The random orientations of the molecules in 2(a) are taken into account in the calculations by giving atoms 9 through 16 weights of one-half. A t the present stage of refinement the average bond length for each crystallographic type of molecule is 2.060A. The average isotropic temperature !actors are 3.6 A . 2 for the molecules in 4(e) and 5.1 A . * for the molecules ia 2(a). The intermolecular contacts (minimum 3.38 A.) are comparable to those in orthorhombic sulfur and in rhombohedral sulfur. This disordered arrangement leads to a residual entropy of R/3 In 2 per mole of Ss molecules, or 0.057 e.u./g.-atom of sulfur. The experimental entropy, based on the available heat capacity and enthalpy data for orthorhombic and monoclinic sulfur,j is 0.045 i 0.050 e.u./g.-atom.
Figure 1. T h e structure of monoclinic sulfur. Each twofold molecule may have either the orientation shown at x = 0 or the orientation shown a t x = 1.
special positions require centrosymmetric molecules, but the crown configuration is not centrosymmetric. A reasonable explanation is that the molecules which occupy special positions are disordered. The structure of monoclinic sulfur ha5 been determined from single crystal data. Crystals prepared from purified sulfur and annealed a t 100" may be maintained a t room temperature for up to a month. Complete data were collected by visually estimating the intensities on Weissenberg and precession photographs of these crystals. Enough signs to produce a recognizable Fourier were obtained by solving the Sayre-Cochran-Zachariasen relationship with the aid of Beurskens' IBM 1620 ~ r o g r a m . ~The details of the determination and of the refinements will be published later. The discrepancy index R = ZIFo - Fc~/Z~Fo1 is presently 0.13 1 for 1270 observed reflections. Table I. Atom
1 2 3 4 5 6 7
8
Atomic Parameters in Monoclinic Sulfur
Y
x
0 0 0 0 0 0 0 0
234 152 256 374 537 553 512 332
0 0 0 0 0 0 0 0
525 356 252 144 228 315 498 525
z
0 0 -0 0 0 0 0 0
Atom 031 006
101 014 037 208 176 202
9 10 11 12 13 14 15 16
x
0 0 0 -0 -0 -0 0 0
Y
182 052 004 152 119 129 053 094
-0 -0 0 0 0 0 -0 -0
z
0 069 0 113 0 126 0 171 -0 009 -0 048 -0 185 -0 108
081 206 188 079 093 193 201 073
The unit cell (Figure 1) contains four S8 crowns in general positions 4(e) of space group P21/c: +(x, y , z ; x, 'iZ - J', z ) with x = 0.367, y = 0.356, and z = 0.072. The remaining two molecules occupy the special positions 2(a): 0, 0, 0 ; 0, Each molecule in 2(a) can assume one of two possible orientations, related by a center of inversion; these are indicated in Figure I by different orientations at x = 0 and at x = I . The atomic coordinates are listed in Table I.
+
( 3 ) P. T. Beurskcns, Acta Crj,st., 17, 462 (1964); P. T. Beurskens, "Technical Report o n Sign Correlation by the Sayre Equation," Crystallography Laboratory, University of Pittsburgh, 1963.
1396
Journal of the American Chemical Society I 87.6
(4) .I.Donohue, A . Caron, and E. Goldish, J . A m . Chem. Soc., 8 3 , 3748 (1961). ( 5 ) E. D. Eastrnan and W. C. ,McGavock, ibid., 59, 145 (1937); E. D. West, ibid., 81, 29 (1959).
Donald E. Sands Department of Chemistry, Universiry of Kenrucky Lexingion, Keniucky Received January 8, 1965
The Influence of Ionic Strength on Polarographic Half-Wave Potentials. IV. Theoretical Considerations Involving Systems of Mixed Uni-Univalent Inert Electrolytes Sir : In a n earlier communication,' we have shown that the shift in the half-wave potential of cadmium, in systems of mixed uni-univalent nitrate inert (supporting) electrolytes, followed the empirical relationship. (El
&bsd
=
(E1,2)r=0
+ (AEi
/)obsd =
f Na(AEl,,>a
+
(1) where (E,,?),= O is the half-wave potential of cadmium at zero inert electrolyte concentration, and N, and Nb are the mole fractions of inert electrolytes a and b, respectively. The half-wave potential shifts, (AEl,Ja and (AE, *)b, are the predicted shifts in systems of electrolyte a or b alone and have been theoretically shown to be2 (in mv.) (E1/z)il=O
(AE,
(29.5 log yk
Nb(AEl,,)b
+ 4.62md)]2.
(2) where yk is the mean activity coefficient and d) is the osmotic coefficient of electrolyte a or b, respectively. It is the purpose of this investigation t o show that eq. 1 possesses some theoretical significance. If the effect of the electrolytes a and b on the change in the half-wave potential for cadmium is a purely extensive one, then eq. 2 for systems of mixed electrolytes would become ,>a or b
or b
+
(AE1,Jobsd = { 29.5 log (y*>t 4.62md)tI (3) where m is the total molality and (y& and d)t are the total activity and osmotic coefficients of the system, respectively. When the two inert electrolytes have a n ion in com(1) Part 11: N. E. Vanderborgh and D. E . Sellers, J . A m . Chem. Soc., 86, 2790 (1964). (2) D. E. Sellers and N. E. Vanderborgh, ibid., 86, 1934 (1964).
/ March 20, 1965
mon, it has been shown3 that q5t can be represented as a linear function of the solution composition, or d't = d'b
+
(@a
- d'b>Na = d'a f (d'b - #'a)Nb
(4)
Q"
If dt is a linear function of a or b, then log (Y& would also be expected t o be, such that
I
+
log (?*It = log (?*)a [log ( Y d b - log (Y*)alNb ( 5 ) Substitution of eq. 4 and 5 into eq. 3 yields, after rearrangement
+
P qH2-c00cH3
Q0
N-C H2CH2COOCH3
(AEl/z)obsd = { 2 9 w - Nb) log ( Y d a Nb 1% (Y+)bl 4 . 6 2 ~ [ ( 1- Nb)d'a f Nbd'b]} (6)
+
Now, 1 (AE'/z)obsd
=
Nb
is equal t o Na, and eq. 6 becomes
+
tNaL29.5 log (Yda f 4.62Wa1 NbL29.5 log ( Y + h 4.62@b]]
+
(7)
qy::;fsH5 II
0
m
X
Y
q$'
O0CH3
a n d since [(AEl/z)obsdlb
=
(29.5 log
(Y&)b
+ 4.62 md'b}
(8)
then eq. 7 becomes identical with eq. 1 when one considers that (AE'/l)obsd = (Ei/z)obsd - ( E I / ~ =o.) ~ (3) R. A. Robinson and R. H. Stokes, "Electrolyte Solutions," 2nd Ed., Butterworths, London, 1959, p. 437.
Douglas E. Sellers, Nicholas E. Vanderborgh Parkinson Laboratory, Southern Illinois University Carbondale, Illinois Received May 23, 1964
The Synthesis of Apo-P-erythroidine
XI a, R=n-C4Hg b, R't-CqHg
m
0
xm
Sir : This synthesis was made possible by an interesting, I n their work directed toward the elucidation of the partial reversal of the Fischer indole ring closure in structure of P-erythroidine, a physiologically active alkathe 1,2-dihydropyrroIo[3,2,1 -hi]indole series and conloid isolated from several species of Erythrina, Boekelstitutes a practical synthesis of 7-substituted indolines. heide and co-workers obtained a rearranged demethoxy Indolines (I) was nitrosated and then reduced with derivative which they called apo-@-erythroidine. The lithium aluminum hydride to give 1-aminoindoline7 latter compound, to which structure XV was assigned,Ia (11) in 7 0 % yield. Treatment of the substituted hydrawas of interest for its unusual tetracyclic structure, zine I1 with either ethyl benzoylacetate o r ethyl acetoits relationship t o the parent alkaloid, and its own acetate gave the hydrazones IIIa,b, which were unstable physiological activity. Several attempts at synthesizing and could not be readily characterized but were conapo-@-erythroidine or its analogs were unsuccessfu12-4; verted, by sulfuric acid in absolute ethanol at remost noteworthy with respect to the results reported flux, to 4-phenyl-5-ethoxycarbonyl-1,2-dihydropyrroloin this communication was the observed4 inactivity of [3,2,1-hi]indole (IVa) in 83% yield [m.p. 137-138'; the carbonyl of l-methyl-2,3,4,5-tetrahydro-5-0~0-1-A,,CHpOH 309 (e 9500) and 251 m p (IS,OOO)], and t o the benzazepine toward normal addition reactions (premethyl analog IVb in 54% yield [m.p. 89-90'; "':A: sumably due to nitrogen-carbonyl resonance inter297 (e 14,000), 240 (22,600), and 220 mp (38,OOO)l: action) and the well-known3 difficulty in preparing 7This ring system was previously synthesized for the substituted indolines. first time by a Fischer reaction on the hydrazone of We now wish t o report the synthesis of apo-8I-aminoindoline and ethyl pyruvate t o give the 1,2erythroidine (XV) and isoapo-P-erythroidine (XVI).5 dihydro-4-ethoxycarbonyl derivative.* When IVa was treated with sulfuric acid in aqueous ( I ) (a) See V. Boekelheide, J. Weinstock, M. F. Grundon, G. L. Sauvage, and E. J. Agnello, J . A m . Chem. Soc., 75, 2550 (1953), for a ethanol at reflux, we obtained 7-phenacylindoline, summary of the structural work o n 8-erythroidine. (b) Also see V. which was acetylated t o facilitate isolation and give 1Boekelheide in "The Alkaloids," Vol. VII, R. H. F. Manske, Ed., Academic Press Inc., New York, N. Y . , 1960, pp. 201-227, for a acetyl-7-phenacylindoline (V) in 9 0 % yield (m.p. 136recent summary of the structural work on the Erythrina alkaloids. 137'). This hydrolytic opening is unknown in simpler (c) F. Koniuszy and K. Folkers, J. A m . Chem. Soc., 7 3 , 333 (1951), systems and presumably is the result of considerable isolated a derivative of @-erythroidine. The latter differed in melting point and particularly in optical rotation from the apo-8-erythroidine steric strain in the 6,5,5-fused ring system of IV. isolated by Boekelheide, e f a1.,la and thus was apparently impure or not the same compound. (2) V. Boekelheide and W. G. Gall, J . Org. Chem., 19, 504 (1954). (3) W. G. Gall, B. D. Astill, and V. Boekelheide, ibid., 20, 1538 ( I955 ) . (4) B. D. Astill and V. Boekelheide, J . A m . Chem. SOC.77, 4079 (1955).
( 5 ) Isoapo-@-erythroidine is an isomer of apo-@-erythroidineobtained when the latter is chromatographed on alumina; see ref. l a . ( 6 ) H. Rapoport and J. R . Tretter, J . Org. Chem., 23, 248 (1958). (7) Satisfactory elemental analyses were obtained for all compounds reported herein. (8) H. Rapoport and J. R . Tretter, J . A m . Chem. Soc., 80, 5574 (1958).
Communications to the Editor
1397
