COMMUNICATIONS TO THE EDITOR
954
Table I : Intercepts and Slopes of 2/@cous. ( M ) at 3660 A (2C1-l X 10-3) Temp, OC
37 150 225 300
I
I
8
s
(measd)
(calcd)
(measd)
(calcd)
20.0 4.6 3.3
15.2 4.1 2.7 1.9
17.6 3.05 1.13 0.97
17.6 2.91 1.56 0.93
0.8
the excited singlet state molecules, a result which strengthens the assumption that (4) occurs on every collision. At intermediate wavelengths such as 3340 and 3130 A, plots of 2/&0 vs. (AI) should still be linear in accordance with (L4)1 the slopes decreasing as the wavelength is shortened. Again this is in agreement with observatio11.~’~ The mechanism predicts that at these intermediate wavelengths the ratio of singlet to triplet methylene should vary with temperature as well as with wavelength. This is a prediction which could readily be tested experimentally. -~
~
~
~~~~
(9) B. T. Connelly and G. B. Porter, Can. J . Chem., 36, 1640 (1958).
where Wj is the apparent mass of the solvated ion of the j t h type, tj is the transference number, zj is the ionic charge, uo is the acoustical velocity amplitude, and d is a correction factor for diffusion. The ionic partial molal volume Pj in dilute solution corresponds closely to the intrinsic ionic volume minus the decrease in volume of the surrounding water molecules arising from electrostriction. Consequently, it can be readily shown that Wj = Mj - Pjsowhere Mj is the molecular weight of the unsolvated ion and so the solvent density. The combination of the partial molal volume of the composite electrolyte with ionic vibration potential data permits the calculation of Pi. Table I summarizes data for 0.03 M electrolytes. Experimental details will be published later. False effects which heretofore have interfered to some extents-9 have been eliminated as significant factors. The values for Pj have been calculated from the over-all partial molal volumes P and the transference numbers ti a t low concentrations or infinite dilution as compiled by Parsons.lo A comparison of the values for Pj for a given ion evaluated from measurements in different electrolytes indicates a consistency of approximately
A. N. STRACHAN DEPARTMENT OF CHEMISTRY LOUGHBOROUGH COLLEGEOF TECHNOLOGY D. E. THORNTONTable I : Ionic Tibration Potentials at 200 kc and 22’ and Partial Molal Volumes LOUGHBOROUGH, LEICESTERSHIRE, ENGL.4ND
RECEIVED JANUARY 31, 1966
v,
%O/ao, PV
Electrolyte
Determinatian of Ionic Partial Molal Volumes
KC1
from Ionic Vibration Potentials’
Sir: Ionic vibration potentials were predicted by Debye2&in 1933 and detected some 16 years later.2b While Debye proposed the effect as a means for evaluating the masses of solvated ions, subsequent cons i d e r a t i o n ~have ~ ~ ~ indicated the effect to depend on the apparent masses (mass of solvated ion minus the mass of free displaced solvent). An important application for this effect, however, has not been called to attention, i.e., the determination of absolute ionic partial molal volumes. The purpose of this communication is to point out this application in the hope that wider interest in this effect will be generated. If ionic atmosphere effects are neglected, for frequencies small compared to the ratio specific conductance to dielectric constant, the amplitude (@o) of the ac potential differences between points separated by a phase distance of one-half wavelength is4 (PO =
3.10 X 10-7~~Z(tjWj - d)/zj
The J O U T T Uof~ Physical Chenistrg
KC1 LiCl NaCl
(volts)
RbCl CsCl NaBr KBr NaI
KI
sec/cm
0.45 -0.4
0.8 1.8 5.1 8.1 -3.2 -1.5 -6.7 -4.4
tt
0.82 0.34 0.40 0.49 0.51 0.50 0.39 0.49 0.40 0.49
t-
0.18 0.66 0.60 0.51 0.49 0.50 0.61 0.51 0.60 0.51
v+,
8-,
cm*/ mole
cma/ mole
cmJ/ mole
18.1 17.0 16.4 26.5 31.9 39.2 23.5 33.7 35.1 45.4
-5.2 -7.3 -7.7 3.1 10.7 15.1 -4.9 4.7 -3.1 5.6
23.3 24.3 24.1 23.4 21.2 24.1 28.4 29.0 38.2 39.8
(1) Research supported by the U. S. Office of Naval Research. (2) (a) P. Debye, J . Chem. Phys., 1, 13 (1933); (b) E. Yeager, et al., abzd., 17, 411 (1949). (3) J. Hermans, Phil. Mug., [7]25, 426 (1938); 26, 674 (1938). (4) J. Bugosh, E. Yeager, and F. Hovorka, J . Chem. Phys., 15, 592 (1947). (5) A. Hunter and T. Jones, PTOC.Phys. SOC. (London), 79, 795 (1962). (6) A. Rutgers and R. Rigole, Trans. Faraday SOC.,54, 139 (1958).
(7) E. Yeager, J. Booker, and F. Hovorka, Proc. Phys. SOC.(London), 73, 690 (1959). (8) A. Weinmann, ibid., 73, 345 (1959). (9) R. Millner, 2. Elektrochem., 65, 639 (1961); private communication, 1965. (10) R. Parsons, “Handbook of Electrochemical Constants,” Butterworth and Co. Ltd., London, 1959, p 59.
COMMUNICATIOKS TO THE EDITOR
955
= t 2 cni3/mole. Since the most data are available for C1-, we recommend the use of the average value 23.4 f 0.5 cm3/mole for this ion as a basis for the evaluation of the absolute partial molal volumes of other ions from existing relative values. (11) On leave from CNRS-CRM, Strasbourg, France.
kr’ (I = 0.1)
kf (I = 0)
kr.
hf-1 seo-1
Cavasino (T-jump
R. ZANA” E. YEAGER
CONDENSED STATECENTER WESTERN RESERVEUSIVERSITY CLEVELASD, OHIO
Table 1 : Comparison of ‘Rate Constants for Nickel Malonate at 250 and Zero Ionic Strength sec -1
7 X l o 4 (+z13%) -4.6
X lo6 44 (11353,)
method)
Our work
(4.2
x
(P-step method)
=!c
0.4) 42
+4
106
RECEIVED DECEMBER 27, 1965
of pH and ionic strength and in the presence of an organic indicator in one case. Comments on the Formation Kinetics of the Nickel Monomalonate Complex
Sir: A paper which recently appeared in this journal’ has described a temperature-jump relaxational study of the kinetics of ionic association and complex formation in nickel malonate solutions. Rate constants were reported at three temperatures and a t ionic strength I = 0.1 M for the reaction of divalent nickel ion with malonate (Mal2-) and bimalonate (HMal-) ions. It is interesting to note that a portion of the results obtained by Cavasino are in excellent agreement with those obtained previously2 by us with the pressure-step method. We determined the rate constants for the reaction kr
Ki(H20)G2+-l- Mal2-
(H20)rNiMal
+ 2H20
kr
at 25’ and zero ionic strength. The forward and reverse rate constants were found to be 4.2 X lo6M-’ sec-l and 42 sec-1, respectively. In order to compare these with Cavasino’s results a t the same temperature and ionic strength of 0.1, we must estimate the activity coefficient of free nickel and malonate ions (f*) a t 0.1 ionic strength. The semiempirical generalized Davies equation3 for activity coefficients had been used in our work to reduce our measurements t o zero ionic strength, and also by Cavasino to calculate some ionic activities. (This equation has been shown4 to give reliable estimates of ionic activity coefficients up to ionic strength 0.1.) The result for a divalent electrolyte in a medium of ionic strength 0.1 is f-+S 0.39. By dividing Cavasino’s bimolecular rate constant Icr ’ by fi2, the two sets of data become comparable. The results are shown in Table I. The two sets of data agree exceptionally well. It should be borne in mind that they were obtained with different relaxation methods under different conditions
Acknowledgment. The work a t Western Reserve University was supported in part by the Office of Naval Research under contract KO. Nonr 1439(04). F. P. Cavasino, J . Phys. Chem., 69,4380 (1965). (2) (a) H. Hoffmann, J. Stuehr, and E. Teager, paper presented at the May 1964 meeting of the Electrochemical Society, Toronto (Extended Abstracts: Theoretical Section, Vol. 2, Abstract 187, pp 98-104); (b) H. Hoffmann, paper presented at the Bunsentagung, May 1964, Berlin [See 2.Elektrochem., 68, 895 (1964)l; (c) H. Hoffmann, J. Stuehr, and E . Yeager, Technical Report 27, Office of Naval Research, Contract Nonr 1439(04), Western Reserve University, Cleveland, Ohio, June 15, 1964 [see Ann. Rev. Phys. Chem., 16,178 (1965)]; (d) H. Hoffmann, J. Stuehr, and E. Yeager, “Study of Relaxation Effects in Electrolytic Solutions with the Pressure-Step Method,” B. E. Conway and R. G. Barradas, Ed., “Chemical Physics of Ionic Solutions,” John Wiley and Sons, Inc., New York, N. Y., 1966, pp 255-279. (3) C. W. Davies, “Ion Association,” Butterworth and Co. Ltd., London, 1962, p 41. (4) C. W. Davies, ref 3, pp 39-45. (1)
H. HOFFYANN J. STUEHR
DEPARTMENT OF CHEMISTRY WESTERNRESERVEUNIVERSITY CLEVELAND, OHIO RECEIVED JASUARY 12, 1966
Solvent Shifts in Charge-Transfer Spectra of Tropylium Ion Complexes
Sir: We have examined the effect of solvent on the charge-transfer maxima of complexes of a cationic acceptor, tropylium ion,’ with two aromatic donors, pyrene and phenothiazine. This is the first study of solvent shifts of positive ion-neutral molecule complexes, and these shifts may be compared with those of other types of complexes which have recently been reported. 2-4 I n our study, the choice of solvent is limited by the properties of the salt, tropylium fluoroborate: it is insoluble in relatively nonpolar solvents, and it reacts (1) A t . Feldman and S. Winstein,
(1961).
J. Am. Chem.
Soc., 83, 3338
Volume 70, Number 3 March 1966
