COMMUNICATIONS TO THE EDITOR
952
absence of breaks in the curve at atom fractions 0.25, 0.33, and 0.50 indicates the absence of LiTee, LiTez, and LiTe, respectively (see corresponding phase diagram of Sa-Te), in the system. If the data could be obtained through the 0.66 atom fraction, a sharp drop in emf would appear, the emf approaching -0.7 v on the plot in Figure 1 or 0 v with respect to a liquid lithium anode. The observed cell potentials were converted to those for the cell
I
Li(1) LiC1-LiFI Li in Te ( X L ~= atom fraction Li in Te)
(1)
by adding 0.7055 v a t 798°K (see ref 6). The standard states are taken to be Li(1) and Te(1) in the cell environment (saturated with electrolyte). Therefore, the excess chemical potential of Li in Te a i the cell temperature (T = 798 f 1°K) may be calculated ApLiE
=
-FE - R T In XLi
(2)
where F is the value of the Faraday and R the gas constant, These results are shown in Table I. The , average excess chemical potential, A ~ L is~-~37,145 135 cal/mole. A least-squares fit of the data to a quadratic function of XLi resulted in the equation A p ~= i ~-36,568
+
- 5736X~i 11,676X~i~ (cal/mole) (3)
The standard deviation of this equation is 29 cal/mole. The cell reaction (1) may be written Li(1)
+ l/zTe(l) (saturated with solid LizTe) + '/~LizTe(s) (4)
for an over-all electrode composition of X L ~2 0.39. For this reaction we may write
AG = -FE = '/zAGr"
- '/zRT In X T ~ '/2ApTeE
(5) where XTe is the atom per cent Te in the Li-Te liquid saturated with LizTe(s), A ~ is Tthe ~excess ~ chemical potential of Te in the same liquid, and AGro is the standard free energy of formation of Li2Te(s) from the elements. The value of A ~ was T calculated ~ ~ from the Gibbs-Duhem relationship. A constant value of A p ~ gave i ~ A ~ =T 0, ~while ~ eq 3 yielded A ~ =T -50 cal/mole. Using either value, the standard free energy of formation of LizTe(s) a t 798°K was calculated to be -77.9 kcal/mole. The standard deviation of this value is estimated as 0.4 kcal/mole. Table I : Calculated Excess Chemical Potential of Li in Te Cumulative total coulombs added
Calculated over-all concentration of Li in Te (atom fraction)
Observed cell potential, v
660 1260 1860 2460 3060 3660 4460 5260 6060 6860 7860 8860 9860 12060
0.056 0.10 0.14 0.18 0.22 0.25 0.29 0.32 0.35 0.38 0.41 0.44 0.47 0.52
1,0912 1.0573 1.0392 1,0244 1,0175 1.0075 0.9966 0.9854 0.9756 0.9686 0.9666 0.9644 0.9646 0.9644
-APLF! cal/mole
36860 37025 37 150 37181 37300 37289 37263 37190 37112 37075
. . .a
. . .a . . .a
. . .a
' Two-phase region existed at this over-all composition (see Figure 1 and text). Acknowledgment. The interest of Dr. J. A. Plambeck in this work is gratefully acknowledged.
C O M M U N I C A T I O N S T O THE E D I T O R The Mechanism of Ketene Photolysis
Sir: The photolysis of ketene has often been used as a source of methylene radicals,1*2yet the mechanism of the photolysis is still in some doubt.* Any proposed mechanism must account for the following facts. (a) At short the formed in the photolysis are almost entirely singlet, The Journal of Physical Chemietry
whereas a t long wavelengths they are predominantly tri~let.~ At an intermediate wavelength, 3200 A, (1) T. Terao and S. Shida, Bull. Chem. SOC.Japan, 37, 687 (1964). (2) F. Casas, J. A. Kerr, and A. F. Trotman-Dickenson, J . Chem. Soe., 1141 (1965). (3) W. A. Noyes, Jr., and I. Unger, Pure A p p l . Chem., 9,461 (1964). (4) S. Ho, I. Unger, and W. A. Noyes, Jr., J. Am. Chem. &c., 87, 2298 (1965).
~
~
COMMUNICATIONS TO THE EDITOR
953
71% of the radicals formed are singlet and 29% t r i ~ l e t . ~(b) At long wavelengths, plots of twice the reciprocal of the quantum yield of carbon monoxide against ketene concentration are linear over a wide range of concentration and show no signs that the quantum yield reaches a limiting value a t high concentrat i o n ~ . The ~ ~ ~intercepts and slopes of such plots decrease as the temperature is raised or the wavelength shortened. At high temperatures or short wavelengths the intercepts approach unity and the slopes fall to zero. Neither the mechanism of Strachan and Noye# nor that of Porter and Connelly' will account for (a), whereas the mechanism proposed recently by Ho, Unger, and Noyes4 will not account for (b). A mechanism which will account for both (a) and (b) is the following.
+ h~ = CHzCO(S) CH&O(S) = CH2(S) + CO CH&O
CH&O(S) = CH&O(T) CH,CO(S) n4 = CH&O
+
+M
CH&O(T) = CH2(T)
+ CO
CH&O(T) = CHzCO CH2(S or T) CH2CO = C2H4
+
+ CO
(1)
(2) (3)
(4) (5) (6) (7)
where (S) denotes a singlet state and (T) a triplet state. Application of the usual steady-state assumption leads to 2 _ '$20
B+ + k3k/(k5 + + k3
h
k0)
state molecules, in contrast to the excited singletstate molecules, will be in thermal equilibrium with their surroundings, undergoing several collisions before either (5) or (6) occurs even at the lowest pressures normally employed. At short wavelengths, k2 will be larger than k3 and also larger than k4(R4) at ordinary pressures, in which case Z/&O = 1 and a = 1, in agreement with observations a t 2700 A.4J At sufficiently long wavelengths, k2 will become either zero or at least very much smaller than k3 so that
and a = 0. Plots of 2/&0 us. (11) will be linear and the slopes and intercepts will decrease with temperature. At 3660 A the experimental evidence is that a is well below 0.5, though whether it is essentially zero is not ~ e r t a i n . Assuming ~ that it is and that (C) is valid, an estimate can be made of the values of the various rate constants at this wavelength. At 23" the intercept of the plot of 2/&0 vs. (11)is 19.5 and the slope has the value 24.8 X l o 3 Between 27 and 154" the inverse slope increases with an apparent activation energy of 4500 cal The latter will be accounted for if (3) has a small apparent activation energy of 1500 cal mole-' and the activation energy difference E5 - E6 equals 3500 cal mole-'. Utilizing this information and assuming a collision diameter for ketene of 4.0 A, we calculate k4
=
9.61 X 1092/T 11-' see-'
k3
=
1.66 x 109e-15W/RT sec-' k5/k6 =
and k2
a = k2
+ k3kS/(k5 +
k0)
(B)
where +CO is the quantum yield of carbon monoxide and a is the fraction of methylenes formed which are singlet. The rate constant for (2) is assumed to have the form k2 = ~ ( 1- Eo/E)S-l.s It will therefore decrease from a limiting value Y when E is large (short wavelengths) to zero when E approaches or becomes less than Eo (long wavelengths). Reaction 3 will also increase with E but much less rapidly than reaction 2 and remain slow even a t high E because of the change of spin involved, Reaction 4 probably occurs on every collision. Reactions 5 and 6 will both be slow, (5) because it has an activation energy and (6) because it involves a change of spin. Therefore, the triplet-
20.7e-35M/RT
With the above values, the intercept and slope of 2/&0 us. (34) at any temperature can be calculated. We have photolyzed ketene at 3660 A at four temperatures between 37 and 300" and Table I shows the experimental and calculated values of the intercepts ( I ) and slopes (8) of such plots. The agreement is reasonable and lends support to the proposed mechanism. We have also photolyzed ketene at the same wavelength in the presence of two inert gases, sulfur hexafluoride and octafluorocyclobutane. We have found both to be equally as efficient as ketene at deactivating ~ _ _ _ _ _
(5) F. H. Dorer and B. S. Rabinovitch, J . Phys. Chem., 69, 1964 (1965). (6) A. N. Strachan and W. A. Noyes, Jr., J . Am. Chem. Soc., 76, 3258 (1954). (7) G. A. Taylor and G. B. Porter, J . Chem. Phys., 36, 1353 (1962). (8) N. B. Slater, "Theory of Unimolecular Reactions," Cornel1 University Press, Ithaca, N. Y., 1959.
Volume 70, Number 3 March 1066
COMMUNICATIONS TO THE EDITOR
954
Table I : Intercepts and Slopes of 2/@cous. ( M ) at 3660 A (2C1-l X 10-3) Temp, OC
I
I
8
s
(measd)
(calcd)
(measd)
(calcd)
37 150 225 300
20.0 4.6 3.3 0.8
15.2 4.1 2.7 1.9
17.6 3.05 1.13 0.97
17.6 2.91 1.56 0.93
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 accorthe slopes decreasing as the wavelength dance with (L4)1 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 JOUTTU~ of 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.
