COMMUNICATIONS TO THE EDITOR
291
By computer simulation it was shown that an additional single proton splitting of 0.15 G or greater would have been observable in the spectrum of 11. I n summary, we conclude that the paramagnetic species detected in solutions of A'Os'O'-bianthroneis the 1O1l0'-bi-9-anthranoxy radical 11. This radical is an expected intermediate in the photochemical conversion of bianthrone to bianthranol, helianthrone, and mesonaphthobianthrone,B or alternatively, could form through an oxidation-reduction reaction between bianthrone and bianthranol.
The symbols have the meaning : A, equivalent conductivity; c, concentration; a,degree of dissociation; K A , association constant; y, mean ionic activity coefficient of free ions; d, closest distance of approach of free ions, or association distance. A , B, S, and E are familiar electrolyte theory parameters3 which do not depend on the choice of d. On the other hand, J1 and J z are functions of d. The physical meaning which we attach to the parameter d differs from that of Fuoss and coworkers;* we merely remark here that our interpretatied gives an excellent fit of results for 2:2 sulfates in water and removes the need for postulating significant Acknowledgments. We wish to thank Dr. Thomas degrees of association for sodium and potassium chloHarris, who performed some of the initial experiments rides in dilute aqueous solutions.4b Some uncertainty in this study, and Mrs. S. B. Wallon for the synthesis still remains concerning the relationship between the of 9,9'-bianthryl. J parameters and d; to facilitate comparison with results in our earlier paper, we have used equations (6) H. Brockmann and R. Mnhlmann, Chem. Ber,, 82,348 (1949). derived by FernBndez-Prini6 from the Fuoss-Hsiae ( 5 ) Alfred P. Sloan Research Fellow. treatment, but do not wish a t this stage to imply a final L. S. SINGER* choice between the conductivity equations of Pitts? UNIONCARBIDE CORPORATION I. C. LEWIS CARBON PRODUCTS DIVISION and of FUOSS, et aL6 The Fernhndez-Prini expressions CLEVELAND, ONIO 441 01 for J1 and Jzare6 DEPARTMENT OF CHEMISTRY UNIVERSITY OF WASHINGTON SEATTLE, WASHINGTON98106
T. RICHERZHAGEN G. VINCOW'
JI =
Ion Pairing in 2 2 Electrolytes
A/Ai = a (YC In
(1)
+
((Yc)
JI(CyC)
K A =
02;
Jz =
- J2(ac)s''
(1 - (Y)/a2cy2
-log y = 8A(ac)'/'/[1
+ 2Bd(ac)'/']
UI
= [(~db)~/24(ac)]( 1.8147
02
=
08
Sir: In a recent paper Masterton and Brierly' reported conductivity measurements on dilute aqueous solutions of [Co(S&)5NOZ]S04. The results were analyzed using the semiempirical conductivity and activity coefficient equations of Shedlovsky and Davies, respectively, and gave the parameter values A" = 144.9 cm2 ohm-' equiv-', K A = 400 1. mol-l. Although the authors do not claim the highest precision for their results, they are obviously of good quality, and seemed to us to be worthy of further analysis using a more recent conductivity equation. There is considerable current) interest in ion association of 2: 2 salts in aqueous solution,2 and we3 have recently made an extensive reanalysis of conductometric data for dilutje aqueous solutions of simple 2:2 sulfates using the following set of equations.
+E
+
0'3 A"
+
0'4
BiBz
+ 2 In [~d/(ac)'/'] + (2/b3)(2b2 + 2b - 1) ]
+ Bz[~d/(ac)"'] - Bz[(~db)/16(~)'/']X
{ 1.5337 + (4/3b)+ 2 In [~d/(ac)'/']1
Publication costs borne completely by The Journal of Physical Chemistry
--,Y(ac)'"
Am
with
RECEIWDSEPTEMBER 14, 1970
ni = A*
0'1
(2) (3) (4)
+
[b2(~d)3/24(ac)8/'][0.6094 (4.4748/b)
Q4
+ (3. 8284/b2)]
+ 1.938'41 + B ~ B ~ [ K ~ / ( ( Y + C ) I[/B~~] ( K ~ ) ' / C-Y ~ ] [ B ~ b ( ~ d ) ~ / 1 6 ~$5405 y ~ ] [+ l (2.2761/b)] -
= [Bi(Kdb)'/24aC][(2/b3)(2b22b - 1) -
[B2z~db/16Am(~~)1/2][(4/3b) - 2,21941 where b = 4 e a / d D ~ Tand B1 and Bz are, respectively, the electrophoretic and relaxation coefficients of the limiting law. For any selected pair of values of A m and d, an estimate of the association constant K A i s obtained for (1) W. L. Masterton and T. Brierly, J . Phys. Chem., 74, 139 (1970). (2) (a) R. A. Matheson, ibid., 72, 3330 (1968); (b) ibid., 73, 4425 (1969) ; ( c ) P. Hemmes and S. Petrucci, ibid., 73,4426 (1969). (3) E. M. Hanna, A. D. Pethybridge, and J. E. Prue, Electrochim. Acta, in press. (4) (a) K.-L. Hsia and R. M. Fuoss, J. Amer. Chem. SOC.,90,3055 (1968); (b) Y.-C. Chiu and R. M.Fuoss, J . Phys. Chem., 72, 4123 (1968). (5) R. Fernindez-Prini, Trans. Faraday SOL,65, 3311 (1969). (6) R. M. Fuoss and K.-L. Hsia, Proc. Nat. Acad. Sei. U.S., 57, 1550 (1967); 58, 1818 (1968). (7) (a) E. Pitts, Proc. Roy. SOC.A., 217, 43 (1953); (b) E. Pitts, B. F. Tabor, and J. Daly, Trans. Faraday Soc., 65,849 (1969).
The Journal of Physical Chemistry, VoZ. 76, No. 8, 1971
COMMUNICATIONS TO THE EDITOR
292 each experimental point from eq 1 through 4. The average value of K A is then used with the same Am and d values to calculate A(ca1cd) for each point and the standartl deviation for the whole set of data. The value of A” is then altered until the standard deviation betmeen the obserl ed and calculated values of the conductivity is a. minimum. A fresh value of d is then selected and the procedure repeated. This approach not only finds the set of parameters which gives the best fit of the expcximental results but also examines the latitude :wailable in varying the parameters while obtaining an acceptable fit of the data. The generirl patxern of the outcome of our analysis closely follows that found for the 2 : 2 sulfates. From the 28 conductivity values reported by Masterton and Brierlyl the best, fit set of parameters is A” = 144.79 cm2ohm-l equiv-I, KA = 368 1. molR1,and d = 12.5 8, with a standnrd deviation between observed and calculated A values of cr = 0.142 cm2 ohmR1equiv-’. Almost identical pzirameter values are obtained by Justice’s method.* If points with a standard deviation exceeding O.l(% are rejected, the 18 points that remain give A” = 144.76, IfA = 367, d = 12.5 8, with Q = 0.860. The msociation constant is substantially less than the value of 400 1. mol-‘ reported by the original wor1iers.l As we expect from earlier experie n ~ evalues ,~ of only slightly greater than the value of 0.060 can be obtained with other suitable combinationii of the three adjustable parameters, e.g., A” = 144.71, KA =; 320, d = 7,2, G = 0.065, but once the value of one parameter (usually d ) is selected, the fit is very sensitive to the values of the other two parameters, and in particular KA. It is a matter of choice, and of the degree of faith in the experimental data, how far one regards the lowest Q value as locating a unique value of K A , but we emphasize that such an association constant cited without specifying also the other parameters iravolved, and in particular d, is meaningless. The same situation pertains in other case^^,^^ and also when ion pairs are invoked to fit osmotic coefficient data for 2 : 2 electrolyte^.^ Indeed, if the Rjerrum type of treatment is correct and sufficiently accurate to be uaief‘ul, the predicted values for physicochemical properties, but not the association constant, should be virtu:tlly independent of d over some nonzero range.9c The difference between the association constants corresponding to tx-o different values of d represents a difference in the allocation of ions between free and associatedoclnsses. If the values of KA given above for d = 12.5 A and d = 7.2 8, respectively, are inserted in the Bjerrum eqrxa!ion9S1O t~
Kq =
jr 4 aLr2 exp(4e2/drkT) dr
*
Acknowledgment. E. M. H. thanks the University of Basrah for a leave of absence and the Calouste Gulbenkian foundation for a Scholarship. (8) J. C. Justice, Electrochim. Acta, in press. (9) (a) J. E. Prue, “Ionic Equilibria,” Pergamon Press, London, 1966, Chapters 6 and 10; (b) J. E. Prue in “Chemical Physics of Ionic Solutions,” B. E. Conway and R. G. Barradas, Ed., Wiley New York, N. Y., 1966, p 163; (c) E. A. Guggenheim and R. H. Stokes, “Equilibrium Properties of Aqueous Solutions of Single Strong Electrolytes,” Pergamon Press, London, 1969, p 61. (10) J. E. Prue, J . Chem. Educ., 46, 12 (1969). (11) G. Atkinson and 5 . Petrucci, J . Phys. Chem., 67, 1880 (1963), and earlier references therein.
DEPARTMENT O F CEIEMISTRY THEUNIVERSITY READING, U. K.
E. M. HANNA A. D. PETHYBRIDGE J. E. PRUE*
RECEIVED JUNE 19, 1970
Radiation-Induced Chain Isomerization of cis-l,2-Diphenylpropene in Cyclohexane Publication costs assisted by the Air Force Ofice of Scientific Research
Sir: The 1,2-diphenylpropenes, although little studied as isomerization solutes in the y irradiation of organic liquids,’ appear to exhibit, reaction properties which make them preferable to the extensively investigated stilbenes2-4 in such systems. Although this desirable
(5)
they should idea,lly give identical u values. The values are in fact 3.48 arid 3.38 8, respectively. A value of The Journal of Physical Chemistry, Vol. 76, N o . 8 , 1971
3.4 d is about 0.4 A less than the average value for the sim le 2: 2 ~ u l f a t e s which ,~ have association constants3 P roughly half that of [Co(IJH3)tiN02]S04. The value u = 3.4 8 is about 2 8 less than a rough estimate from crystallographic radii suggests, and ion association is certainly considerably more pranounced than corresponds to the Bjerrum model. It is another example of enhanced association between pairs of large ions with a well dispersed charge; causative factors are probably weak hydration of the ions reinforced by dispersion forces. ln9 A few years ago, Atkinson and coworkersll concluded from an analysis in which the Fuoss-Onsager conductivity equation was applied to results for a series of 2 :2 benzene disulfonates that these salts could be treated as essentially completely dissociated. This conclusion is not confirmed by an analysis using our set of equ& tions. For the nine salts Atkinson, el al., studied, we obtain association constants within the range 40-80 1. mol-l with d = 11.0 1.5 8. These association constants are approximately one third of the values for simple ~ u l f a t e s ,but ~ nevertheless significant.
(1) R. A. Caldwell, D. G. Whitten, and G. 9. Hammond, J . Amer. C h m . Soc., 88,2659 (1966). (2) E. Fischer, H. Lehman, and G. Stein, J . Chcnz. Phys., 45, 3905 (1966).
