NOTES
3328 Hg(63P1)-PhotosensitizedIsomerization
length by a U-shaped lamp (Hanovia 87-A-45). This lamp has a Vycor envebpe which limits emission to wavelengths above 2200 A. Both lamp and cell were immersed in a water bath operated at 25.0 *0.1".
of Octafluorobutene-21B by D. M. Graham and Takumi Hikidalb
Results
Department of Chemistry, University of Western Ontario, London, Ontario, Canada (Received December 18, 1967)
Since only small amounts of reactants were available,
it was necessary to carry out the experiments a t pres-
It is now reasonably
ell established that the Hg(63P1)-photosensitizedisomerization of butene-2 may be explained by the mechanism2
+ Hg* T + Hg*
C
+ Hg P* + Hg
-+P*
(qc)
--+
(qt)
P* + pC
+ (1 - p)T
(i)
where C and T refer to the cis and trans forms, respectively, and P* represents the excited olefin triplet state. The probability factor, p, has been shown to be 0.5 from quantum yield measurements, and the ratio of the quenching rate constants is thoqght to control the photosensitized equilibrium such that
K
=
(T)q'(C)e = k,,/k,t = 1.13
A recent investigation3 of the mercury-photosensitized isomerization of the perfluoro compound has indicated the possibility of a much more complex mechanism. The quantum yields reported were less than onefifth of those reported for the hydrogenated compound, and no definite conclusions were reached concerning the establishment of a photostationary equilibrium. Because of the extensive success of cis-trans isomerization reactions in actinometric measurements of triplet quantum yields, it was felt that the isomerization of octafluorobutene-2 warranted further investigation, if only because of its relatively high stability with respect to decomposition at low pressures.
Experimental Section Octafluorobutene-2 (Xatheson Co.) was equilibrated by passing it through a column of activated alumina at 25". The remaining 13% of the cis isomer was separated by glc on a 25-ft, 1/4-in.0.d. pentadecafluorooctyl acrylate column. This column was also used with a flame ionization detector for analysis. Complete baseline resolution of the cis and trans peaks could not be obtained, and areas were calculated using the Gaussian approximation which was shown to hold for an isolated peak. This procedure required greater than 15% reaction to give reliable results. cis-Butene-2 (Phillips Research Grade) was analyzed on a 8 ft X 3/16-in. 0.d. dimethylsulfolane column at 0". Tetrafluoromethane (Matheson Co.) was distilled from silica gel a t -77" to remove traces of impurities which quenched Hg(3P,). The photolysis apparatus consisted of a cylindrical quartz cell, 250 X 42 mm o.d., illuminated along its T h e Journal of Physical Chemistry
sures where complete quenching of excited mercury atoms could not occur. A technique using cis-butene-2 sensitized isomerization as an actinometer under these conditions has been developed and will be discussed more fully in a subsequent p~blication.~Briefly, it is based upon the not unreasonable assumption that the effective lifetime of an excited mercury atom depends primarily upon the rate of quenching in the cell, all external factors remaining constant. In order to eliminate the possibility of pressure-broadening effects, all measurements are carried out in the presence of a constant excess of CFI which has been shown to be virtually a nonquencher. Thus, the determination of the quantum yield for a sensitized reaction of octafluorobutene-2 requires an actinometric run using cisbutene-2 at a concentration such that the calculated quenching rates are equal for the two experiments; this gives the effective number of quanta (IOrf)which are transferred. The required relative quenching rate constant is readily obtained from retardation of cisbutene-2 isomerization by the fluorinated olefin. The competitive quenching plot is given in Figure 1, the slope of which gives directly a ratio of 0.15 f 0.01 for the quenching efficiency of octafluorobutene-2 relative to that for cis-butene-2. These measurements were made on a mixture of 13% cis- and 87% trans-octafluorobutene-2 under conditions such that only slightly better than 1% of the cis-butene-2 and virtually none of the perfluoro compound was isomerized. A number of experiments were carried out to determine the photostationary equilibrium; these are summarized in Table I. Since a t pressures less than 0.1 torr some decomposition was observed, the low olefin pressure runs were carried out in the presence of 50 torr of CF4 which is a very efficient vibrational energy quencher. On the basis of these results there seems to be little doubt that an equilibrium is established, with K = 1.35. This is not too different €rom that observed for the hydrogenated compound. The isomerization rate measurements are given in Table 11. I n calculating the initial quantum yields given in Table 11, it is necessary to correct for the high (1) (a) This work was supported by a grant from the National Research Council of Canada. (b) Province of Ontario Graduate Fellow. (2) R. B. Cundall and T. F. Palmer, R u n s . Faraday Soc., 56, 1211 (1960). (3j D. Saunders and J. Heicklen, J. Phys. Chem., 69, 3205 (1965). (4) D. M. Graham and T. Hikida, to be submitted.
NOTES
3329
Table I : Photosensitized Equilibrium of Octafluorobutene-2 --Initial CiS
presaiure, torrtrans
0 0 0.068 0.066 0 1.94 2.00
0.065 0.070 0 0 1.90 0 0
Final 7% trans
Time, hr
2
55.4 56.0 58.7 57.6 56.5 58.0 58.4
3 2 3 2 0.5 2
Table 11: Isomerization Quantum Yields of Octafluorobutene-2 Octafluorobutene-2, torr
1.96" 1.89 1.08" 0.20" 0.14a 0.105 0. 097a 0.090a 0 . 077b o.o95a,c 0. 077b1c
'Conversion,
%
Time, min
19.9 18.5 18.9 l5.8 18.0 19.1 33.3 116.9 116.7 22.3 l7.7
240 120 90 30 30 15 38 20 10 40 30
Teff x 109, einsteins
I.-]
see-1
8.95 12.4 10.7 4.21 3.22 3.88 3.69 2.24 3.05 2.03 1.72
5 IO (OCIAFiUOROBUTENE-a1(CIS-BUTENE-2)
G 0
0.22 0.26 0.26 0.30 0.32 0.43 0.43 0.41 0.36 0.34 0.30
trans. cis. $0.065 torr of butene-2. All experiments were carried out in! the presence of 50 torr of CFa.
Figure 1. Competitive quenching of octafluorobutene-2 and cis-butene-2.
05
04
Q
degree of conversion required by the analytical technique used. This has been done using an integrated rate equation derived from the mechanism described previously for butene-2. There are two possible ways that this correction may be made depending upon whether the equilibrium constant is a result only of different quenching efficiencies for the cis and trans isomers, or whether it depends primarily on the ratio of the probability factors, p / ( l - p ) . The form of the integrated equakion is different in each case, but the initial quantum yields calculated using these equations differ by less thLan 5%. For reasons given below, the yields given in Table I1 were calculated assuming K = k,,/k,, = 1.35. In determining Iefffor these calculations, the measured relative quenching efficiency of 0.15 was used. If the above assumption is valid, relative efficiencies of 0.114 and 0.19 for the trans and cis isomers, respectively, would be more correct. However, over the pressure range investigated, small changes in quenching rates are, to a certain extent, compensated by a corresponding change in the mean rate of radiative energy loss, and the use of these different quenching efficiencies results in a change of only about 5% in the calculated quantum yields. Whatever corrections are made, the quantum yields exhibit the same behavior as shown in Figure 2. The
a
0-3
0.2
04
OLEFIN PRESSURE
(TORR)
Figure 2. Variation of initial quantum yield with olefin pressure: 0, actd;a, with 0.065 torr of butene-2; 0, @trans; 8, @trans with 0.065 torr of butene-2.
quantum yields decrease with increasing olefin pressure, probably approaching a limiting value. A high concentration limit would be consistent with the results of Saunders and Heicklen,a who obtained roughly constant quantum yields from 0.5 to 6 torr. Their values are, however, smaller since they used a different actinometer and did not attempt to allow for incomplete quenching. Their results also indicate (as does the one value of OtrUnswhich we were able to obtain) that the sum of the quantum yields, @trans, cannot possibly be unity even with any reasonable correction for incomplete quenching. This implies, as these
+
Volume 72,Number 9
September 1968
NOTES
3330 authors have suggested, a barrier to internal rotation in the excited state (or states) produced by sensitization. The olefin pressure dependence of the quantum yields must result from efficient deactivation of the excited state by olefin which competes with internal rotation. Butene-2 appears to be about as effective as the perfluoro derivative. Deactivation by olefin has also been shown to be important in the sensitized isomerization of hexafluorocyclobutene4 and in the photoisomerization of 1,2-dichloroethylene, although the interpretation is less clear in the latter case due to the possibility of chlorine atom catalysis. Since the equilibrium constant is independent of olefin pressure, it appears most likely that the equilibrium constant depends primarily upon the quenching efficiencies of the cis and trans isomers, The change in the probability factors with olefin pressure, that is reflected in the change in quantum yields, must occur in such a way that their ratio remains constant. This would be the case if the barrier t o internal rotation were symmetrical and should result in limiting low pressure quantum yields of 0.5 which are not inconsistent with possible extrapolations on Figure 2.
Formation Constants of Some
2 :2 and 3 :3 Ion Pairs
by R. A. nilatheson Chemistry Department, Victoria University of TVeZlington, New Zealand (Received February 14, 1968)
When calculating the formation constant of an ion pair or molecule from cryoscopic, ultraviolet absorption, or conductance measurements, one commonly uses the Deby e-Huckel formula -log
-y& =
1
A~l~zl/f Bddj
+
(1)
for the activity coefficient of the free ions and, if necessary, one of the following conductance equations: the Onsager limiting law, the Leist equation A=AQ-
a’AQ
((1
+ 2-’l2Bd&
+ ’I)
1
+dT Bddi
(2)
the Robinson and Stokes (RS) equation (eq 2 without the factor + 2-’/”dl/i), Or the Fuoss Onsager (Fo) equation A =
A0
-
(a + @O),/E
+ EC log C + J C
(3)
in which J is a function of the distance of closest approach parameter d. sometimes the value of + he. formation ‘Onstant depends On the figure assumed for d. Thus in water a t 25”, Covington, et aL,l obtained The Journal of Physical Chemistry
for the bisulfate ion K = 95 M-l when d = 5.17 and K = 86 i44-l when d = 3.04 8, while Prue and coworkers2found larger variations of K with d for several sulfate ion pairs involving divalent cations. The model implicit in the calculation of K from experimental data via eq 1 considers pairs of ions of separation3 less than d t o be associated, while those of greater separation are regarded as free. This implies some dependence of K upon d, since when d is increased from dl t o dz a number of pairs of ions formerly considered free become classed associated, thus increasing the value of K . By using Bjerrum’s formula to calculate the number of ion pairs having separations between dl and dz, Guggenheim4 obtained an equation for the variation of K with cl which is consistent with Covington’s results for the bisulfate ion. We shall examine the implications of this equation in regard t o the dissociation of some 2 : 2 and 3 : 3 ion pairs. For a species dissociating into two ions of valency 2, Guggenheim’s equation becomes ZaS/di
Kz - K1 = ~ T N ( Z ~ S ) ~ X-4eXd X
(4)
Z2S/dz
where K t corresponds t o a distance of closest approach d,, N is Avogadro’s number, and S is the length e2/DkT (7.15 for water a t 25”). A moles per unit volume concentration scale is assumed. In Table I me compare values of K Z - K1 for CuSO4 and hIgS04 calculated from formation constants obtained from various experimental measurements with those given by eq 4. Equation 4 gives values of K z - K1 consistently larger than the figures obtained from “experimental” formation constants, especially those derived from conductances via the Leist and Pitts equations. Although agreement between eq 4 and the other experimental figures is better, there are still discrepanciesoin excess of t,he uncertainty in K z - K1,when dl < 10 A. Dunsmore, Kelly, and Nancollass reported precise conductance measurements for dilute aqueous solutions of several rare earth cobalticyanides and ferricyanides from which they calculated, via the limiting laws, ion pair formation constants of about 5.5 X lo3 M-’. In the case of such 3 :3 aqueous ion pairs, eq 4 requires a substantial variation of K with d, unless d in the vicinitv of the Bierrum critical distance (32 A). We have tierefore reanalyzed the data for lanthanum ferricy(1) A. K. Covington, J. V. Dobson, and W. F. K. Wynne-Jones, Trans. Faraday Soc., 61, 2057 (1965). (2) (a) P. G. M. Brown and J. E. Prue, Proc. Roy. Soc., A232, 320 (1955); (b) W.G.Davies, R. J. Otter, and J. E. Prue, Discussions Faraday Soc., 24, 53 (1957); (c) R. J. Otter and J. E. Prue, ibid., 24, 106, 123 (1957); (d) “Ionic Equilibria,” J. E. Prue, Pergamon Press Ltd., London, 1966; (e) R. J. Otter, Ph.D. Thesis, University of lg60(3) By separation, we mean the distance between ionic centers. (4) E. A. Guggenheim, Trans. Faraday Sac., 62, 2750 (1966). (5) H.S. Dunsmore, T. R. Kelly, and G. H. Nancollas, ibid., 5 9 , 2606 (1963).
