XUMBEKOF STRUCTURAL ISOMERS OF ALIPHATIC COMPOU~S
Jan., 1934
[CONTRIBUTION FROM
THE
DEPARTXENT O F CHEMISTRY, UNIVERSITY
OF
15i
TEXAS]
The Number of Structural Isomers of the More Important Types of Aliphatic Compounds’ BY HENRYR. HENZEAND CHARLES M. BLAIR I t has been shown that, by separating the isomers of each specified carbon atom content into types, arbitrarily chosen upon the basis of their structural formulas and deriving mathematical formulas of the (finite) recursion type for each, it is possible to calculate the total number of structural isomers of the methanol, paraffin, ethylene, and acetylene series2 The method has been extended to include all of the more important types of aliphatic compounds and the numbers of structural isomers of such compounds are indicated in the following tables.
Acetals Acids monocarboxylic dicarhoxylic amino hydroxy sulfinic sulfonic .Udehydcs i\lkyl halide:; Amides urisubstitutcd monosubst ituted disubsti tu1 ed Amines primary secondary tertiary
\To of tkoniers
a b C
d d
e e 2,
e 2,
f a E g
’
’
-+
TABLE I S U M B E R O F STRUCTURAL ISOhlERS
Allphdtl t>W
Equal to the number of methanols of N - 1 carbon content. ‘ Equal to thc uuniber of disubstitution products of the paraffins containing two identical substituents, C\Hz\Xz, of LV - 2 carbon content, scc Table 11. Equal to the number of disubstitution products of the paraffins containing two unlike substituents, C.VH~.YXY, of iV - 1 carbon content, see Table 11; the number of structurally isomeric alpha amino or hydroxy acids is equal to the number of acetylenes of the same carbon content. ‘ Equal to the number of methanols of the same Equal to the number of esters of the carbon content. same carbon content, see Table 11. ’’ The nuinberi of p., s. and t. amines are equal to the numbers of p , , s. ai:d t . methanols, respectively, of .Ir.+ 1 carbon content. See Equal to the number of Table 11. See Table 11. secondary niethanols of N 1 carbon content. Thc “simple” ethers equal the methanols of :I’/3 carbon content. k See Table 11. Equal to the numbcr of methanols of same carbon coutcnt; the numbcr of iuttliyl ketoiies is equal to that of the methanols of - 2 eCt~-lmi content. 7’1 See T a l k 11. Equal to tlic number of ctliylenes of N 1 carbon contcnt.
Aliphatic type
No o i iborners
Disubstituted paraffins C.vHz.vXY CMHZ.VX: Esters Ethers Glycols Isoni trilcs Ketones Mercaptans Kitriles Quaternary aiiimonium compounds Sulfones Sulfoxides Thioethers Thioureas Ureas
g Equal in number to that of Group C of the ethylenes of 1\: 1 carbon content, THISJOURNAL, 55,681-682 (1933).p a
+
(1) Abstractcd from P a r t I1 of t h e doctoral dissertation of Charles Lf. Blair, University of Texas, June, 1933. J O U R N A L , 53, 3042, 3077 (1931); 55, (2) Henze atid Blair, THIS 680 (1933); Coffman, and Blair with Henze, ibid.,55, 252 (1933). (3) T h e variGms formulas from which t h e calculations of t h e numbers of structural isomers were made, together with t h e necessary theoretical foundations for t h e same, appear in Chapters 11-IV of P a r t I1 of t h e dissertation on file in t h e University of Texas Library. 1LIr .Iuli;Ln &I. Mavity has called t o our attention t h a t t h e numher oi dructurall>- isomeric tctradccylenes reported on page
‘
+
T A B L E 11 Number of No. of dihuIt5ti. quaternary tuted parafins Carbon No. of ammonium No. of Type T1.p content esters compounds glycols C S H ~ . ~ X YC2.y€3 \ . 1 1 1 2 1 1 2 3 2 5 t 4 4 1 li 12 n 5 9 1 1,I 31 21 6 20 3 38 SO 52 7 45 7 Si 210 12.0 8 105 18 260 555 332 9 249 42 688 1479 850 10 599 109 1856 3959 2261 15 57,564 11,733 273,824 576,221 312,246 20 6,589,734 1,451,178 42,599,485 88,594,746 46,972,357
Summary The structural isomerism of the more important types of aliphatic compounds has been considered and for each of these types the numbers of structural isomers, for certain carbon atom cow tents, hare been calculated. AUSTIN,TEXAS
RECEIVED AUGUST22, 1933
685 under Group C , t y p e (2) a s being 200 should he corrected to rend 100. Hence the total nuinher of .;tructur;rl isomers of C:IIII- i. 14.:497.
