Specific Dispersion of Pure Hvdrocarbons J
R. E. THORPE AND R. G. LARSEN Shell Development Company, Emeryville, Calif.
Specific dispersions for a large number and a wide variety of pure hydrocarbons, obtained from the literature and from additional experimental measurements, have been analyzed with the object of correlating specific dispersion with molecular structure. It has been found possible to calculate the specific dispersion of a hydrocarbon from the number of saturated carbon atoms present and the number of carbon atoms associated with double
R
ECENT activity in the study of hydrocarbons has led t o the need for physical constants which can be used not only as a criterion of purity, but also as an indication of structure. Many physical constants, such as molecular volume, parachor, molecular refraction and dispersion, and magnetic rotation, are related to constitution and might thus fill the need; of these, the property of dispersion is perhaps most closely related t o the fine structure of organic molecules. One of the obvious advantages of dispersion is that it is a differential value and should be independent of errors in absolute units of. calibration, etc. Also for reasonable ranges of temperature it is essentially independent of temperature. By purely empirical means we have found it possible to calculate the specific dispersion of hydrocarbons of widely varying types. Extensive comparisons of the calculated values with experimental results have confirmed the validity of the method.
Calculation of Specific Dispersion from Structure Many early investigators attempted to calculate specific dispersion by the methods used for other molecular properties, particularly for mol,ecular refraction, by a summation of the dispersivity constants for the elements constituting the molecule, due consideration being given to the mode of linkage of each element by changing atomic values, depending upon the type of linkage involved. The agreement between calculated and observed values was poor, however, since constitutional differences in conjugated systems affect the magnitude of the specific dispersion much more intensely than they influence specific refraction. Von Auwers (9) endeavored to evaluate the effect of conjugation on molecular dispersion and introduced a measure of the exaltation of the dispersion in terms of the percentage exaltation over the value calculated for olefinic unsaturation only. He concluded that although, in general, the exaltation depended upon the number of double bonds involved in the conjugated system, the configuration of the molecule was also of great importance. More recently, particularly with the increasing use of
bonds. The presence of conjugation of the sort which is not confined within a single ring invariably produces an exaltation of the specific dispersion. The exaltation effect may be anticipated by a consideration of the various double bond formulas. Since the specific digpersion depends upon molecular configuration, the method of calculation frequently may be used to obtain information concerning structure. specific dispersion as an analytical tool, various investigators have noted the general effect of structure upon the value of the specific dispersion. Thus Ward and Fulweiler (68) state that the number of carbon atoms and the length and character of the chain must all be considered as affecting the dispersion value for substituted aromatics. These authors do not, however, calculate the specific dispersions for individual hydrocarbons. Specific dispersion has been related to the number of double bonds per molecule by Grosse and Wackher (45) and by Deanesly and Carleton (38). The latter authors show that the increase in specific dispersion per double bond depends upon the type of linkage; thus the increase for anthracene compound&is larger than for naphthalene derivatives, and this in turn is larger than for benzene derivatives. The present study examines the general relationships noted above in more detail, with the aim of predicting the values of the specific dispersions for individual hydrocarbons rather than for general groups. The Gladstone-Dale expression for specific dispersion (the difference of the refractive indices for two wave lengths of light divided by the density) has been used throughout. It can be shown that this expression is a simple function of the theoretically deduced Lorenz-Lorentz equation over a wide range of refractive index; moreover, it is more convenieni for practical use. The refractive index is measured on a suitable refractometer a t each of the wave lengths of light corresponding to the hydrogen CY and p (C and F) lines. When the dispersion obtained by this method is divided by the density measured a t the same temperature, the specific dispersion results. To convert this value to more useful figures, it is multiplied by 104: specific dispersion*= H
d
lo4
When the hydrocarbons melt above about 60" C., the constants are determined by extrapolation from their solution in solvents of related chemical structure. Similar methods have been used by others and apparently afford a good approximation. 853
Vol. 34, No. ‘I
INDUSTRIAL AND ENGINEERING CHEMISTRY
854
DISPERSION OF NONCONJUQATED OLEPINS TABLEI. SPECIFIC Sp. Dispersion __-
Compound
Calcd.
Aliphatic. Olefins 2-Pentene 138 2-Methyl-2-butene (trimethylethylene) 135 2-Hexene 129 129 129 129 129 129 159 124 124 150 121 121
l-Hep”teneA 5-Methyl-l,4-hexadiene 1-Octene 2-Octene
4-Methyl-3-heptene 121 121 3-Ethyl-3-hexene 121 2-Propyl-1-pentene 139 2 6-Dimethyl4 6-heptadiene 139 2:6-DimethyI-&-heptadiene i-nornnn 116.5 I-Decene 148 2.fi-Diruethyl-2,5,8-nonatriccc148 5-Eth 1 1,4,S-nonatriene 110 r ~ e x a d e k n e(cctene) Cyclopentene Derivatives 135 Cyolopentene
.
1--”1-
1-IIethylcyclopentene 3-lIethylcyc1openter.c 1,2-Diniethylcyclopenrene 2,3-Dimcthylcyclnpenfenc 1-Ethylcyclopentene 1-1,2,3-TriniethyIcyclopentene
129 129 124 124 124 121
d-1 2 3-Trimethylcyclopenten~ 2 3~3~Trirnc.thylcyclopentene l~~lethyI-2-erhp1cyc!opcnrcne 1-Propplcyclopentene 3-lIet hyl-4-propylcyclopc.ntene 1,2-Diet hyl-r-cyclopentene 1-Butylcycloprnrcne
121 121 121 121 118.5 118.5 118.5
Cyclohexenc l->Ier hylcyclchrxene
Cyc1ohc.rer.e Derivatives 129 124
Exptl.
Citation
134 134 128 132 128 130 127 123
131
145 126 123 144 119 120 121 123 123 124 143 140 118’ 148 148 108
!!4 138
124 117 126 121 119 129 124 124 116 121 116 121 116 115 119 121 120 120
The method of calculation developed is, in a sense, a compromise between the method of von Auwers and that of the earlier workers such as Bruhl, Eisenlohr, etc.; that is, we do not consider the whole molecule and give its percentage exaltation, nor do we classify it in terms of individual atoms. Rather, the molecule is considered in terms of the portion which is paraffinic, naphthenic, or unsaturated. Values for unsaturation remain constant whether conjugated or nonconjugated bonds are involved. Exaltation is accounted for by considering the number of double bond forms which are possible rather than by changing the fundamental value for the unsaturated bond itself. Thus, the specific dispersion may be calculated by a summation of the partial values for the dispersion of the portions of the molecule in each of three types of linkages: n- Y specific dispersion = 2 X Z
c
+c +C
where p = number of paraffinic carbon atoms n = number of naphthenic carbon atoms u = apparent number of carbon atoms associated with ethylenic linkages C = total number of carbon atoms in molecule X,Y , 2 = constants representing, respectively, the specific dispersions of a paraffinic system, a naphthenic system, and an unsaturated linkage, C=C The problem is thus to evaluate the constants and to correct for conjugation or resonance. The specific dispersions of all paraffins are considered identical, regardless of chain length or complexity of branching. I n the present work a value of 98.4, the average value for a great number of hydrocarbons tabulated by von Fuchs and Anderson (&), is accepted as the specific dispersion of a
Sp. Dispersion __ Calcd.
Compound
Exptl.
Citation
Cyclohexene Derivatives (Cont’d) 124 4-Methylcyclohexene 121 1 2-Dimethylcyclohexene 121 1’3-Dimethylcyolohexene 121 1’5-Dimethylcyclohexene 121 3:5-Dimethylcyclohexene 1,4-Dimethylayclohexene 3 3-Dimethylcyclohexene 4:4-Dimethylcyclohexene 1-Ethylcyclohexene 1 2 3-Trimethylcyclohexene 2’3’3-Trimethylcyclohexene
2‘4’4-Trimethylcyclohexene
1'3'5-Trimeth ylcyclohexene
1’4’4-Trimethylcyclohexene l~4~5-Trimethylcyclohexene 1-Isopropyloyclohexene 1 2 4 5-Tetramethylcyclohexene l:M&hyl-4-isopropenylcyclohexene
121 121 121 121 118.5 118.5 118.5 118.5 118.5 118.5 118.5 117 135
135 1- 3 l c t h y l - ~ - i ~ o p r o p c n y l c y c l o h c ~ e ~ i e 135 d-3-llet hyI-fi-iooprupcnylcycl~Ii~si~ne 138 l-Methvl-4-isopro VI1,4 cpclohexadiene 2.4-Dimrthvl-?-et~~:;.rlvlc;cluhrlrne 135 116 l~Isopropyl~4-methyl~yc~ohoxene 116 3-Methyl-6-isopropylcyclohexene 111 1 2 4-Trimethyl-4-isopropylcyclohexene 1:2~4-Trimethyl-4-isopropenylcyclohexene124 Cyclopentane and Cyclohexane Derivatives hlethylenecyclopentane 129 120 Methylenecyclohexane 124 127 Ethylidenecyclohexane 121 127 1-Methyl-4-methylenecyclohexane 121 128 Isopropylideneoyclohexane 119 122 1,3-Dimethyl-5-methylenecyclohexane 119 123 Terpenes and iVliscellaneous Pinene 117
!!:
Cycloheptene Dodecahydro-9.10-diisobutylanthraoene 3-Cvciowrowvl-2-~entene _0 Properties determined b y t h e authors. ~
~
117 11’ 139 129 116 124 107 121
iig 129
137 122 112. 114 120 106 126
pure paraffinic system. I n a more recent article by Wibaut (71), the average specific dispersion of twenty-four paraffins was found to be 98.3, the variation of any individual being within *1.0 of the average. The value of the constant X thus chosen is 98.4. The average value for naphthenic systems is not so well defined. The variations found in such hydrocarbons are due, perhaps, to the considerable differences in bond strains among the members of this class, which become particularly evident in cyclopropanes and cyclobutanes, but may also involve minor corrections for fused six-ring naphthenes. The average value of von Fuchs and Anderson (98.3) has again been accepted; however, for certain naphthenes this value is high. Wibaut (71) finds an average specific dispersion of 96.8 =L. 0.6 for six pure naphthenes. The average value of 2 determined from the data on a number of monoolefins is 189. Since, as discussed later, the benzene nucleus is optically equivalent to an unconjugated system, and since all double bonds are to be considered optically equivalent, the value of 189.3 for the specific dispersion of benzene (the accuracy of the measurement being considerably more reliable than that for any single olefin) was taken as the basis for the value of constant Z. The equation for the calculation of the specific dispersion then becomes: specific dispersion
= $(98.4)
+ ~(98.3) n + &189.3) U
Nonconjugated Unsaturated Systems Calculating the specific dispersion of nonconjugated unsaturated molecules gives little trouble; the calculated values
INDUSTRIAL AND ENGINEERING CHEMISTRY
July, 1942
generally agree well with experimental results. This undoubtedly arises from the fact that double bonds separated by two or more single bonds have little exalting effect on specific dispersion. There is evidence based on heats of hydrogenation that, while double bonds separated by three single bonds exert no tautomeric effects (which may be considered responsible for exaltation), such effects do exist when the separation is but two single bonds. Such effects, however, would introduce but a small error in the calculation of specific dispersion and may be neglected. A more serious discord between calculated and experimental values arises, however, from the fact that it is often difficult to obtain pure samples of dienes and trienes, which are characterized by their pronounced tendencies to polymerize. For example, von Auwers and Moosbrugger (90) determined the density a t 19.6" C. of freshly distilled 2,6-dimethyl-2,5,8-nonatriene and found it to be 0.8178. On standing 18 hours protected from the atmosphere, the density increased to 0.8352. A typical calculation is given below, and complete data on a comparison of experimental and calculated values are listed in Table I: Limonene Empirical C atoms Ethylenic C atoms Paraffinic C atoms Naphthenio C atoms Calcd. sp. dispersion
= 10 = 4 = 2 = 4 = =
4
lo (189.3) +
4
(98.3)
+ lo2 (98.4)
134.5 (exptl. 133)
Simple Conjugated Systems Calculation of the specific dispersion of conjugated systems presents a difficult problem, and the exalting effect of such conjugation must be approximated. The first step is to define the conjugated system of the molecule and to determine the number of carbon atoms associated with the double bonds of the system (ethylenic carbon atoms). Next the exaltation equivalent is evaluated by replacing each single bond within the system by a double bond and determining the number of carbon atoms associated with the new ethylenic linkages. Thus, in the molecule,
the number of ethylenic carbon atom is 6. Upon replacing the single bonds as described above, the new system becomes
7 8
910
----B=C-D=&
---
resulting in an exaltation equivalent of 4. The apparent number of carbon atoms associated with double bonds or the apparent ethylenic carbon atoms (u)becomes 6 4 or 10. When the above rules are applied to conjugate systems involving branched chains, the exaltation due to conjugation is altered by an amount depending upon the degree of branching. This fact was recognized by von Auwers and others in a qualitative way. To obtain the exaltation equivalent of simple branched hydrocarbons, the molecule is reduced to the longest normal conjugated system involved. Additional combinations are then written for each case in which it is possible to substitute a branch (involving conjugation) for a part of the system at the point of branching. Each branch is used only once. The exaltation is then calculated for each combination exactly as in the above example. The summa-
+
855
TABLE 11. SPECIFICDISPERSION OF NONAROMATIC CONJUGATED HYDROCARBONS Sp. Dispersion Compound Calcd. Exptl. Aliphatic Conjugated Olefins 2 Methyl-1,3-butadiene 247 1 3-Pentadiene 247 2:3-Dimethyl-1,3-butadiene 222 2-Methyl-2 4-pentadiene 2,CHexadiine 1 3 5-Hexatriene 2:B:Heptadiene 5-Methyl-2,4-hexadiene 4-Methyl-3,5-heptadiene 4-Methyl-2,4-ootadiene 7-Methyl-2,4-octadiene
Citation
222 222 316 204 204 191 181 181
Cyolobntane Derivatives 1 2-Dimethyl-3 4-diethylideneoyclobutane 173 1 :2-Dimethylede-3,3,4,4-tetramethylcyclobutane 173 1,l-Dimethyl-2-methylene-3-isopropylideneoyolobutane 173 l,2-Dimethyl-3,4-diisopropylideneayolobutane 161
(66)
163
(66)
176 162
Cyclohexene Derivatives 1,6-Dimethyl-3-methylenecyclohexene 181 1.5-Dimethyl-3-(2-methylenepropylidene) oyolohexene 207 Cyclohexadienes 191 1 6-Dimethyl-1 3-oyalohexadiene 191 1'3-Dimethyl-i 3-cyclohexadiene 191 1'4-Dimethyl-1'3-oyalohexadiene 191 dirnethyloyolo&exadiene 3,3-Dimethyl-6-methylene-l,4-cy,olohexadiene 222 181 l-Methyl-4-ethyl-l,3-oyolohexadiene 173 1-Methyl-4-isopro yl 1 3 cyclohexadiene 173 1-Methyl-4- ro yfl,&clohexadlene 2,3,3-Trimet%y~6-methylene-l,4-~yolohexa210 diene 1 1-Dimethyl-4-ethylidene-2 5-oyclohexadiene 210 2:3,3,5-Tetramethyl-6-meth~lene-1,4-oyclo200 hexadiene 2,3,3,4-Tetrarnethyl-6-methylene-l,4-~yclo200 hexadiene 3 3-Dimethyl-6-prop lidene-1 4-cyolohexadiene 200 1:3,3-Trimethyl-6-et$lidene-i ,4-cyclohexa200 diene 2,3-Dimethyl-6-isopropenyl-l.3-oyclohexadiene 182 2-Methyl-3-ethyl-5-isopropenyl-l,3-~yolohexa175 diene 1,3,3,4-Tetramethyl-6-ethylidene-l,4-cyolo191 hexadiene 2-Meth 1 3-propyl-6-isopropenyl-l.3-o~clo169 hexa&ne Miscellaneous 1.3-Cycloheptadiene 204
183
172 184 158
(81)
(14) (8f)
170 159 192 187 232 182 168 177 lj7 216 226
201 203 201 200 173
168 192 161 185
~
(78)
tion of the various exaltations obtained in this manner, minus 1 for each degree of branching, is the exaltation equivalent of the entire system. A=B EXAMPLE I. Type F,E>C=D1 ethylenic C atoms = 6. The Longest normal chain is one of four carbon atoms involving, first, atoms A and B and then F and E successively with C and D. Each of these systems has an exaltation equivalent of 2: A=B-C=D ---A-B=C-D---
and
F=E-C=D ---F-E=C-D---
The total exaltation equivalent is thus 4-1 (one degree of branching) or 3. The apparent ethylenic carbon atoms are 3 or 9. then 6
+
EXAMPLE 11. Type ~ ~ ~ > C = D - P = Qethylenic , C atoms = 8. The longest normal chain contains six carbon atoms. Each combination contributes an exaltation equivalent of.4. The total exaltation equivalent = 4 4 - 1 (one degree of branching) or 7. The apparent number of carbon atoms associated with double bonds = 8 7 or 15.
+
+
A=B
R=S
>C=D
-C=D
in our calculations, since only one of the double bonds in each resonating form is in active conjugation with the external linkage. From what has been said it is evident that the resonance within a particular ring exhibits a neutralizing effect upon the exaltation, as shown by lack of exaltation for benzene and by the fact that phenanthrene has an exaltation far below that of anthracene. In a manner somewhat similar, no exaltation is gained by a new resonating form (the alternative benzenoid structure as shown by naphthalene) if i t is the mirror image of another form already being considered. With these rules in mind, the calculation of specific dispersion of various aromatic nuclei will be given as examples. BENZENE.While the lack of exaltation in benzene might a t first be striking, there is an analogy with a system containing isolated ethylenic linkages. Thus, von Auwers ( 2 ) showed that the diphenyl polyenes of the general formula Ph(CH= CH),Ph are very resistant to oxidation by permanganate. Diphenylhexatriene is the most stable member. If, however, the molecule is altered to form Ph-C-C=C-C-C-C-Ph, it becomes very reactive and lacks entirely the stability or near aromatic character of the former compound. It is apparent that an open-chain polyene attains maximum stability when it is conjugated with phenyl groups a t the ends of the chain. It is but one step further to the more peifect conjugation of benzene where the hexatriene system ends in itself. The shaded ring is considered to be the NAPHTHALEXE. benzenoid or true benzene ring in all examples:
... ...
The ncutr:ilizntion of the conjugstion ivliicli ia evident in the parent unsntur:itcd cyclic deriwtive is not nearly so efiectiw in the su1)stituttd tlerivativcs ( z c ~t1.e tlisubstitutecl cycloIics:icliencs oi T:tlde IIj. .IROL\TIC SLXLEI. l\.llilc :ill oi tile aromatics eshiljit market1 neutr:Jization of conju%:itic,n,tlie specific dispersion of polynuc1e:ir aromatics may be very high, a result of the many po+ihle iornis whicli ~irnyexist for these compouncl~ by conjugstion of true benzene rings with the external rings. By “tnw” benzene ring is mennt nn nromntic ring in 2 polynuclc:ir :ircmutic n-liicl, is chosen and considered to h a w rhrcc t i o u l h lmntls. T o cdcrilutc tlic di=qwrsic,n of tlicsc hydruc:,rlwns, the gencrul rules already given w c applied. First of all, the logical configurations of a given aromntic niust be drawn. Thcsc logical configurations nil1 include only tliose forms in lvliicli tlir I i x i s i m u i n nnmlier of berizeiioid
Both naphthalene and anthracene are systems in which one benzenoid ring interacts with one or more ortho-quinoid structures. Only one structure is possible for naphthalene, as the interchanging of benzenoid and quinoid rings produces mirror images. The general concept of the benzene ring possessing two double bonds reacting upon the side chains is applied. Thus two equal systems bearing the configuration Ep-C=D A
are t o be considered in determining the exaltation equivalent of naphthalene : Empirical C atoms = 10 = 10 Ethylenic C atoms Exaltation equivalent = 3 X 2 o r 6 Apparent ethylenic C atoms = 16 = g(189.3) = 302 (exptl. 297.6) Calcd. sp. dispersion
INDUSTRIAL AND ENGINEERING CHEMISTRY
July, 1942
OF COMPLEX BENZENE TABLEIIL SPECIFICDISPERSION HYDROCARBONS
Compound Styrene o-Methylstyrene Isopropenylbenaene 1-Phenyl-1-propene o-Ethylvinylbenzene o-Divinylbenaene 1-Phenyl-1-butyl-1-octadeoene 1-Phenyl-1-butyl-1-docoaene 2-Methyl-3-phenyl-5-isopropenyl-l,3-cyclohexadi en e Di henyl 1-3henyl-1-cyclohexene 1,l-Diphenyl-1-propene 1 1-D'phenyl 2 2 dimethylethylene 2:Methyl-5-i~o~r~pyldiphenyl l-Benzyl-2-methyl-4-isopropylbensenzene 1,2-Diphenyl-1-methylethene 2 3-Diphenylbutane 1:l-Diphenyl-1-octadecene 1-Phenyl-l-butyl-l0-phenyl-lO-butyl-l,9decadiene 1-Diphenyl-1-butyl-1-octadecene 1-Di henyl-1-butyl-1-docoaene Tripgenyleth ylene l,l,Z-Triphenyl-l-propene
Sp. Dispersion Calcd. Exptl. 260 258 264 249 249 242 230 242 256 233 238 302 301 144.5 144 138 136 214 268 206 246 233 237 185.5 309 177 172.5 185 192 182 346 330
Citation
222 267 209, 210 249 234 216 189 325 181 171 188 197 177 374 2,777
Anthracene and all similarly condensed aromatic systems may be treated in like manner. ANTHRACENE.The following configurations are assigned to anthracene in accordance with the rules:
A>-c=D-p/Q E Empirical C atoms Ethylenic C atoms Exaltation equivalent Apparent ethylenic C atoms Calcd. sp. dispersion
857
(equivalent to 10)
\R = 14 = 14 = 5 = 29
+ 10 or 15
= :(189.3)
= 393 (exptl., about
385, extrapolation)
INDENE. The structure commonly accepted is I:
(p \ -
cn 0 \ =
I
I1
IIb
Assuming this benzenoid form, the indene system becomes a benzene ring in conjugation with an ethylenic linkage, accompanied by an extension of nuclear conjugation into one side chain: Empirical C atoms Ethylenic C atoms Exaltation equivalent
= 9 - 8 = 3 . 3 (conjugation of type
A>-C=D) together with E effect of satd. side chain Apparent ethylenic C atoms = 8 3.3 or 11.3 Naphthenic C atoms = 1 1 Calcd. sp. dispersion = 'g(189.3) ~ ( 9 8 . 3 ) = 248 9 (exptl., 233.4 and 224.5)
+
+
A, System 1. Conjugation of the type )\B-C=D-P=Q,
E/
which affords an exaltation equivalent of 7, occurs in two positions (at points of X and Y ) with the benzenoid ring, making a total of 14. 'B-C=D, which A> E/ affords an exaltation equivalent of 3, occurs four times, making a total of 12.
System 11. Conjugation of the type
Empirical C atoms Eth lenic C atoms ExaTtation equivalent Apparent ethylenic C atoms Calcd. sp. dispersion
= 14 = 14 = 14 plus 12 = 40 = g(189.3) = 541
The experimental values were determined in solution by von Auwers and the extrapolated data affords values for the specific dispersion ranging between 525 and 555.
PHENANTHRENE. The following configuration is the one containing the greatest number of benzenoid rings:
On the other hand, cyclopentadiene rings exhibit a negative exaltation and thus appear to be optically more stable than cyclohexadienes or benzene. Assuming that I1 is the structure for indene, better agreement is obtained between experimental and calculated values. The two resonating pairs are mirror images, and so only one is considered: Empirical C atoms Ethylenic C atoms Exaltation equivalent
= 9 = 8 = 2 (conjugation of type A=B-
C=D) Apparent ethylenic C atoms = 8 2 or 10 Naphthenic C atbms = 1 10*0(1S9.3) $98.3) 1 Calcd. sp. dispersion
+
=9
+
= 221
DIPHENYL.For systems of this type,
0-0 let us consider successively the two resonating forms of the right-hand ring:
4
Each of these forms contributes an exaltation of 4 (a total of 8) from which must be subtracted 1 for each of the three new arrangements over and above the original A=B-C=D. The net exaltation equivalent is thus 5 :
' No other configurations are possiblein which so many benzenoid rings are present. This system is comprised of two benzene rings in conjugation of the diphenyl type, contributing an exaltation equivalent of 5 , and the two rings interacting across the 9,lO double bond so as to establish conjugation of the type,
Empirical C atoms Eth lenic C atoms Exartat ion equivalent Apparent ethylenic C atoms Calcd. sp. dispersion
= 12 = 12 = 5 = 12 5 or 17 17 = riz(189.3) = 268 (exptl. 268)
+
'
858
INDUSTRIAL AND ENGINEERING CHEMISTRY TABLE Iv.
SPECIFIC Sp. Dispersion Compound Calcd. Exptl. Alkylbensenes Benzene 189.3 189.3 Toluene 183.8 184.5 184.5 186.3 c-Xylene 181 181 m-Xylene 181 182 p-Xylene 178 181 183 Ethylbenaene 174 176 n-Propylbenzenc 165 168 Isopropylbeneene 165 166 172 o-bf ethylethylbenzene 172 170 174 nr-Methylethylbenzene 172 177 p-&.I ethylethylbenzene 172 174 1 2 3-Trimethylbenzene 178 176 1:3:5-Trimethylbensene 178 179 sec-Butylbenzene 159 167 Isobutylbenzene 161 159 1 2-Diethylbenzene 164 168 1'4-Diethylbensene 164 166 l:Methyl-3-propylbenzene 164 169 1-Methyl-4-prop ylbenaene 164 159 1-iMethyl-2-~sopropylbenzene 164 166 1-1Clethyl-3-isopropylbenzene 164 166 I-Methyl-4-isopropylbenzene 166, 162 164 1 2 3 4-Tetramethylbenzene 176 174 1:2:4:5-Tetrarnethylbenzene 176 176 Pentamethylbenzene 174 171 1 2 4-Trimethyl-5-ethylbenzene 169 170 1'3:5-Trimethyl-2-ethylbenzene 173 169 1:2-Dimethyl-4-propylbenzene 163 175 1,2-Dimethyl-4-1sopropylbenzene 163 164 153 tert-Amylbenzene 161 l-I\.Iethyl-3-n-butylbenzene 163 158 158 1-Methyl-4-tert-butylbenzene 160 153 Phenylcyclopentane 157 l-Methyl-2-ethyl-4-isopropylbenzene 159 159 154 156 1-~Methyl-2-propyl-4-isopropylbenzene 164 1,3,5-Trimethyl-2-isobutylbensene 158 159 Pentaethylbeneene 150 Hexaethylbenzene 148 l60(?) 1-Phenyl-4-tetralylbutane 168 171 Hexadeoylbenzene 126 126 Ootadecylbenzene 123.5 130 133 120 Docosylbenzene 120 1-Phcnyl-1-butyloctadecane 120 128
Vol. 34, No. 7
DISPERSION O F SATURATED ALKYLAROXATICS
Table I11 gives the complete data for hydrocarbons involving conjugation of nuclear double bonds with external unsaturated groups, or with other rings. Of the groups of aromatic hydrocarbons omitted from this classification are those containing saturated side chains as well as those where two aromatic rings are separated by one saturated carbon. Each of these groups requires special consideration and will be discussed later.
Extension of Nuclear Conjugation into Saturated Side Chains
It has already been mentioned that, while the cyclohexadiene nucleus exhibits complete neutralization of exaltation, the same is not true for substituted cyclohexadienes, which behave normally. A degree of the same behavior occurs in the case of substituted cyclohexatrienes and other aromatics, even where the possibility for conjugation with external olefin bonds is excluded. The apparent extension of nuclear conjugation into side chains probably results from the mobility of the hydrogen atoms attached to the carbon atom alpha to the ring, and results in a weak unsaturation being established between the ring and the a-carbon atom. Thus toluene should show this effect, and it should be proportionately greater, the larger the number of such side chains attached. Both expectations are substantiated by experiment. From the experimental values of specific ALKYLBENZENES. dispersion for such compounds, it appears that extension of nuclear conjugation into a single saturated side chain results in 0.3 olefinic carbon atom, and that where more than one
Sp. DispersionCalcd. Exptl.
Compound
Alkylbenzenes (Cont'd) 1-Phenyl-2-benzylheptadecane 130 1-Phenyl-1-butyldocosane 117 Alkylnaphthalenes 1-hlethylnaphthalcne 295 290
2-Methylnaphthalene
1-n-Octadeoylnaphthalene Tri-n-hexylnaphthalene
I-Kaphthyl-1-butyl-1-hexadecene I-Naphthyl-1-butyl-1-ootadecene 1-Naphthyl-1-butyloctadecane
1-Naphthyl-2-butyleicosane I-Naphthyl-1-butyldocosane 1-Naphthyl-1-ethyl-2-butyleicosane I-Naphthyl-1-butyl-2-butyleicosane 1-Naphthyl-1-butyl-1-docosene
1-Naphthyl-1-ethyl-2-butyl-1-eicosene 1-Naphthyl-1-butyl-2-butyl-1-eicosene Di-or-naphthylmethane
9-Ethylphenanthrene Retene 0
6
(61) (66)
$.44
295
294 _-
294.7 291, 288 +1
283
1 4-Dimethylnaphthalene l:B-Dimethylnaphthalene I-Methyl-2-ethylnaphthalene 1-Methyl-4-ethylnaphthalene 1,4-Diethylnaphthalene l-Methyl-2,4-diethylnaphthalene 1-n-Amylnaphthalene 2-te~t-Butylnaphthalene 2-sec-Butylnaphthalene Nonylnaphthalene
l-.\Iethg!snthrncene B-.\lcrh~liinriir,ictnc 9-Ethglsnrhrscc:ie 9-lsoanylintlirn iene 9,10-Diie,,bui\lnn:hriiceiie
143 121
292.7 I-1 287 281 288 291 283 289 269 273 273 276 261 264 254 262 242 241 249 253 239 241 209, 212 213 176 173 182 191 192 192 186 197 166 172 162 162 158 149 158 158 155 157 176 166 176 172 171 167 321 322*5
1,2-Dimethylnaphthalene
Citation
illkylanthracenes 519 564 535 466 452 Alkylphenanthrenes 355 323
(Ffi) (16) (MA) (16)
(64) (44) (16)
(49) (49)
(49)
(4:) a CI
a (1
(6:) (66) (66)
(66)
(66) (66) (66) (6:)
517 554 534 466 4591.10
(60) (49) (60)
349 340b
(49) (17)
'$
Properties determined by t h e authors. Approximately (extrapolated data).
group is attached, it is the corresponding multiple of this Thus the following equation may be used: calcd. sp. dispersion
=
(189.3)
+ P (98.4)
where TZ
= number of side chains C = empirical number of carbon atoms P = number of paraffinic carbon atoms
As an example, 1-methyl-Ptert-butylbensene C- -+IC
Empirical C atoms Ethylenic atoms Paraffinic C atoms
= 11
Calcd. sp. dispersion
= ~ ( 1 8 9 . 3 ) -(98.4) 11
= 6.6 = 5
66
+5
= 158 (exptl. 160)
The complete data are given in Table IV. NAPHTHALENE DERIVATIVES.Alkyl derivatives of naphthalene may be treated similarly to benzene derivatives in regard to the extension of nuclear conjugation into the side chains, although the intensity of the extension varies with the alpha and beta positions. [Examination of absorption spectra for monosubstituted naphthalenes by LBszl6 (62, 65) showed that alpha derivatives were optically clearly differentiated from beta compounds.] The resonating forms of alpha- and beta-alkylnaphthalene are :
859
INDUSTRIAL AND ENGINEERING CHEMISTRY
July, 1942
Empirical C atoms = 15 Eth -1enic C atoms = 14 Exaftation equivalent = 26 0.6 Apparent ethylenic C atoms = 40.6 Aliphatic C atoms = 1 = 406((189.3) Calcd. sp. dispersion 15 (exptl. 517)
+
+
The extension of nuclear conjugation into the side chain results when the double bonds of a benzenoid ring are in a position favorable to conjugation with the bond between the ring and the side chain-i. e., double bonds beta to the substituent. The double bonds of the benzenoid rings in forms 3 and 4 can thus extend conjugation into either the alpha or beta position, contributing, as in the case of benzene, a total of 0.3 to the exaltation equivalent. I n forms 1 and 2, however, the benzenoid double bonds can extend their conjugation only as far as the alpha position; they thus contribute an additional 0.3 to the exaltation equivalent. No additional exaltation is given to the beta position by these forms. Thus for beta-methylnaphthalene: Empirical C atoms = Ethylenic C atpms = Exaltation equivalent = Apparent ethylenic C atoms = = Calcd. sp. dispersion
11 10 6 0.3 16.3 16.3 1 ~ ( 1 8 9 . 3 ) -(98.4) = 290 11 (exptl. = 290.8, 287.7, 280.9)
+
+
For alpha-methylnaphthalene: = 11 Empirical C atoms Ethylenic C atoms = 10 Exaltation equivalent = 6 0.6 Apparent ethylenic C atoms = 16.6 Aliphatic C atoms = 1 = F(l89.3) n1( 9 8 . 4 ) = 295 Calcd. sp. dispersion (exptl. = 295.6, 295.5, 290.6,
+
+
294.0, 292.0, 293.7, 294.0, 294.1)
The experimental data for a number of naphthalene derivatives are given in Table IV. ANTHRACENE DERIVATIVES.The principle discussed in the preceding section of estimating the effect of nuclear conjugation on the side chain is applied to anthracene. The alpha and beta derivatives are treated exactly as were the corresponding naphthalene derivatives. The extension effects on a mesoalkyl group are extremely great (in accordance with the generally great reactivities of these positions), as is evident when the number of beneenoid double bonds which can affect this position are considered. Since, however, the theoretical possibilities are not well understood, we selected the experimental value of 4.2 carbon atoms to represent the extension of conjugation into a side chain a t this point:
=
519
Complete data for anthracene compounds are given in Table IV. PHENANTHRENE DERIVATIVES. In calculating a value for the specific dispersion of a phenanthrene derivative substituted in the meso positions, the 9,lO double bond is considered as possessing little tendency to extend into the side chains. Although the number of phenanthrene compounds on which optical data have been determined is too small to provide substantiation, it is believed that the ample opportunity to form stable benzenoid configurations in the phenanthrene molecule reduces the extension effect t,o a small value. Other positions are accounted for, as with benzene derivatives (0.3 carbon atom per side chain). (See Table IV.)
Secondary Conjugation (Diphenylmethane Type) Extension of nuclear conjugation from one ring into the side chain provides an exaltation equivalent of 0.3 ethylenic carbon atoms. This has the effect of introducing a weak unsaturation between the ring and the adjacent carbon atom; that the unsaturation is introduced here is evidenced by the fact that toluene, which has only one carbon atom in the side chain, shows this extension effect. The ethylenic character thus imparted to the bond between the first ring and the methane carbon atom makes possible a conjugation with a second ring; but this conjugation is relatively weak, for the methane carbon atom has an ethylenic strength of only 0.15, corresponding to its share of the extended nuclear conjugation -for example, Diphenylmethane c > - C - c I > Since the carbon atoms of the second ring have full ethylenic Rtrength, the resulting exaltation for the type: A 0.15
E>~-c=~
is equal to 1.15 f 1.15 = 2.30 (instead of 4 as for a full double bond) minus 1 for the usual degree of branching. Adding 0.3 for the extension of the conjugation from the first ring, the net exaltation is 1.6: Empirical C atoms = 13 Ethylenic C atoms = 12 Total exaltation equivalent = 1.6 Apparent ethylenic C atoms = 13.6 13.6 1 Calcd. sp. dispersion = ~ ( 1 8 9 . 3 ) ~ ( 9 8 . 4= ) 205.5 (exptl. 203, 205)
+
9-Ethylanthracene
Empirical C atoms = 16 Ethylenic C atoms = 14 Exaltation equivalent = 26 4.2 Apparent ethylenic C atoms = 44.2 Aliphatic C atoms = 2 Calcd. sp. dispersion = 4g(189.3) &(98.4) 2 (exptl. = 534)
Data for other hydrocarbons of this type are listed in Table V.
+
+
= 535
TABLE V. SPECIFIC DISPERSION OF HYDROCARBONS EXHIBITING SECONDARY CONJUGATION Hydrocarbon Diphenylmethane
lj
I
1-Methylanthracene
1 -(98.4) 15
co3
1-Bensylcyolohexene p-Bensyltoluene 1 1-Diphenylhexadecane 1’1-Diphenyloctadecane Tkphenylmethane
Sp. Dispersion Calcd. Exptl. 206 203 206 176 I75 202 200 148 148 143.5 146 213 216
Citation
Vol. 34, No. 7
INDUSTRIAL AND ENGINEERING CHEMISTRY
860
Aromatic-Naphthenic Fused-Ring Hydrocarbons In keeping with a desire to have the method of calculation as general as possible, it would perhaps be preferable to apply the extension-of-nuclear-conjugation methods t o calculating the specific dispersions of aromatic-naphthenic hydrocarbons. However when this is done, the calculated values are usually found to be somewhat low. Accordingly a different method of calculation is used for this type of hydrocarbon, which recognizes that one of the resonating forms of such a hydrocarbon will always leave the carbon atoms common t o both rings naphthenic-i. e., free of unsaturated linkages. This will leave one ring completely naphthenic. To calculate the specific dispersions of such hydrocarbons, the system is regarded as comprising complete aromatic rings and complete naphthenic rings. I n such instances the carbon atoms common to both rings will be counted twice, once as aromatic rings and once as naphthenic rings. I n some cases, however, for one reason or another the C-C linkage common to both rings cannot be counted as being both ethylenic and naphthenic'. The examples given below will illustrate these views. EXAMPLE I. Tetralin,
Empircal C atoms Ethylenic C atoms Naphthenic C atoms Calcd. sp. dispersion
= 10 = 6 = 6 =
6
a(l89.3)
+ ~6( 9 8 . 3 )= 173 (exptl. 173)
TABLEVI.
AROMATIC-NAPHTHENIC HYDROCARBONS
SPECIFIC DISPER5ION O F
Sp. Dispersion Calcd. Exptl.
Hydrocarbon Tetralin
173
1 ,Z-Dihydronaphthalene
248 191 293 252 127 123 123 121 181 286 160 192 187 175 258 154
1,4-Dih dronaphthalene Acenapzthene 5-Isobutylacenaphthens Octadecyl-Tetralina Docosyl-Tetralin 1-Tetralyl-1 -butyloctadecane I-Tetralyl-1-butyldocosane Hydrindene Fluorene Octahydroanthraceneo 9-Isobutyl-9,lO-dihydroanthracene 9-Isoamyl-9,10-dihydroanthracene 9 10-Diisobutyl-9 10-dihydroanthracene cx-Tetrahydrophehanthrene Octahydrophenanthrene a Properties determined by the authors.
174 173 246 178 286 289 255 127 120 128 129 175, 179 288 162
190 187 179 262 155
Citation
(44) (7)
(7) (7 )
(44) (1:)
(6'3) (66) (66) (66) (6.9) (49) (18, 23)
'3 (1
(1 7) (18)
Notwithstanding the fact that the resonating partner to this system would consist of a n aromatic and two purely naphthenic rings, this form is regarded as the basis for optical calculations. Although i t appears to contradict the rule enumerated above, an opportunity for the maximum optical neutralization is afforded by this structure. It produces a system which is more symmetrical and thus of greater optical stability : Empirical C atoms Ethylenic C atoms Naphthenic C atoms Calcd. sp. dispersion
= = = =
14 6 8
+ 1.2 8 + -(98.3) 14
72 '(189.3) 14
= 154 (exptl. 155)
The examples illustrate the difficulty of applying the general rules to a wide variety of compounds without proper consideration of structure. The available data on hydrocarbons of this type are given in Table VI.
EXAMPLE 11. Octahgdroanthracene,
Induced Conjugation Part of the molecule (left) is treated as the Tetralin type, leaving the remainder to be considered by the extension-ofnuclear-conjugation method : Empirical C atoms Ethylenic C atoms Naphthenic C atoms Calcd. sp. dispersion
= = =
=
14 6
+ 0.6 +
6 4 6.6 -(189.3) 14
10 + -(98.3) 14
=
160 (exptl. 162)
EXAMPLE 111. Octahydrophenanthrene,
As previously stated, the exaltation equivalent of a conjugated system depends generally upon tautomeric changes. Sometimes, however, a spatial or induced effect becomes important, as when one part of the conjugated system is brought into favorable proximity with another part. This latter effect is made possible by the configuration of the double bonds so as to tend to form a closed system instead of the more or less extended molecules which have been treated heretofore. One type of induced conjugation may be accounted for approximately by assuming that two indirectly connected bennene rings may interact (if they are brought close enough together more or less over each other). Each ring is regarded as inducing a n alternate resonating structure in the other, and this is treated as an interring conjugation. The resulting exaltation equivalent is two additional rings or 12. 1,4-DIPHENYL-l ,&BUTADIENE. I n the CiS-tranS isomer,
oc=c-c=c- 1 Since this paper was prepared very recise data for the specific dispersion of Tetralin two isomeric mkthyl-&tralins and 1 2 3 4-tetramethylbenzene have bee; published b y Mair and Streifi [J. Refiearch Xat2. Bur. Standards, 27, 343-57 (1941)l. T h e ,value given by them.for t h e specific dispersion of Tetralin (165.5 i 1.0) is considerably lower t h a n t h e earlier value used in our calculations. This low value agrees better with t h e value calculated b y t h e extension-of-nuclear-conjugation method (164.2) t h a n the modified method just described. T h e values for t h e methyl-Tetralins (163.9 + 0.5, 166.2 * 0.5) agree somewhat better with t h e value calculated by the modified method (165.5) t h a n with t h a t calculated by the general method (163.3). For most compounds t h e agreement between t h e two methods is close and i t may be t h a t , as more precise data become available it will rove poasible t o make sufficiently reliable calculations by the mord generafmethod.
the induced effect will not be important as the ethylenic system is as extended as possible: Empirical C atoms Ethylenic C atoms Exaltation equivalent Apparent ethylenic C atoms Calcd. sp. dispersion
= 16 = 16 = = =
16 16
+ 16 or 32 g(189.3) = 379 (exptl. 379). 16
INDUSTRIAL AND ENGINEERING CHEMISTRY
July, '1942
Besides the exalting effect already present in the cis-trans isomer, cis-cis-diphenylbutadiene is characterized by a large induced conjugation:
to omit data obtained on impure samples or considered unreliable for any reason. Unfortunately, descriptions of the compounds in the literature are not sufficiently complete to justify such omissions. Accordingly, experimental data for every compound discussed 'are included. For a few compounds a choice had to be made between discordant values in the literature; the references indicate in all cases the source of the data. Considering the compounds as a whole, the distribution of differences between calculated and experimental values around zero justifies the choice of constants used for the calculations. The fact that nearly 75 per cent of the experimental values reported in the literature agree within 5 units of the calculated values is considered a satisfactory correlation, particularly since variations of one unit can be expected in the experimental determination of specific dispersion under
P
.Ae /
c-c
The configuration of the molecule is such that the two benzene rings may interact. The result is that an exaltation equivalent of two additional rings or 12 is produced, each benzenoid structure being capable of forming the alternate resonating structure in the other: Empirical C atoms = 16 Eth lenic C atoms = 16 = 16 + 12 EAafttrttion equivalent Apparent ethylenic C atoms = 44 Calcd. sp. dispersion = g(189.3)
861
~
=
520.5 (exptl. 497)
~~
~~
TABLEVII. SPECIFIC DISPERSION OF PHENYLBUTADIENES (47) Compound
Also, a double bond on the end of an externally conjugated ring system may be so placed relative to the ring that conjugation may sweep through the free end of the molecule as well as through the end fixed to the benzenoid nucleus. Consider, for example, the phenylbutadienes of Klages (47). The specific dispersions of members of this group will be difficult to calculate since the induced effects are capable of becoming large. This last effect will result in an exaltation of the specific dispersion which is approximately equal to the exaltation already created by the usual conjugation. The results of calculations on this basis, in comparison with experimental values, are given in Table VII.
Sp. Dispersion Calod. Exptl.
Structure
l-Phenyl-l,3-butadiene
454
417
l-Phenyl-l,3-pentadiene
422
416
I
C 373
l-Phenyl-5-methyl-l,3-hexadiene
376
I
I
Analysis of the Method
C/c\C
The proposed method for calculating specific dispersion has been analyzed by comparing the calculated and experimental values for the hydrocarbons listed in the tables. This analysis is summarized in Table VI11 according to the type of hydrocarbon. I n analyzing the method it would be preferable
l-phenyl-6-methyl-l,a-heptadiene
0 ' AC
352.5
363
WC I
E
c/ \c THE METHOD" Deviation between Calculated and Experimental
TABLEVIII. ANALYSISOF 7
Hydrocarbon Type Nonconjugated olefins Aliphatic olefins Monoolefins nioirfina .........
Triolefins Cyolo entene hydrocarbons Cyclofexene hydrocarbons One double bond Two double bonds Cyclohexane and cyclopentane derivatives Terpenes and miscellaneous Nonaromatic conjugated hydrocarbons Conjugated aliphatic olefins Cyclobutane derivatives Cyolohexadienes Aromatic hydrocarbons Benzene derivatives with unsatd. bonds Alkylbensenes Alkylnaphthalenes Alkylanthracenes Secondary conjugation Aromatic-naphthenic hydrc)carbone Phenvlbutadienes
-11 Over t o -20 -20
.. .. .. .. ..
-10 - 9
.... ...... .. .. .. .. .. .. .. 1 1
..
3
. . . . .. 1
1 1 1
-8 -7
-6
-4
-5
-3
-2
.... * .1 ..1 .4. .. .. . . . . .. .. .. .. * . .. 2 2 .... ..1 ..1 .. .. .. .. .. ..1 ..1
..1
1
0
+1 +2
4-3 + 4 + 5
+6
f7
+8
..
1 .. ...1. .. 1.. ... ... 2 1 .. 1 1 2 2 ..3 ..1 72 . . .. .. .. .. . . *. .. .... .3. ..2 .... ..1 .... .. . . . 1. .. ..1 ..2 .... ..
.. .. .. .. .. * . .. .. . . .. .. ..
..
-1
--.
2 1
1
..
2 1
5
3
.. .. ... . .. .. .. . . .. 2 1 4
%'Over +20
+9 +10 +20
.. .. .. ..
..
.. .1. . . .. 1 ... . 1 .. .. ..
.. 1 . . . . . . 1 . . . . . . 1 . . . . . . 1 . . . . . . . . . . . . 1 1 .. .. .. .. . . . . .1 . .. .. . 2 . 11 . . .. 51 .1. . .. .. .. .. .. . . . 1. .. .. .. .. . .1. . 1. 1 .1. .. .. . 2.
...1. 211 .... . 11. .. . . .. .. .. .. . . ., ,. ., .. 1 , .
1
3
1
1
.. .2.
.. ..*... .. ..
2
2 .
3
.
1 5 2
4 3 i 6 ' 5 3 2 2
............
...... ... . . 1. . 2.
1 . . 1
1 1
1
3
1 3
..
7 4
..1 1
3
1 . . 1 . . . . . 3 1 . . 1 1 1 2 . . . . . . . 1 . . . . . . . . . . . l . . . . . . . . . . . .
. . . . . . . . .. .. .. . .2 . . 1. . 1 . . .
1 . . . . 1 . . . . . . . . . . .
2 1 3 . . 3 1 1 . . . . . . . . . . . . 1 ................ 1 ..........
Total 2 9 . 4 2 7 1 7 7 1 6 2 1 2 1 2 0 6 T h e figures represent the number of compounds for each deviation.
28
1426
8
9
7
3
4
2
3
5
7
. .
1 5
862
INDUSTRIAL AND ENGINEERING CHEMISTRY
Vol. 34, No. 7
optimum laboratory conditions. We believe that variations outside of 5 units are due mainly to impure compounds or to errors in measurement of physical properties. Considering the separate groups, the experimental values for the olefins are frequently lower than the calculated values, as would be the case if polymerization occurred. I n the case of the aromatics the reverse is true, and the experimental values are frequently higher than those calculated. The experimental and calculated values for the aromatics can be brought into better agreement if the arbitrary value chosen to account for the extension of nuclear conjugation into the side chain is changed from 0.3 to 0.305. However, the reliability of available data is not believed to be sufficiently great to warrant selection of a value more precise than 0.3.
are considerably different, the presence of one in the other may be conveniently detected. Also such a procedure was used by von -4uwers (3) in analyzing ketoenol mixtures. The specific dispersion is likewise convenient for detecting the presence of aromatics in hydrocarbon mixtures The position of substitution in polynuclear aromatics can often be determined for pure compounds from consideration of the specific dispersion. While these methods were developed largely upon an empirical basis, the consistency of treatment found possible for widely varying types of structure indicates a fundamental unity which should be capable of theoretical analysis.
Applications of Specific Dispersion in Organic Chemistry
(1) Auwers, K. von, Ann., 413, 294 (1917). (2)Ibid., 415, 98-168 (1918). (3) Ibid., 415,185 (1918). (4)Ibid., 420, 84-111 (1920). (5) Ibid., 499, 130 (1932). (6) Auwers, K.von, Ber., 42, 2424-39 (1909). (7) Ibid., 46,2988-95 (1913). ( 8 ) Ibid., 53, 944 (1920). (9) Ibid., 62,700 (1929). (10) Auwers, K. von, and Bergmann, F., Ann., 476,276 (1929). (11) Auwers. K. von, and Eisenlohr, F., Ber., 43,827-34 (1910). (12) Ibid., 43, 1545 (1910). (13) Auwers, K. von, and Eisenlohr, F., J . prakt. Chem., 82, 66-180 (1910). (14) Auwers, K.von, and Ellinger, P., Ann., 387, 200-39 (1912). (15) Auwers, K.von, and Friihling, A., Ibid., 422,192-230 (1921). (If3 Auwers. K. von. Hinteraeber, R., and Treppmann. W.. Zbid.. .~ 410, 257-87 (1915). (17) Auwers, K. von, and Kraul, R., Ibid., 443, 181-91 (1925). (18) Auwers, K.von, and Krollpfeiffer, F., Ibid., 430,230-68 (1923). (19) Auwers, K. von, and Lange, H., Ibid., 409,149-82 (1915). (20) Auwers, K.von, and Moosbrugger, W., Ibid., 387,167-99 (1912). (21) Auwers, K,von, and Peters, G., Bw., 43,3094-110 (1910). (22) Ibid., 43,3111-20 (1910). (23) Auwers, K. von, Roth, W. A., and Eisenlohr, F., Ann., 373, 267-90 (1910). (24) Auwers, K. von, and Treppman, W., Ber., 48,1207-25 (1916). (25) Auwers, K. von, and Westermann, H., Ibid., 54,2993-9 (1921). (26) Auwers, K. yon, and Ziegler, K., Ann., 425,217-80 (1921). (27) Briihl, J. W.,Ber., 25,151 (1892). J . Chem. Soc., 91,115-23 (1907). (28) Brtihl, J. W., chim. Belg., 36,591-604 (29) Chavanne, G., and Becker, P., Bull. SOC.
Values for the specific dispersion of hydrocarbons were a t first used by the authors in connection with the purification and identification of alkylbenzenes. Since then increasing use has been made of such calculated values in identifying and ascertaining the purity of hydrocarbons. I n effecting the complete hydrogenation of aromatic compounds, the specific dispersion affords a convenient analytical check. This is especially true for hydrocarbons of high molecular weight. Thus in the preparation of octadecylDecalin there was no simple way of ascertaining whether the product had undergone practically complete reduction. The melting point was indefinite. However, the specific dispersion was eventually reduced to a value of about 97, and the combustion analyses then proved excellent. The above value for the specific dispersion gave assurance that the concentration of octadecyl-Tetralin in the sample must be small and justified the more involved confirmatory precision combustion analysis. As an example of the use of specific dispersion in identifying structures, the action of isobutyl chloride on the sodium addition product of anthracene results in a small amount of lower boiling by-product that had not previously been mentioned in the literature on the reaction. The specific dispersion of this product was 190. This is close to the value 192 calculated for a monoallrylated dihydroanthracene, a compound which had been little considered previously. The combustion analyses and molecular weight agreed closely with the theory. I n the synthesis of 9,lO-diisobutylperhydroanthracene from the corresponding dihydro derivative, three pure compounds were finally isolated, and the specific dispersion was employed in conjunction with combustion analyses in the identscation of the products as the following:
(a).
Literature Cited
\-
I
,.
n"",
(lY.61).
(30) Chavanne, G., and Devogel, L., Ibid., 37, 141 (1928). (31) Chavanne. G., Miller, O., and Cornet, Mlle., Ibid., 40, 673-88 (1931). (32) Chiurdoglu, G., Bull. sci. acad. TOY. Belg., 17, 1404-15 (1931). (33) Chiurdoglu, G., Bull. SOC.chim. Belg., 43,38-48 (1934). (34) Ibid., 47, 241-59 (1938). (35)Ibid., 47,363-81 (1938). (36) Crossley, A. W.,J . Chem. Soo., 85,1417 (1904). (37) Crossley, A. W.,and Renouf, N., Ibid., 89,35 (1906). (38) Deanesly, R.M., and Carleton, L. T., IND.ENQ.CHEM.,ANAL. ED., 14, 220 (1942). (39) Doeuvre, J., Bull. SOC. chim., 53, 170-7(19 (40) Eisenlohr, F.,and Polenski, R.. Ber., (41) (42) (43) G. H. von, and Anderson, A. P., IND. 29, (44) Puchs, .. . - - , - - -. l _ l
With derivatives in which an equilibrium exists between two isomers or in which one isomer undergoes rearrangement into the other, the specific dispersion sometimes proves useful. Thus the methylene cyclohexadienes show pronounced tendencies to rearrange to the corresponding phenyl derivatives. As the two types of derivatives have specific dispersions which
__
~ _ _ .
(45) Grosse, A. V.,and Wackher, R, C., IND.ENG.CHEM.,ANAL. ED., 11, 61424 (1939). (46) Keersbilok, N. van, Bull. soe. chim. Beto., 38, 205-11 (1929). (47) Klages, A., Ber., 40, 1768-72 (1907). (48) Ibid., 40,2360-73 (1909). (49) Krollpfeiffer, F.,Ann., 430, 161-229 (1923). (50) Krollpfeiffer, F., Ber., 56, 77-83 (1923). (51) Landa and &oh, Chem. Zentr., 106,I, 1228. (52) L&szl6,H.de, J. A m . Chem. Soc., 50, 892 (1928). (53) LBsz16. H. de, Proc. Roy. SOC.(London), 111, 335 (1926). (54) Lebedev, J . Russ, Phys. Chen. Soc., 43, 820 (1911). (55) Lebedev, 8.V., and Merezhkovskii, B. K., Ibid., 45,1354 (1913). (55A) Mair, B.J., and Streiff, A. J., J.Research Natl. Bur. Standards, 24,395 (1940). (56) Mikeska, L. A., IND.ENQ.CHEM.,28, 970-83 (1936).
July, 1942
INDUSTRIAL AND ENGINEERING CHEMISTRY
(57) Noyes, W. A,, and Skinner, G. S., J . A m . C h m . SOC.,39,26922718 (1917). (68) Gatling, G.J., J . Chem. SOC.,101,471 (1912). (59) Perkin, W. A., Ibid., 69, 1230 (1896). (60) Ibid., 91, 815 (1907). (61) Richard, A. H., Compt. rend., 153, 116-20 (1911). (82) Riaseehem. H.van. Bull. SOC. chim. Bela.. - 42.. 219-28 (1933). . , (63j 1bid..47, 261 (1938). (64) Schroeter, G.,Lichtenstadt, L., and Irineu, D., Ber., 51, 1601 (1918). (65) Stobbe, H., and Reuss, F., Ann., 391, 151 (1912).
863
(66) Timmermans, J., and Hennrtut-Roland, Mme., J . chim. phys., 34,693 (1937). (67) Vogel, A. I., J . Chem. SOC.,1938, 1332-8. (68) Ward, A. L., and Fulweiler, W. H., IND. ENQ.CHEM.,ANAL. ED.,6,396 (1934). (69) Ward, A. L., and Kurtz, 8. S., Ibid., 10, 559-75 (1938). (70) . , Waterman, H. I., and Westen, H. A. van, Rec. t m u . chim., 48, 1084-6 (1929). H., Langedijk, S. L., Overhoff, J., and (71)Wibaut, J. P..HOOK, Smittenberg, J., Ibid., 58,329 (1939). Willstatter, R., Ber., 31, 1544 (1898). (72)
Equations for the Specific Heats of Gases JULIAN C . SMALLWOOD The Johns Hopkins University, Baltimore, Md. H E purpose of this paper is to present condensed equations for the gases entering the combustion of fuels and the products of combustion. Up to a decade ago thermal properties of gases were based on specific heat determination by calorimetric methods or by the indirect method of sound velocity measurements. Results were evaluated by equations for molal specific heat of the form ... c, = u bT cT*
T
+ +
This is undoubtedly true, but Sweigert and Beardsley did not include in their original paper any equation for mixtures, although one for air is particularly desirable in connection with combustion calculations. The Sweigert and Beardsley equations for molal specifio heat are as follows:
+
where T is absolute temperature, and a, b, and c are constants with plus or minus values from zero up, depending upon the gas and upon the estimates made by various investigators in correlating the results of different experimenters. The basic methods of experiment, however, were subject to certain inherent errors and uncertainties. Since 1930 a number of researches have been made, based upon quantum theory and spectroscopic observations. Because of the more refined experimental methods and advanced theory, results from these researches are more accurate than older ones. These new data were correlated by Heck (1) in tabular form, with resulting values of enthalpy and internal energy. A year later the same authority issued addenda to his original paper, including tabulations for pure dry air and for some typical combustion gas mixtures (2). He did not, however, .present any equation for either elemental gases or for gas muctures, maintaining that complete tabulations were of greater convenience. Heck’s contributions were also discussed (8) by an unusual number of eminent authorities, including chemists, physical chemists, and engineers. The general trend of this discussion was to accept spectroscopically determined specific heats and resulting thermal properties of gases in preference to those resulting from previous experiments, and to approve Heck’s tabulations computed from spectroscopic data. Prior to Heck’s publication, Sweigert and Beardsley proposed equations based on spectroscopic data @)which, they stated, gave results within 2 per cent of error for a temperature range between 540’ and 5000” R. The discussion of Heck’s paper brought out a very satisfactory agreement between these equations and Heck’s tabulations. (Since the publications cited contain a complete bibliography of the basic experiments, i t is not repeated here.) Sweigert contributed to the discussion his opinion that for many purposes equations for thermal properties of gases are more convenient than tabulations, especially when mixtures of gases are involved.
where c,,
T
=
=
For 03,HoO: c, = a
b c -.d/p+ T
molal specific heat, B.
a
-b + c
For NI, CO, COS: c,
$. u./lb. mole/’
= absolute temperature, F. a, b, c = constants depending only upon the gas
F.
Values of these constants appear in Table I. A combined equation representing any of the five gases or a mixture of them may be obtained by selecting a single symbol. for the coefficient of 1/T, and includingthe terms -b / l / T and c/T2. Thus, to avoid confusion, change the notation for the constants as follows: I n the preceding equations let the coefficient of (namely, -b) = x
I/&‘
:$& +
(namely, -b or c) = y
(namely, c)
Then
c, =
a
xT-1’2
+
=z
YT-1
+ zT-*
in which the appropriate values of the coefficients are given in Table I. TABLEI. CONSTANTS AND COEFFICIENTS Gas 01
NI
co
Ha0 GO2
Air
a 11.515 9.47 9.46 19.86 16.20 9.90
Z
-0172 0 -597 0 -36
Y +. ioa 4-1.53 -3.47 -3.29 1-7.50 -6.53 -2.42
z
+
106
0 Cl.16 1-1.07 0 4-1.41
+0.917
For the first five gases the coefficients, when inserted in the combined equation, yield the equations presented by Sweigert and Beardsley (8). For any mixture of gases the values of the coefficients are readily obtained by an average weighted according to the number of moles of each gas in the mixture.
