NOTES
459
lower oxides as LO. However, IO+ and IO2+ were also observed along with the dimeric iodirie species of Figure 4 arid were seen t o uudergo marked fluctuations in intensity relative to the dimeric species, thus indicatiug ari independent existence for IO? in the gases produced by vaporization of IzOs. Acknowledgment. We are grateful to Mr. Leori P. Moore for technical assistance.
&
Concerning the Spectroscopic Determination
1’ HIi
IOt, HIO’
IO;
HI05
Hg’
Figure 3. Mass spertrum of iodic acid.
of the Structure of Water
by Gerhard Boettger, Hartwig Harders, Rechenzentrum der Badischrn Anilin- & Soda-Fabrik AG, Ludwioshafen am Rhcim
and Werner A. P. Luck Harrptlaboratoririm der Badisden Anilin- & Soda-Fabi-ik AG, Ludwigshafon am Rhein. Gcrmny (Rrceiue,l Februar~25. l g l X )
Figure 4. Mass spectrum of iodine pentoxide
19s to 192. Hypoiodous acid was formed as an independent species. It varied in intensity relative t o the other peaks and persisted in the mass spectrometer after heating of the sample had been discontinued and the spectrum of HIOnitself could no longer be observed. Ro evidence was obtained for periodic acid anhydride, Ip07. Iodic acid similarly mounted on a filament yielded the mass spectrum of H I 0 3 as shown in Figure 3. After the sample was sufficiently dehydrated, heating of the filament caused sufficient volatilization of IIOs to give the mass spectrum of Figure 4. Scans of these various peaks showed no substantial variation in relative intensities and no evidence for formation of such
I n a former publication, it was attempted to estimate the approximate proportions (if open and closed hydrogen bonds of water (from the change of iiifrared bands) in order to test the available theories concerning the structure of watcr.’ By exteusive measurements up t o and above the critical it mas attempted to increase the probability of the approximations. During these measurements, Buijs and Choppin’ reported a method of calculat,iori in which, by use of measurements in a small area of temperatures, the relative concentrations of the iudividual species of water without H bonds, co, with one H bond, cI, and with two H bonds, el, and also the unknown extinction coefficients could he determined. Therefore, they took the gross molar extinction coefficients E”’ at three wavelengths X. (n = 1, 2, 3) and at different temperatures T,(i = 1 , 2 . . . .).
(1) W. A. P. Luck, Vortrng Tagungder Deutsehen Bunsengesellsehnft fllr l’hysikdische Chemie. RIUnster, Feb G. 1962: Z. Eleklmhem., 66,766 (1962): Be?. Rtmscnges.. 67, 186 (1963). (2) W. A. P. Luck, Fortschr. Chom. Forsch., 4, 653, 877 (1964).
(3) W. A. 1’. Luck, Nachr. Chem. Teehnik. 12, 345 (1904). (4) W. A.
(5)
1’.
Luck, Ber. Bunswes., 68, 895 (1964): 69, 69 (1965).
W.A. P. Luck, ibid., 69,626 (1965).
(6) W. A. 1’. Luck, NoArrwlissmchajtrn, 5 2 , 25, 49 (1965). K.Bugs and G . R.Choppin, J . Chrm. Phgs., 39, 2035 (1903).
(7)
Volume 71, Nvmbcr B Janzrary 1967
NOTES
460
cot
+ c1i +
CZZ = 1
For simplification of this problem, it was assumed that the enk is not a function of temperature. I n the meantime, Goldstein and Penner,8 and Thomas, Scheraga and Schrier9 have followed this procedure and solved eq 1 using a least-squares procedure. For simplification of the problem, all three teams have introduced the following assumptions: eo = 0; el1 = €3'; en2 known from ice spectra. Under these assumptions, seven temperatures are required to make the number of equations at least equal the number of unknowns. The spectroscopic results found in this manner have already been discussed further. Therefore, we wish to point out that the nonlinear system of eq 1 (also by using the introduced assumption of approximations) may have more than one solution. In other words, the reported solutions are possibk solutions but not the only ones. Using the solution reported by S ~ h e r a g a we , ~ calculated as an example the gross molar extinction coefficients Ena and received from (1) the additional systems of solutions shown in Table I.
Table I System 2= 0.01; €21 = 35.72; di,2 = - 0 . 6 5
System 1
a,,* =
TI,
AC = F with
c = (CI,
c2..
. .c,),
*
ci =
@
If A and C already represent a solution, then A = A D and c = D-'C because ADD-IC = A C is also a solution of (1).
7-
= 3 . 1 3 ; a1 = 10.69;
~ $ = 1
teams only limit the variety of the possible solutions. Therefore, it seems that there exist certain ranges of concentration for possible solutions. Our two systems of solutions have been chosen near the limits of the free selectable parameter dl,2. We did not vary Thus, we left the eno unchanged. This corresponds with the status of our experiments which enable us b y measurements at the critical point to estimate elo, eo,and e30. Now we demonstrate the possibility of getting additional solutions from one given solution of system 1. First, we write (1)as a matrix equation
€31
0.1
=
€1'
OC
CU
c1
c2
cc
C1
C?
12.5 32.0 41.3 54.8 68.2 73.4 82.5
0.188 0.239 0,262 0.298 0,332 0.347 0.371
0.553 0.575 0.583 0.590 0.593 0.590 0.586
0.259 0.187 0.156 0.112 0.075 0.063 0.043
0.315 0.370 0.395 0.433 0.468 0.482 0.506
0.110 0.114 0.116 0.117 0.118 0.117 0.117
0.576 0.515 0.489 0.449 0.414 0.400 0.378
€1'
= 19.06
€2'
=
€12
=
1.33
€2'
=
1.25 5.78
€30 €3'
D
(m = 1, 2, 3; n = 1, 2, 3)
= d,,,
Clearly, with the additional assumptions introduced for several B by the three teams, not every 3 X 3 matrix D , det D # 0, is allowed. The elements of D must apply the following conditions 3
because the
E , ~are
given 3
= 0 = 8.97
k=2
because
eSo =
a3, k.dkrI =
0 3
Together with the solution reported by Scheraga, et al., there are already three possible solutions. According to the following formulas one can calculate any number of solutions. Therefore, by use of the method of Buijs and Choppin,' it is not possible to reach unequivocal solutions without additional assumptions t o the problem. The assumptions used by the three The Journal of Physical Chemistry
Cal, k=l because
0
3 2
Caa, k.dk,2
=k = 2
ell = e31 is required.
I n addition, there must be
( 8 ) R. Goldstein and S. S. Penner, J . &want. Spectry., 4, 441 (1964).
(9) M. R. Thomas, H. A. Scheraga, and E. E. Sohrier, J . Phys. Chem., 69, 3722 (1965).
COMMUNICATIONS TO THE EDITOR
3 k=l
461
3
a4, k ’ d k , n =
dk, n
k=l
initial solution A,C in a clear manner. We choose dl, 1 = 1 for the reason just pointed out and get
= 1
because of the structure of (1). Under this condition, the matrix D becomes
1
D
= (0
0
D =
!
di, 2 - as, 3 - (al,3 - a3,3 - a1,1)d1,2 a13 - a33 - a12 a32
dl, 1 (1 - dl,1)a3,3!1,3 a3, 3 - a3, 2
+
- (1 - 4,1 ) a 3 .a32 ~ - a1,2 - ( a 3 , ~ - al, 2 as, 3 - a3.2 a l , 3 - a3,3 - al, 2
7
+ a1 , d d ~1 + a3,Z 2
Here dl, 1 and d l , 2 are free selectable parameters. The physical condition that the elements of the new solution A and c should be positive limits the two parameters to ranges the limits of which depend upon the
dl, 2 1 - 3.4948d1, 2 2.4948d1, 2
