COMMUNICATIONS TO THE EDITOR
1942
against concentration is linear and extrapolates to A,. For the data of Table I the A’-c plots are linear and give the values of limiting conductances shown in parentheses. The last column of the table gives AA = A’ - A0
which is seen to be proportional to concentration, within experimental error. The slope of the A’-c plot for Bu&PF6 is 2500; if K A = 0, J ( a ) = 2500, whence d = 5.44. This value seems reasonable; if d were 6.00, K A would be 1.3. Hence we conclude that association is
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a t most slight for this salt. On the other hand, the slope for Me4NPF6is 1730; if K A is set equal to zero, J ( a ) = 1730, a value which leads to (& = 2.90, which definitely seems too small. If d = 5.00, the slope 1730 leads to K A = 5.0 for this salt. Our conclusions, based on these results, are that Me4NPFBis slightly associated in acetonitrile and that Bu4NPF6shows negligible association. Both conclusions are those expected on the basis of the structure of the salts and the dielectric constant of the medium. Therefore the association2 of KPF6 in water represents a special case of specific ionic interaction.
COMMUNICATIONS TO THE EDITOR THE FORMAL REDUCTION POTENTIAL OF THE EUROPIUM(II1)-EUROPIUM(I1)SYSTEM Sir: The formal reduction potential of the Eu3+-Eu2+ system was determined by McCoy1 in a potentiometric study of the cell: Pt I Eu(COOH), Eu(COOH)~ HCOOH N KC1In.c.e. The value obtained was -0.43 v. 11s. n.h.e. During a chronopotentiometric study of the europium couple in various supporting electrolytes, we obtained evidence for preferential complex formation between europium(II1) and formate ion in aqueous solution. The formation of such a complex would shift the equilibrium potential to more negative values. This leads us to believe that McCoy’s value is in error. I n order to estimate the true formal reduction potential we carried out a chronopotentiometric study with M europium in the noncurrent reversal of 3 X complexing medium, 1M sodium perchlorate-perchloric acid (pH 2.08) a t 25.0’. The Eu3+-Eu2+ system is chronopotentiometrically irreversible in this medium, and the absolute rate theory must be applied according to the method of Delahay,2in order to obtain the formal potential. This technique requires a linear plot of E, the observed potential, us. a log term in t, the time of electrolysis. The resulting straight line is extrapolated to the potential at which the time equals zero (E2=,0). The standard heterogeneous rate constants, k o f , h and kob,h, for the reduction and oxidation, respectively, may then be obtained using the equations
+
+
kof,h = (io/nFCo)exp(n,FE+o/RT) kob,h =
(iO’/n’FC0)/eXp((l - CX’)na’Ff?’+O/RT)
ErO = RT/nF In
(3)
(kr,ho/kb,ho)
The results are summarized in Table I. TABLE I STANDARD FORMAL REDUCTION POTENTIAL OF THE Eu3+-EuP+ COUPLEIN NONCOMPLEXINQ MEDIUM
+
Run no.
I I1 I11 IV
kor.h, om. sec.-1
6.03 x 10-lo 1.42 x 10-9 1.60 X l o w 8 6.64 x
k b , om. sec.-1 2.26 X 10” 5.47 x l o o 1.81 X 10’ 1.29 X 10’
ErO us. Ag-AgC1-NaC1 (satd.)
-0.566 V. -0.566 V. -0.535 V. -0.549 V . average = -0.554 v.
On the basis of these results, we would recommend the use of the value of -0.55 v. us. Ag-AgC1-NaC1 (satd.) (-0.35 v. us. n.h.e.) for the formal reduction potential of the Eu3+-Eu2+ couple in noncomplexing medium. Further studies of the electrochemical behavior of the Eu3+-Eu2+ system in sodium perchlorate-perchloric acid medium, as well as in other supporting electrolytes, are in progress. A more detailed paper describing experimental techniques and results will be forthcoming. CHEMISTRY DEPARTNEXT LARRYB. ANDERSON SYRACUSE UNIVERSITY DANIELJ. MACERO SYRACUSE 10, X. Y. RECEIVEDJULY 15, 1963
THE SQUARE WAVE APPROXIMATIOK AND
(1)
RADICAL LIFETIME MEASUREMEKTS
(2)
Sir: Rotating sector techniques are widely used for determining individual rate constants and/or radical lifetimes. The method is particularly well suited for photochemical work where pure square wave pulses of radiation are readily obtainable. The greater penetration of ionizing radiation, particularly yradiation, makes it virtually impossible to obtain a square wave form in a rotating sector experiment. Thus, penumbral effects distort the result. The magnitude of the distortion is unknown. Ghormley’s results on the electron beam decomposition of water, for instance, show steady-state peroxide concentrations
where io is the current density, Co the original concentration of the oxidized species in the solution, n the number of electrons in the over-all electrode reaction, and n, the number of electrons in the rate-determining step; F , R, and T have their usual significance. The primes in eq. 2 indicate that the appropriate parameter is for the oxidation process. Using these values, the formal reduction potential of the system may be calculated from the relationship (1) H. N. McCoy, J . Ana. Chem. Soc., 58, 1577 (1936). (2) P. Delahay, “New Instrumental Methods in Electrochemistry,” Interscience Publishers, Inc., New York, N. Y., 1954, Chapter 8.
