It. L. LIVINGSTON ANI C. K. I~AMACHANURA RAO
756
dialysis membrane. These considerations all apply, of course, in similar fashion to any three-component system, whether or not ionic species are present. Scatcliard2 has chosen the polymeric component in such a way that one mole of neutral component contains one mole of particles with the advantage that the change of chemical potential upon addition of one mole of solute to the system does not reflect primarily the addition of many moles of diffusible ionh. For a polymeric ion Pzof valence 2 in the prescnce of a uni-univalent electrolyte, Scatchard's definition requires simply that component 2 he formulated as including one mole of Pz ions, - 2 / 2 moles of univalent cations, and 2 / 2 moles of univalent anions. This definition has been utilized in discussions of light scattering by Edsall, et aZ.,16 and Doty and Edsall," and of sedimentation equilibrium by Johnson, Kraus and S ~ a t c h a r d . ~ ~For , ' ~ a solution in which p23 of equation 4 is zero, Scatchard's definition of component 2 sild that proposed here become equivalent in the limit as Zmz 'm3 approaches zero. For example in the case that component 3 is a uniunivaleiit electrolyte, these conditions give ala =
C uzl/m3 z
(16) J. T. Edsall, €1. Edelhoch, R. Lonticand P. R. Morrison, J . A m . Chem. Soc., 7 2 , 4 6 4 1 (19.50). (17) P. Doty and J. T. Edsall, "Advances in Protein Chemistry," Vol. VI, Academic Press, Kew York, N. Y., 1951. p. 35. (18) J . S. Jolinson, K. A . Krans and G. Scatchard, Tms JOURXAI, 68. 1034 (1954).
Vol. 64
Electroneutrality and our requirement that be zero are then satisfied by values of - 2 / 2 and Z / 2 for the moles of salt cations and anions included in a mole of component 2. The generalization of the relations presented here to systems containing more than one macromolecular component is readily effected. As in the threecomponent system, interactions between all the non-diffusible solutes and component 3 can be eliminated with the choice of components suggested by dialysis equilibrium. The equations resulting a re completely analogous formally to those obtaining for a mixture of macromolecular components in a single s 0 1 v e n t ~and ~ ~ ~their ~ npplication involves the same problems. NOTE ADDED I N PROOF. --4n article by Scatchard and Bregman [G. Scatchard and J. Bregman, J . Am. Chem. Soc., 81, 6095 (1959)) published after this paper was submitted is pertinent to our work. I n connection with their light scattering study of bovine serum albumin in sodium chloride solutions, they nom define the protein component as Na(,Th)/2[HhPCl,] Cl(h -.) ' 2 , n-here P represents isoionic protein arid h and Y are, respectively, the numbers of protons and chloride ions "bound." Although n e have preferred t o omit explicit introduction of ion binding, this definition is the same as ours in the particular instance that Y is defined by membrane equilibrium and HC1 is not regarded as a diffusible component. It differs from Scatchard's older definition by addition of v / 2 moles of salt. However, since Scatchard and Bregman have formulated activities and refractive index increments differently than m suggest, they arrive at an analog of our equation 8 only by making approximations (justified for their system) which are not required in our derivation. (19) J. (1959).
S. Johnson, G. Scatchard
and K. A . Kraris, i b z d , 63, 787
AN ELECTROK DIFFRACTION ISVESTIGATION OF THE MOLECULAR STRUCTURE OF METHYL AZIDE' B Y R.L. LIVINGSTON AND c. s. l%AhlA4CHANDRAR-40' Contribution from the Department of Chemistry, Purdue University, Lujauetle, I n d u n a Receaved *Vovember S O , 1363
The molecular structure of methyl azide has been studied by the sector-microphotometer and the sector-visual methods of electron dipaction and the parameters determined as follows: C-N = 1.47 f 0.02 A., iV1-K2 = 1.24 =t0.01 A., XZ-N3 = 1.12 f 0.01 4.and < C K 4 = 120 f 2'.
Early electron diffraction work3 on methyl azide mas done by the visual method which empIoyed nonsectored photographs with data extending to a qvalue of 55. It was decided to reinvestigate the structure of this molecule by the more refined techniques iiow available. Of particular interest were the C-S distance and the two N-N distances. Experimental Methyl aside was prepared by the dropwise addition of dimethyl sulfate to a basic solution of sodium azide heated (1) Contains material from t h e doctoral dissertation of C. N. R. Rao. Presented a t t h e 135th meeting of the American Chemical Society. Boston, Mass., April, 1959. ( 2 ) Purdiie Research Foundation F e l l o x , 1950-19,ji; Standard Oil Foundation Fellow, 1957-1958. Indian Institute of Science, Bangalore, India. ( . 3 ) L. Paulirip and L. 0. Brockwaj., J . .4m. C'hern. Soc., 5 9 , 13 (1937).
to about 80" under constant ~tirring.~'5The vapors were ~msscdt,hroiigh a water condenser and over anhydrous calcium chloride and collected in a Dry Ice-trichloroethene
trap. The yields were about 80%. The product, a.fter a fmv v:wiiiim distihtions, gave acccpfable vlemental analyF i e and the boiling point was found to be about 21". The infrnrcd qiectriim of the vapor showed no obvioiis impurities. Electron diffraction photographs of methyl azide were taken using an +-sector and Kodak Lantern Slide cont,rast plates. The patterns were taken both a t a short (10.19 cm.) and a long (25.10 cm.) camera dist'nnce. A sample pressure of about 25 mm. was fouGd to be adequate. The electron wave length was 0.05452 A . , obtained by applying an accelerating potential of 48.322 kv. This voltage was measured by determining the potential drop across an acciirately known portion of a rcsistnnce which it>srlfis across the entire nccclerating potmtinl; the result manner have been checked against zinc o. ( 4 ) 0. Iliiiiroth a n d \V. Wialiccriua. BET.,38, 1,573 (J9O.j). ( 5 ) 0. A1;~ndulz~ arid (;. Caronna, Garz. c h i m . i t d . . 71, 182 (1941).
A visual intensity curve ‘ivas obtained from these sectored p1:ttcs. The resulting sector-visual data extend from y = 20 to q = DO ttnd the visual intensity curve is shown in Fig. 1. 11icrophotoineter traces of sevrral plates were taken on a Le& and Northrup microphotometer while spinning the plates a t a high speed. The transmittancics were converted to arbitrary intensity units over a tots1 range rxtending from q = 18 to q = 7 5 . The total intensity data were convcxIted to the molecular intensity data by the equation
‘VI here
Y. 1
.
1
20
’
1
40
- 1 - 7 -
’
60
1
80
I,(y) is the molecular structure scattering function to
be comparec with the calculated intensity curves, I t ( y ) is the total intensity, I b ( q ) is the (estimated) background
intemity and K is a constant. Radial distribution curves were calculated using the equation6
where r D ( r ) I S the radial distribution function, T is the inttxrnurlear srpaiation and exp( -b@) = 0.10 at p = qmay. 111 e:tch case the intensity data for thc inner part of the pattern were obtained from a theoretical intensity curve calculated by means of the equation6
Fig. 1.-Observed
and calculated intensity curves for methyl azide.
using punched cards.
The first r:tdial distribution curve calculated from the sertor-microphotometer data showed some fairly large negative areas and other extraneous features. By making successive improvements in the background line, the final radial distribution curve shown in Fig. 2 was obtained. The final euprrimsntal intensity curve is shown in Fig. 1.
Results and Discussion The sector-microphotometer radial distribution curve for c1cthyl azide
i \
H
H
shows four peaks. The first peak has a prominent shoulder on the right side, presumably due to the C-N1 distance. The remainder of the peak should, therefore, be due to the two N-Ti distances and the C-H distance. This peak was analyzed by the resolution procedure described by Karle and Karle.’ The shoulder to the right of the first peak was fitted by the Karles’ method assuming that the right side of the shoulder did not have any contribution from any other distance. Similarly, assuming that the right side of the peak is not affected by the C-I1 distance, the area was fitted by trial and error with the Karles’ function for the two K-Ti distances. The areas of the three peaks were subtracted from the total area of the first peak and the remGining area formed a smooth curve about r = 1.09 A, which _\vas -attributed to the C-H distance. The secclnd peak was decomposed in a similar fashion taking the Nl-N3 distance as the sum of the Nl-N2 and Ns-NY distances from the decomposition of the first peak and assuming that the Nl-H distance did not affect the right side of the peak. (6) P. A. Sliaffer, Jr., 1’. $chornaker and L. Pauling, J . Chem. Phys., 14, 85g 1918). (7) I. L. Karle-and J. Kdrle, zbzd.,.18, 963 (1950).
I
Fig. 2.-The
2
A.
3
4
radial distribution curve for mrthyl azide.
After obtaining the C-X2 and Kl-Y3 distances, the N1-H distance was fitted a t the left side of the peak. The area obtained by subtracting the areas of C-N2, Nl-nT3 and N1-H peaks agreed well with the area expected for the Kz-H1 di$ance and formed a smooth curve about 2.45 A. (In interpreting the radial distribution curve and in calculating theoretical models, CtV symmetry was assumed for the methyl group with the hydrogen atoms oriented so as to give one short n’z-H distance (nT2--H1) and two longer K,-H distances
(XrHz).)
The third peak could be decomposed by assuming that the right side of the peak mas mainly due to the C - S , distance and was not greatly affected by the other distances. The area olltained by subtraction of the C-N1 peak area was comparable to the expected area due to N2-H2 and Sa-Hz distances. The fourth peak represented only the N3-H2 distance and although no attempt was made to fit it exactly with the Karles’ function, the observed area corresponded closely to the expected area for this distance. The results of the radial distribution curve are summarized in Table I. In general, the areas under the peaks are in good
attempt was made to decompose the composite peaks in order to obtain the individual distances. In order to determine the ranges of uncertainty for the various parameters, a correlation procedure was carried out. The sector-microphotometer and 1.14 the sector-visual intensity curves resembled each other closely and so the correlation procedure has been carried out using the sector-microphotometer 116 M N 0 P data between q = 17 and y = 75 (Fig I ) and sectorvisual data from y = 7 3 to q = 87. Several theoI etical intensity curves were calculated okeeping the S1-N2 distance constant at 1.24 A. The 118 parameter field chosen jn the C-SI = 1.47 planc z is shown in Fig. 3. z Curves for model^ AI, A, E and I show obrioiic 120 faults in maxima 3 , 7, 9 and 10 a$ illustrated by curve E in Fig. 1. Curves F and ,J show similar faults in maxima 5 and 10; curve E’ is illuqtrated. These faults are present but not as serious in curve 122 B and the model for this curve is accepted as a borderline case. In curve N, maximum 7 is too low. In curves 0, P and D, maxima 5 and 7 are too weak. In curves H, L and R, the main fault 124 Q R lies in maximum 9 as is illustrated hy curve H in Fig 3 ---ParamPtri firld used for cslculntions of intensity Fig. 1; in addition, these curves shoiv some faults riirvy for methj 1 azide The principal plane had C - S = in the region of maxima 5 and 7 . Max 3 i. not llodels 1 1, I3 1, C 1. etc , nere in the plane C-9 = 1 47 1 45 sand rnotlc>l. h 2, B 2 , C 2, etc n e r e in the plane C-X well-defined in curves L, R and Q: in addition, = 1.49 A maxima 5 and 7 are somewhat too high. Model G, which corresponds exactly to the radial distribuagreement with the expected values of nZ,Z,/r,,, tion curve is. of course, acceptable and gives the even for distances involving the hydrogen atoms best qualitative curve of those calculated. Curves The valueq of the root mean square amplitudes of C and K are acceptable but somewhat less satiq1 ibration, AT],, for the distances involving hydrofactory than G. The acceptable parameter field gen atonii cannot be determined with much cer- in the C-S1 = 1.47 A. plane is shorn 11 by the dotted tainty since small oscillations in the zero line of the line in Fig. 3 . radial distribution curve can change the shape of Severalomodelswere also calculated in two plane:, these small peaks considerably. The values of the one 0.02 A. beloiy (X1 plane) and the$ther 0.02 A. interatomic distances obtained by the radial above (X2 plane) tbe C-S1 = 1.47 A. plane. In distribution method correspond to a linear geome- the C-X1 = 1.45 A. plane, model G I is barely try for the azide group, CBv symmetry for the CHB acceptable and C1 is *an extreme borderline caqe. group and 120” for the C S K angle. In the C-SI = 1.49 A. plane, model G2 is bnrcly acceptable and model K2 is a borderline case. All T4BLE 1 other models in these two planes were regarded as RESULTSOF THE RADIAL DISTRIBUTIONCURVE FOR unacceptable. ~ I E T H YAZIDE L BY THE SECTOR-MICROPHOTOMETER METHOD The observed q-values by the sector-microDistance ! 41’1, Peak a r m nZIZi/r, photometer method and the qcslc/qobs ratios for the C-H 1 OB 0 075 45 9 46 6 acceptable models are listed in Table 11. The Xz-x 1 12 05 90 1 89 8 principal parameters calculated for the acceptatde N,-Xs 1 21 04 100 100 models are given in Table 111. The radial distric-SI 1 47 06 64 3 64 8 bution values are taken as the final results with S,-H 2 10 10 25 0 27 3 Uncertainties eqtahliqhed by the correlation proC-X? 3 35 10 41 1 40 9 Cediire
N,N, Nl- N, 108 !lQ 1.12 1.24 1.24 1.24
1.24
3
A &
~
i-1)
j
?;,-S,
S,-H, K;,-H2 Kq-Hi
c-?;
3
Y 1-HA
2 36 2 33
08
3 35
14
26 2
47 7 8 2 12 5 6 8 28 4
10 1
10 2
47 3
7 3
1
18 2
The radial distribution curve calculated from the sector-visual data showed four peaks and resembled the sector-microphotometer curve rather closely. In spite of a few negative regions, the areas of the peaks agreed well with the expected results; these areas had observed values of 67.3, 27 9, 10 0 and 2 4 compared with the expected values (nZiZJ/r,,) of 6.1 1, 28.3, 10.0 and 2 1, respectively. No
c-SI = 1 1 7 zt 0.02 Pir-N? = 1.24 5 0.01 d XZ-Na = 1.12 =I= 0.01 and :i I 1
qt>*
B
C
20.0 24.2 26.0 31.2 37.1 .40.7 43 . 0 48.5
0.999 1.010 1.021 1.013 1.009 0.998 1 ,013
0,997 1,009 1.015 1.006 1 . 00?J 0 998 1 007
1.013
1 ,008
0
1.004 1.005 1 , O(L5
0,998 1 ,000 1.004
...
...
--
.)i).
05.0 7 0 ,9
I
8
..
... ...
..
!I
.. Mean i; tlcv from the mean
G
0.994 1.006 0.999 1.007 0,998 0 993 1 ,002 1.001 0 9!)B ,
1 , 00 1
...
..
__
__
1.008 0 005
1.004 0 004
.. 0,9994 004
TABLE I11 I'RIYCTP iL
P iR \\IF,TERS
FROM -4CCEFT4RLE
~ I E T I I I ~I J3
c
?\lOIlEI.E. TOR
I D F
(1
R
G1
G?
I
