is as good as i t is. tions are not systematic which indicates that systematic The precision of this tabulation is not sufficient to serve as a error is not likely to be introduced in extrapolating to higher check on the value used for the CH" a t ring junctions, but it molecular weight. The dotted line in Figure 3 corresponds does give assurance that average curves based on the general to the Calingaert type equation for the average paraffins. equation will not be seriously in error. The few data included Tables 11,VIII, and IX show the degree of agreement on a for tricyclic compounds tend to conilrm the dicyclic data. molecular volume basis of Equation 3 with available data I n connection with the question of condensed against nonfor paraffins, monocyclic naphthenes, and naphthenes of condensed dicyclics, it is worth while to point out that our large molecular volume of the mono-, di-, and tricyclic classes. equation predicts almost identical molecular volumes for condensed or noncondensed dicyclics having the same number of carbon atoms. If, for example, one compares dicyclohexyl TABLBI VIII. COMPARISON OF CALCULATED AND EXPERIMENTAL with ethyl decahydronaphthalene, the calculated molecular MOLECULAR VOLUMES BOR MONO-AND DICYCLIC NAPHTHENES volumes are 189.0 and 188.4 cc., respectively. This is true Mol. . _.Wt. . because the side-chain CH: groups occupy 3.13 cc. each Groupsvi^N~ tion of Max. Deviamore than the ring CH: groups, but CH" at ring junction ocA ~for . tion of Any of ' cupies 3.45 cc. less than a ring CH: group.. I n other words, G ~ Isomer, ~ ~Co. ~ , cornRange pounds Cc. Plus Minus Citations in changing from an uncondensed dicychc to a condensed Monocyclic Naphthenes dicyclic of the same molecular weight, an equal number of Cyclo ropaneri CrCi 7 +0.9 3.2 0.8 chain CH: groups and ring junction CH" groups are formed, CycloEutanes CK-ClO 5 +0.2 3.2 1.0 Cyclo entsnes Cr-Cis 23 -0.6 5.1 3.3 so that the net effect on molecular volume is practically negliCyolcBexanes CrCn 51 -0.3 4.5 7.6 (IS,3.9,60) gible. where
nl = nt = n8 =
number of chain CH: groups number of ring CH; groups number of ring junction CH" groups
Dicyclic Naphthenes
Cyclopentanes (unoondensed) Cyclohexanes Uncondensed Condensed
CII CrCu Cio-Caz
1
-1.0
2 -0.5 9 -0.3 Average 0.5
... 0.5 3.2 3.8
1.0
(60)
1.5
(33 60) (fa,b.9, 60)
2.9
2.6
Application of Curves for Density 2)s. Molecular Weight in Hydrocarbon Analysis The data presented in Tables VI11 and I X justify the belief that our equation for calculating the molecular volume of naphthenes with or without side chains is essentially correct. Curves for density against molecular weight (Figure 4) were therefore calculated for the paraffins and naphthenes of the cyclopentane and cyclohexane types on the basis of the polycyclics being the condensed type. The curves are a p plicable to polycyclics of the decahydronaphthalene condensed type rings as well as the uncondensed types. It is evident that similar curves can be calculated for cyclopropane, cyclobutane, cycloheptane, and cyclooctane rings.
It is well known (4,6, IS,S4,60)that structural differences produce changes in density and molecular volume, and if desired a quantitative system of correction for structural effects can be worked out (4, 6, 6, IS, 90,60). This paper is concerned only with the deviation in average properties. The maximum deviation, which might be encountered in the case of isomers, is not likely to be more than 4 cc. per gram mole. Table VI11 mesents data for eightv-six monocyclic naphthenes and tweive dicyclic naphthenes." The deviation of group averages is of the order of 1 cc. and only a few show over 4 cc. deviation. Mikeska's average data on four cyclohexane derivatives with long side chains agree within 0.1 per cent with the calculated values, and the worst deviation of any of these fdur compounds is 0.5 per cent. Table I X presents data for ninety-eight naphthenes of large molecular volume, arranged in groups according to the number and type of saturated rings. Mikeska ($3) provides density and molecular weight data X PARAFFIN-KURT2 8 on only eight naphthenes of high molecular + PARAFFIN-KREULEN volume; data on five more completely saturated dicyclic naphthenes (samples 599, 602, 603, 766, 775) were obtained from Eaton's tabulation (12). Data for the other eighty-five compounds were obtained by calculating the molecular volume of aromatic and olefinic hydrocarbons to the corre50 100 150 200 250 300 350 400 450 500 sponding naphthenes, using the factor 6.8 m I G H T cc. per aromatic double bond and 6.2cc. per olefinic double bond (Table V). The average BETWEEN CALCULATED AND EXPERIMENTAL DENSITIES FIGURE 3. AGREEMENT
784
Vol. 33, No. 6
INDUSTRIAL AND ENGINEERING CHEMISTRY
Figure 4 shows that for any particular molecular weight and given number of rings per molecule there is an appreciable density difference depending on the number of carbon atoms in the rings (i. e., cyclopentane or cyclohexane type rings). The density difference for compounds containing an average of two or more rings per molecule is sufficient t o justify using this type of graph to determine the average number of carbon atoms per ring, provided accurate data are available for density, molecular weight, and number of rings per molecule, and provided the sample is completely saturated. This method will be described in full in a subsequent paper. These molecular volume increments should provide a means of calculating on a reasonable basis the percentage cyclization in hydrocarbons over 3000 molecular weight (where the end-effect constant is 1 per cent or less of total molecular volume), provided condensed rings are not present. The density of the compound should be equal to the density of the CHY grqup. The volume of the CHZ group in highmolecular-weight paraffins is certainly between 16.28 and 16.50 cc. Therefore, the density of noncyclic hydrocarbons of high molecular weight is between 14.026/16.28 = 0.861 and 14.026/16.50 = 0.850. Density of cyclic noncondensed hydrocarbons of high molecular weight is 14.026/13.15 = 1.067. The amount of cyclization can be calculated by interpolation between the two extremes on a percentage basis. The residual volume may be neglected because of the size of the molecule. It is of interest to apply this system to hydrocyclorubber for which Staudinger (45) reports a density of 0.992 gram per cc. a t 16" C. which, corrected to 20" C., is approximately 0.984. The hydrocyclorubber density corresponds to the density of a mixture of paraffin chains and uncondensed rings in which 60 to 62 per cent of the CH, groups are in the rings. The molecular weight of this hydrocyclorubber material is not definitely known, but it is probably well over 3000 so that the residual volume is not important. Even though the TABLEIx.
Group NO.
IIb
I11
Iv
Relation of Molecular Volume Data to X-Ray Data I n order to obtain a check on the physical reality of the molecular volume equations for paraffins, a comparison has been made with available data on molecular dimensions. An equation for the length of normal paraffins in the crystalline state, based on the publications of Hengstenberg (I@, of Francis and Piper ( I @ , and Clark (7), may be written as follows: L = 1.27~f ~ 12 . 0
where L = length of molecule in Angstrom units
If we are justified in comparing molecular dimensions of crystalline wax with liquid normal paraffins, division of the volume increment for CH2 by 1.27 will give the effective cross section of the CH2 chain in liquid paraffins. We feel justified in doing this since both the spacing between and the angle between the carbon atoms is essentially the same in the crystalline state and the vapor state for hydrocarbons (56,36) and is probably the same in the liquid state. The volume increment 16.28 cc. [or CHZ on a gram molar basis oorresponds to 28.86 cu. A. per actual CH2 group. Dividing this volume increment pgr CHZby the length increment 1.27 A., we obtain 21.1 sq. A., which is in good agreement with the value 20.6 sq. A. obtained by Adam ( I ) , using the film balance technique of Langmuir (,%). Values of the order of 21.0 to 24.0 sq. A. are obtained for what is called the "liquid" condensed state of the film (58). Washburn and Berry (63)recently checked the cross section of sodium palmitate and obtained 20,s sq. A. cross section by Langmuir's procedure and 22.9 sq. A. from surface tension data. Values of this order
C O V P A R I S O N OF CALCULATED A N D EXPERIMENTAL MOLECULAR V O L U M E S FOR SATUR.$TED CYCLIC OF LARGEMOLECULAR VOLUME"(BASEDON 98 Colupouxns)
Ring Structure Exclusive of Side Chain
I
IIao
values above suggested for the density of the paraffin and the cyclic hydrocarbon are slightly arbitrary, this type of calculation should prove of value in studying cyclization.
03 (3-0
'Z>-.-c>
No. of ComCode No. of pounds pounds Mikeska or Eaton 14 Mikeska 1 to 14
8
Calcd. Av. Mol. VOl. 57-7 5
Deviation of Av. Cc,/dl. (200 C.) +2.0
Av. Deviationb. Cc./Mol. (200 C.) 4.3
332.0
332 9
-0.9
2.1
30
Mikeska 15 to 26 28 29 31 t o 36. Eaton 456, 458, 461, '488: 5i7, 544, 670, 572, ,593, 680
423.7
420 0
t3.7
4.3
15
hIikeska 40 to 46: Eaton 464, 456, 486, 487, 510, 513. 514, 515
369.7
372 4
-2.7
7.4
24
hlikeska 47, 48, 50, 51; Eaton 484, 501, 503, 505, 506, 536 to 539, 541, 636, 637, 638, 642, 648, 652, 765, 766, 772, 775
316.6
316.5
fO. 1
3.1
Eaton 646, 679, 738, 771
337.3
331.5
f5.5
6.1
362.0
+4-0
4
3 Mikeska 49; Eaton 581. 704 366.0 Total 9% 398.4 .z Molecular volume of aromatics converted to molecular volume of naphthenes by adding 6.5 cc. per double bond. b Sum of deviation irres ective of sign divided by number of compounds. c Composed of codpoun& with saturaied rings only; therefore, no aromatic ring oorrection is involved. VI
Tricyclic, nonoondensed
Exptl. Av .Mol. Vol. (20" C.) 579.5
602,603
where R = CHa or other chain structure V
Mikeska 37, 3.3,39; Eaton 573, 594, 599,
HYDROCARBONS
m
f1.3
4.4
INDUSTRIAL AND ENGINEERING CHEMISTRY
June, 1941 1.04
785
needed for average Daraffins or for the side chains of naph1.00 thenes. 0.98 5. There is an appreciable differ0.94 ence in density be------ ---_______ tween naphthenes ------_______ -----____ -----____ ---------_-___________of the same molecular weight and number of rings per molecule, depending ____----on whether the rings are of the 5 carbon 0.8 or 6 carbon types. 6. The number PARAFFINS a CYCLOHEXANE TYPE RINGSof carbon atoms in 0.76 CYCLOPENTANE TYPE RINGS ----naphthene rings can 0.74 be calculated if the 0.72 density, molecular 0.70 1 1 1 1 , , , , 1 , 1 , 1 0 1 I I I , , , , I , , , , weight, and number 00 140 180 220 260 300 340 380 420 460 500 540 580 820 660 700 of rings per molecule MOLECULAR WEIGHT are accurately FIGURE4. DENSITY os. MOLECULAR WEIGHTFOR PARAFFINS AND NAPHTHENES OF CYCLOPENTANE known. AND CYCLOHEXANE TYPES 7. The cross section of the normal CH2 chain is 21.1 sq. of magnitude have also been deduced from x-ray data by A., and this value is in good agreement with data on moWarren (62)and Stewart (46,47). lecular dimensions calculated from other physical measurements. The value 21.1 sq. A. for the cross section of the normal CH2 chain obtained from our molecular volume data, there8. I n order that the density of naphthenes could be calfore, is in substantial agreement with the available data obculated from data for the corresponding olefins or aromatics, tained by other methods. the volume change on hydrogenation was obtained. Hydrogenation of an olefinic double bond increases molecular volAccording to Francis and Piper, the effective cross section ume 6.2 cc. on the average. Hydrogenation of a n aromatic of a normal paraffin chain in the crystalline state is 18.5 sq. double bond increases the molecular volume 6.8 cc. on the i., indicating a decrease in effective cross section on going average. from the liquid to crystalline state of 2.6 sq. A. and a decrease in volume of 3.15 cu. A. per CHs group. This contraction, 9. The percentage of uncondensed ring CH2 groups can according to this point of view, is due to a decrease in the efbe calculated in hydrocarbons of over 3000 molecular weight fective lateral spacing of the chains during crystallization. from the density. By this method Staudinger’s hydrocyclorubber contains 60-62 ring CH2 groups and 38-40 per cent chain CH2 groups. 1.02
TG
\&RING
1
Summary
1. The molecular volume of average saturated hydrocarbons can be calculated by the following equation:
+
+
+
V = 16.29 n1 13.15 nz 9.7 n8 31.2 where V molecular volume, cc./gram mole at 20’ C. n1 = number of chain carbon atoms n2 = number of ring carbon atoms nii = number of ring junction carbon atoms 31.2 = residual volume constant 2, Molecular volumes calculated by this equation are usually accurate within 1 cc. per gram mole for mixtures of isomers. Individual compounds of the simpler structural types seldom deviate by more than 4 cc. per gram mole. The data for dicyclic naphthenes show an average deviation of about 3 cc. per gram mole, which for these compounds is 1per cent. 3. I n terms of density the accuracy is usually within =t0.005 except for the first few members of any homologous series. The deviations are not, however, systematic. 4. I n the case of normal paraffins, the volume increment for the CH: group has been shown independently by Calingaert and by Huggins not to become constant until high molecular weights are reached. A table of corrections to apply to the 16.28 cc. term for paraffins has been given. All the available evidence indicates that these corrections are not
Acknowledgment The authors wish to acknowledge the assistance of J. A. Davison and I. W. Mills in connection with the preparation of these data for publication. They also wish to acknowledge the helpful oorrespondence received from M. L. Huggins and George Calingaert.
Literature Cited Adam, N. K., Proc. Roy. SOC.(London), 101,452 (1922). Aranda, V. G., Anales soc. @pan. fia, qufm., 34,513 (1936). Ibid., [5]35,46 (19401). Boord, C. E., “Science of Petroleum”, Vol. 11,p. 1349, London, Oxford Univ. Press, 1938. Calingaert, George, IND. ENQ.CHEM.,33, 103 (1941). Calingaert, George, and Hladsky, J. W., J. Am. C h m . SOC.,58, 163 (1936). Clark, G. L., and Smith, H. A., IND. ENQ.CHEM.,23,697(1931). Coffin, C.C.,and Maass, O., J. Am. Chem. SOC.,50,1427 (1928). Cohen, J. B., “Organio Chemistry”, Vol. 2, pp. 3-17, New York, Longmans, Green and Co., 1918. Dana, L. I., Jenkins, A. C., Burdick, J. N., and Timm, R. C., Refrig. Eng., 12,387 (1926). Davis, G. H. B., and McAllister, E. N., IND. ENQ. CHEM.,22, 1326 (1930). Eaton, G. L.,“Science of Petroleum”, Vol. 11, p. 1302 (1938). Edgar, Graham, and Calingaert, George, J. Am. Chem. SOC.,51, 1640 (1929).
INDUSTRIAL AND ENGINEERING CHEMISTRY
786
Egloff, Gustav, “Physical Constants of Hydrocarbons”, Vol. I, New York, Reinhold Pub. Corp., 1939. Francis, F., snd Piper, S. H., “Science of Petroleum”, Vol. 11,p. 1203 (1938). Grosse, A. V., data in Egloff’s book (14). Grosse, A. V., Refiner Natural Gasoline Mfr., 18, 149 (1939). Hengstenberg, J., 2.Krist., 67,583-94 (1928). Huckel, W., Kraemer, A., and Thiele, E., J . prakt. Chem., 142, 207 (1935). Huggins. M., J . Am. Chem. SOC.,63, 116 (1941). Kay, W. B.,IND. ENQ.CHEM.,32,358 (1940). Komshilov, N. F.,J . Gen. Chem. U. S. S . R., 9,701(1939). Ibid.. 10. 945 (1940). Kopp, H.,Ann., 72; 1, 223 (1847). Ibid., 96,153,257 (1855). Kreulen, D.W., J . Inst. Petroleum Tech., 24, 554 (1938). Landa, S.,and Mach&Eek,V., Collection Czechoslov. Chem. Communications, 5, 1 (1933). Langmuir, Irving, J . Am. Chem. SOC.,39,1848 (1917). L e Bas. G.. “Molecular Volumes of Liquid Chemical Compounds”, New York, Longmans, Green & Co., 1915. Maass, O., and Wright, C. H., J , Am. Chem. Soc., 43, 1098 (1921). Mair, B. J., Willingham, C. B., and Streiff, A. J., J . RMearch Natl. BUT.Standards, 21,565 (1938). Ibid., 21,581 (1938). Mikeska, L. A., IND. ENQ.CHEM.,28,970 (1936). Morgan, G. T.,Carter, S. R., and Duck, A. E., J . Chem. SOC., 127, 1255 (1925). Pauling, Linus, “Nature of the Chemical Bond”, p. 151,Ithaca, N. Y.,Cornel1 Univ. Press, 1939.
GOLDMACHER NARR. .
(36) Pituling, Linus, and Brockway, L. O., J . Am. Chem. SOC.,59,1223 (1937). (37) Richards, T.W., Proc. Am. Acad. Arts Sci., 39,597 (1904). (38) Rideal, E. K., “Introduction to Surface Chemistry”, Chap. 111, London, Cambridge, Univ. Press, 1930. (39) Rossini, F. D.,IND. ENG.CHEM.,29,1424 (1937). (40) Rossini, F.D.,J . Research NaU. BUT.Standards, 13,21 (1934). (41) Rossini, F.D.,Proc. Am. Petroleum Inst., 111, 18,36 (1937). (42) Ibid., III,19,99(1938). (43) Sage, B. H.,Schaafsma, J. G., and Lacey, W. N., IND.ENQ. CHEM.,26,1218 (1934). (44) Sage, B. H.,Webster, D. C., and Lacey, W. N., Ibid., 29, 1188 (1937). (45) Staudinger, H., “Die hockmolekularen organisohen Verbindungen”, p. 392,Berlin, Julius Springer, 1932. (46) Stewart, G.W., Phys. Rev., 33,889-99 (1929). (47) Stewart. G.W.. Rev. Modern Phvsics. 2. 116 (1930). (48j Traube,‘I., Ahrens Vortrage, 4,255 (189’9). (49) Vlugter, J. C., Waterman, H. I., and Westen, H. A. van, J . Inst. PetroZeum Tech., 21,661 (1935). (50) Ward, A. L., and Kurts, S. S., IND. ENQ.CHEM.,Anal. Ed., 10, 559 (1938). (51) Ward, A. L., Kurts, 8. S., and Fulweiler, F. W., “Science of Petroleum”, Vol. 11, p. 1172 (1938). (52) Warren, B. E.,Phys. Rev., 44,969 (1933). (53) Washburn, E. R., and Berry, G. W., J . Am. Chem. SOC.,57, 974 (1935). (54) Waterman, H.I., and Leendertse, J. J., J.Inst. Petroleum Tech., 25,89 (1939). PRESENTED before the Division of Petroleum Chemistry a t the 98th Meet.
ing of the American Chemical Society, Boston, Mass.
. . . . . . .By Johann Christoph Weigel(16561725)
As announced in April, we bring as No. 126 in the Berolzheimer series of Alchemical and Historical Reproductions the second of Weigel’s engravings of an alchemist. This latter one is called the “GoldMaker Fool”. It is from Weigel’s “Ein Schock Phantast’n in einem Kasten”-Threescore Visionaries in a Chest, published in Niirnberg, Bavaria, about 1690. We extend our thanks to Mr. M. K. Howes of the “Special Collections” Division of the library of Columbia University, through whose good offices this print was obtained. This is No. 23 in the collection of sixty-seven Phantasten (“Nuts”) representing all walks of life. Plate 67 contains a blank rectangle labeled “Gar kein Narr” and intended for the insertion of the likeness of the reader on the assumption that the shoe fits him. There is one change in the poem from that of No. 124; the word “ausprobiert (trying out) has been changed to “ausfiihrt” (executing). D. D. BEROLZHEIMER
East 41st Street New York, N. Y. 50
The lists of reproductions and directions for obtaining copies appear 88 follows: 1 to 96, January, 1939, issue, page 124; 97 to 120. January. 1941, page 114. An additional reprcduotion appears each month.
Vol. 33, No. 6
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