840
D. R. STRANKS AND J. K. YANDELL
Figure 7, it can be deduced that the parent ion formed by electron impact in reaction l l a has in excess of 2.0 eV internal energy, probably in the form of vibrational energy. As already shown (reaction 6), charge transfer is more probable for this ion by a factor of 30 than an ion-molecule reaction resulting in a change of identity. Thus only a small fraction of the total reaction of this ion leads to the higher mass condensation products. Probably, in this case, any intermediate complex formed by an intimate collision is sufficiently excited that it fragments almost entirely t o the original reactants. The parent ion produced by charge transfer in reaction 12a, however, is expected to differ considerably in internal energy from that produced by direct electron impact and it is apparent that ion-molecule reactions leading to condensation products (by way of an intermediate complex having less excitation energy) are much more favorable for this ion. It seems clear from the data presented in Tables I V and V that the collision complexes produced in reactions l l b , 12, and 14 must have different amounts of internal energy. It also appears that with increasing pressure, the complexes formed in all these processes fragment similarly, since the product distributions all approach the same ratios at higher pressures. This presumably indicates that, at some pressure, all the complexes are reduced to
the same level of internal excitation by collisional deactivation. Our results clearly establish that excitation energy of the reactants can dramatically affect the internal energy of the reaction complex. For the vinyl chloride system, however, the translational energy of the reacting ion appears to be much less important than internal energy. There remains t o be explained the fourth-order dependence observed for the c4H6c1+ ion in the highpressure study. This is possibly explained on the basis of an extra reaction step which would logically involve reaction 7b. That is, two protonation sequences would precede the production of Cd&Cl+, and this is perhaps understandable if the C2H4C1+ precursor is highly excited. This additional reaction step would further isolate the C&Cl+ yield with respect t o the influence of the various reaction parameters discussed in this work, and, indeed, the relative yield of this product seems to be very little affected by these factors.
Acknowledgment. The authors express their gratitude to Professor A. G. Harrison for access to his data prior to publication and also for stimulating discussions of ion-molecule reaction problems. They are also indebted to Dr. J. L. Beauchamp for permission to cite unpublished results from his doctoral thesis.
Chemical Effects of Charge-Transfer Absorption. I. The Photoinduced Chain Reaction between Thallium(1) and Thallium(II1) by D. R. Stranks and J. K. Yandell Department of Physical and Inorganic Chemistry, The University of Adelaide, Adelaide, S o u t h Australia 5001 (Received J u l y 1 6 , 1 9 6 8 )
Ultraviolet irradiation of 204T1-labeledthallium(1) -thallium( 111) solutions induces rapid exchange with quantum yields ranging from 2 to 30 or higher. Initiation is due to charge-transfer absorption in Tlaq3+and T10H2f producing a thallium(I1) chain carrier. Rate constants for the propagation reactions of thallium( 11) with thallium(1) and thallium(II1) are derived. Chain termination is largely quadratic disproportionation of thallium(II), but a t low light intensities, a linear termination reaction is more important. The relevance of these observations to the thermal mechanism for thallium( I) -thallium( 111) exchange is discussed.
Introduction The high-intensity absorption band of metal complexes, which normally occurs in the 2500-3200-A region, is often described as a charge-transfer An alternative molecular orbital description4 is one of electronic excitation from a bonding orbital to a nonbonding or antibonding orbital. Whereas the chargeThe Journal of Physical Chemistry
transfer microsymmetry is linear suggesting that the excitation involves only a single ligand and the central (1)R. 8 . RIullikerl, J. Am. Chent. SOC.,74, 811 (1952). (2) J. S . Murrell, Quart. Rev. (London), 15, 191 (1961). (3) F. 8 . Dainton, Special Publication KO.1, T h e Chemical Society, London, 1954,p 18. (4) 0. K. Jfix’gensen, “Absorption Spectra and Chemical Bonding in Complexes.” Addison-Wesley Publishing Co., Reading, Mass., 1962.
CHEMICAL EFFECTS OF CHARGE-TRANSFER ABSORPTION metal, the molecular orbital description suggests that all ligands are involved. The two descriptions are however very similar in that they both represent a transfer of charge from ligand to metal occurring with a large transition moment, as reflected in a high molar extinction coefficient. I n accord with these interpretations, the absorption of light in the charge-transfer bands of transition metal, lanthanide, and actinide complexes is known t o initiate a variety of oxidation-reduction reaction^.^ A basic mechanism for these photochemical reactions may be envisaged as the homolytic dissociation of an excited state into a reduced metal ion and either an oxidized ligand or an oxidized associated anion, I n the presence of suitable scavengers or in the event that the initial products are mutually stable, a reduced metal ion is observed as a product. Since dissociation of the excited state is in competition with other energy loss processes operating within a solvent cage, such as fluorescence, internal conversion, intersystem crossing, and energy transfer, the primary quantum efficiency for homolytic dissociation is often significantly less than unity. Additional recombination of dissociative fragments outside the solvent cage will further reduce the quantum yield observed for net product formation. The known photochemistry of metal cations other than those of the transition elements, lanthanides, or actinides, is very sparse since only a single well-defined oxidation state of main-group elements usually exists in aqueous solution. However in perchloric acid media the +1 and +3 oxidation states of thallium can coexist and in the ultraviolet spectra both of these oxidation states exhibit high-intensity bands which may be assigned t o charge-transfer transitions. At 2537 A, the principal absorbing species in 1 M perchloric acid is the hydrolyzed thallium (111) species T10H2+ and a minor absorption occurs owing t o the aquated species Tlaq3+. Absorption by TI,,+ only becomes significant at wavelengths shorter than 2537 A. Absorption of 2537-Lk quanta by thallium (111) solutions would be expected to induce the reactions T10H2+ ~1,,3+
+ hv
+ hv
-+
+ OH TP+ + OH + H+ 3
T12+
841
tributory reaction
+
Tlaq3+ Tl,,+
---f
2TlaqZ+
(1%)
The present study has sought evidence for the photolytic formation of the unstable intermediate oxidation state thallium (11) by investigating the photocatalysis of the thallium (I)-thallium (111)homonuclear electronexchange reaction
*TP
+ T1I @ *Tll + T1"'
detected by isotopic labeling with 204Tl. If reaction I accurately represents the initiation reaction induced by 2537-A photolysis of a thallium (I)-thallium (111) mixture, then this could be followed by chain-propagation reactions involving a T12+chain carrier
+ TP+~t *TP+ + TP+ *T12++ T1+ @ *T1+ + TIz+
*TF+
(kIrI)
(k~) and a quadratic chain-termination reaction.
TP+
+ w+
-+
TI++ TF+
(kt)
Our generalized treatment of photoinduced chain reactions7 suggests that, for this anticipated mechanism, the quantum yield for the over-all electron-exchange reaction is
(1) where $ex is the observed rate of electron exchange per absorbed light intensity, ie., Rex/Iabs. The second term of eq 1 represents the contribution to electron exchange from the termination reaction in the absence of any propagation reaction. Alternatively, if the T12+ chain carrier were to undergo linear termination by reactions with a trace impurity or at the vessel walls, both proceeding at the same rate, as in
+
T12+ S' then
$ex
---t
+ S"
T1I and T12+
---f
TIIII
(ICt')
would be independent of light intensity.
In the presence of added Tlaq+, scavenging of all hydroxyl radicals which escape primary and secondary recombination reactions would occur.6
Tl,,+
+ OH
T12+
+ OH-
The 2537-A photolysis of a thallium (111)-thallium( I) mixture should therefore result in the over-all initiation reaction
+ Tl,,+ + hv -+
$1
T10H2+
with a quantum yield
$1,
2T12+
+ OH-
(I) together with a minor con-
This study has therefore aimed at a quantitative (5) A . W.Adamson, W. L. Waltz, E. Zinato, D. W.Watts, P. D. Fleischauer, and R. D . Lindholm, Chem. Rev., 68, 541 (1968). (6) M . Anbar and P. Neta, Intern. J. A p p l . Radiation Isotopes, 16, 277 (1965). (7) D . R. Stranks and J. K. Yandell, "Exchange Reactions" I A E A , Vienna, 1965. Volume 73, Number 4
April I060
D. R. STRANKS AND J. K. YANDELL
842 evaluation of the catalytic effect of thallium(I1) on the TI (I)-TI (111) exchange reaction. The findings are relevant to the general question of whether this thermal exchange reaction proceeds by a concerted transfer of two electrons or by a one-electron transfer to form thallium (11) followed by rapid disproportionation to thallium(1) and thallium(II1); the latter reaction is the quadratic termination reaction described by kt.
Experimental Section Thallous perchlorate solutions were prepared by dissolving BDH thallous carbonate in dilute perchloric acid. Thallic perchlorate solutions were prepared either by dissolving BDH thallium(II1) oxide in 5 perchloric acid Or by the anodic Oxidation Of perchlorate solutions. m'ater which was twice distilled from KMn04 and KzCrO, was used for all purposes. The use of vacuum-distilled perchloric acid, instead of AR grade perchloric acid, made no observable difference to measured quantum yields. The z04Tl tracer was prepared in both oxidation states by treatment of thallous carbonate irradiated in the HIFAR reactor, Sydney, Australia. Photolyses were performed in a cylindrical silica reaction vessel (2.5-cm diameter, 1-cm length) located in a constant-temperature water bath. Solutions in this vessel could be stirred and deaerated, but as these parameters did not affect quantum yields, these procedures were not followed in most photolyses. The 2537-A line, isolated from the output of a Hanovia low-pressure spiral mercury arc, was used as the principal light source. The arc was aligned with the reaction vessel on an optical bench. Light from the arc passed through 3 cm of water before it impinged on the reaction vessel thereby completely filtering out the 1849-A radiation from the arc. Incident light intensities were determined by the ferrioxalate method of Hatchard and Parker.* A correction of 10% was necessary for light of wavelengths greater than 2537 A which is photoactive in the ferrioxalate system but is not absorbed by the thallium solutions. An Osram 400-14' xenon arc coupled to a Bausch and Lomb high-intensity grating monochromator was used as a light source for measurement of quantum yields as a function of wavelength. The slits used with the monochromator were claimed by the manufacturer to give 90% emission within f 5 0 A of the dialed wavelength. A 1-cm path length silica spectrophotometric cell, located in front of the exit slit such that all the reactant solution was illuminated, was used as a reaction vessel. The intensity of the light absorbed by each thallium species was calculated from the measured incident light intensity and individual extinction coefficients either reported by Waind and Rogers9 or determined experimentally. The Journal of Physical Chemistry
0501li c I
03-
0.2
I
I
10
20
I
30 TIME
I
I
I
10 lrnin I
50
60
I
70
Figure 1, rate plots: (*) preirradiated, [Tl(III)] = 0,005 M , [Tl(I)]= 0,0051 M , Tl(I) labeled; (B) not preirradiated, [T~(III)] 0.0051 M , [TI(I)] = 0.005 M , Tl(II1) labeled.
Fractions of exchange were determined by a separation schemelo based on thallium(1) chromate precipitation which in thermal exchanges gave less than 2% zero-time exchange. Both oxidation states were subjected to radioactive assay in a conventional GM liquid counting assembly. Rates of exchange were then determined from the customary log (1 - F ) vs. time plots. Initial rate experiments with carefully purified reagents gave excellent linear plots but small induction periods of a few minutes were observed; L e . , extrapolation of log (1 - F ) to F = 0 gave positive time intercepts. These small induction periods evidently arose from traces of impurities, probably organic in nature. The induction periods were completely removed by preirradiating reactant solutions at 2537 A for 1 hr prior to the addition of 2 or 3 drops of the 204Tltracer. The observed half-times for exchange were identical for preirradiated solutions and for solutions exhibiting small induction periods (Figure l ) . Quantum yields quoted below all refer to freshly prepared reagents subjected to this preirradiation treatment.
Results Half-times for the thermal thallium (1)-thallium (111) electron exchange at 25' range from 20 to 100 hr, depending on the reactant concentrations. When irradiated a t 2537 A, half-times for the electron-exchange system fell within the range 4-120 min. Consequently, no significant correction for the thermal-exchange rate was necessary. Uncertainties in observed quantum yields, &x, are (8) 0. G. Hatchard and 0. A . Parker, Proc. Roy. SOC.(London), A235, 518 (1956). (9) G. M. Waind and T. E. Rogers, Trans. Faraday Soc., 5 7 , 1360 (1961). (10) I. R. Jonasson and D . R . Stranks, Electrochim. Acta, 13, 1147 (1968).
CHEMICAL EFFECTS OF CHARGE-TRANSFER ABSORPTION
843
~
Table I: Dependence of lOS[Tl(I)I, M
0.11 0.26 0.50 0.51 1.00 2.00 5.00 7.50 10.0 15.0
&ex
on Thallium(1) Concentration at 25", 0.005 M Tl(III), and 1.1 M HClO, 11/z,
min
10sl,ba,
einsteins 1.-1 min-1
32 f 4 31 f 3 29,30 33,33,31,31,29 42 28 28 23 11 20,a 22" 11
&exb
@exc
1.51 3.12 4.90 4.65 4.61 6.94 10.0 12.1 7.90 13.6 8.75
12.9 11.9 12.1 11.8 12.0 12.0 11.9 11.3 37.7 11.4 34.3
Psxd
1.55 3.10 4.90 4.62 4.61 6.9 9.47 12.1 11.8 13.4 12.7
1.88 3.75 5.95 5.62 5.61 8.43 12.1 14.7 14.3 16.3 15.4
This thallium(II1) solution was prepared from dissolution of T1203; all other solutions were from dissolution of Tl&Ol and anodic oxidation. = Re./Iaba. is the quantum yield for absorption by both TI,,*+ and TIOH2+,corrected to Isba = 12.0 X 10-6 einsteins I.-' min-I. = 12.0 X 10-6 einsteins I.-' rnin-'. d &,=2 is the quantum yield for absorption only by T1OH2+,corrected to a
+ex
compounded from errors in both I a b s and R e x . Errors in Isba arise from both the experimental measurement of Io and the estimate, made from measured extinction coefficients, of the fraction absorbed of the incident light intensity. A total random error of &3% and a systematic error up to &9% is estimated in l a b s . The latter error is dependent on the magnitude of I a b s / I o . Rates of exchange, as evaluated from log (1 - 8') vs. time plots, were subject to variations not exceeding * 5 % for thermal rate measurements, but a variation of &lo% arose for photochemical rates. At a constant incident light intensity, the random error in $ex will be &lo%, but, a t different light intensities, a random error of &12% applies. It may be shown that even for solutions of high optical absorbances, the correction to (pex for nonuniform light absorption lies within the error limits and no correction for this effect was applied. The errors quoted above are expressed at the 90% confidence limit. Under all conditions of reactant concentrations, light intensities, and temperature, the observed quantum yields for exchange exceeded unity and typically fell in the range 2-30. The general chain characteristics of the photochemically induced exchange are thereby established. Quantum yields were unaffected by the presence or absence of dissolved oxygen or by mechanical stirring. The photochemical exchange was extraordinarily sensitive to traces of Fez+ and Fe3+ and the reaction could be virtually stopped at concentrations exceeding 10 p M . Dependence of +ex on Thallium(I ) Concentration. with thallium( I) Table I summarizes the variation of concentration. The observed value of 4ex( =Rex/Iabr) is calculated from the absorbed light intensity due to TIas+,Tlaqa+, and T10H2+. The quantity 'lex refers to quantum yields calculated on the basis of absorption by both T1aq3+ and T10H2+ and treating TLq+as an inactive absorbing species. Similarly refers to quantum yields based on absorption by T101-12+as the
11
0
/
0
li
1(
ol,
t
t
1
I
0.02
I
0.04
I
I
I
I
I
0.06
0.08
0.10
0.12
0.14
[arri]
I
0.16
mote t:'
Figure 2. [TI(I)] dependence.
only active chromophore. Both 'lex and values have been normalized to a constant absorbed light intensity using the experimental intensity exponents summarized below. Figure 2 shows that, a t constant [TlIII], values of $lex (and also $ex and $2ex) are approximately linear a t low [TlI] and approach a limiting "plateau" value a t high [TP]. This functional behavior is consistent with eq 1 for the important condition
k~[Tl']
+ k"'[T1'I1]
>> 2(ktIab~$I)~'~
such that eq 1 simplifies t o the form
A convenient form of (3) t o test the experimental results is
Figure 3 illustrates a plot of l / ~ vs. $ l/[Tll], ~ ~ and the Volume 75, Number 4 April 1969
844
D. R. STRANKS AND J. K. YANDELL
Table 11: Intensity Exponents of Photocatalyzed Exchange at 25"; 1.1 M He104 10*IT(I)I.M
102[T(III)],M
Number of measurements
Range of 1O8z,ba, einsteins 1.-1 min-1
10.0 5.0 0.51 0.32
0.51 0.60 4.0 4.1
7 10 5 5
0.90-36.2 0.96-73.8 2.24-32.3 3.08-130
n
($1
-0.27 -0.34 -0.37 -0.44
n
= 0)
($1
f 0.05 f 0.02 & 0.05 f 0.03
-0.28 -0.35 -0.40 -0.51
= 0.6)
f 0.05 f 0.02 f 0.05 f 0.05
log Iabs.
Figure 4. dependence. [Tl(I)]= 0.050 M ; [TI(III)]= 0.0051 M .
0
2
4
1 [E] [
6 mole-'
8
10
x lo2
Figure 3. [Tl(I)]dependence. a = l/$L; b = l/&
linearity of the plot, within the experimental errors, suggests that 4ex>> $1 under the experimental conditions. A value of klll/kI = 1.6 f 0.5 is derived from the ratio of slope to intercept of this plot. Equation 4 appears to be applicable over a 150-fold variation in [TI']. An expression analogous to (4) would also apply to the linear termination mechanism described by eq 2. The applicability of these alternatives is decided by the intensity dependence of qb,,. Equation 3 predicts that a t vanishingly low [TlI] 4ex tends to 41. Extrapolation of (pex at [TP] 5 0.005 M yields a value of cpl = 0.5 f 0.3; the relatively large systematic and random errors in +ex, together with difficulties of working at low concentrations, preclude a really satisfactory estimate of 41. Intensity Dependence of hex. A chain mechanism terminated by a quadratic OF mutual reaction requires an intensity exponent of -0.50 (eq 3) while a linear termination reaction would require r$eex to be independent of Jabs (eq 2 ) . Four series of measurements were undertaken; each series was conducted at constant [Tl'] and [TlIII] and over as wide a variation of light intensity as possible. One such series is illustrated in Figure 4 wherein the intensity exponent n in the equation rpex
- 41 =
(constant) (I&b8)n
is deduced from a graphical plot of log The Journal of Physical Chemistry
$ex
us. log
labs.
In this instance n = -0.34, assuming 41 rv 0, and n = -0.36, assuming the approximate value deduced above, namely, $1 = 0.5. Intensity exponents deduced in this manner are summarized in Table I1 where it is seen that the -0.5 exponent required by a quadratically terminated chain mechanism is approached a t higher light intensities. I n each series, plots of 4exus. Iabs-1'2 were linear a t high values of l a b s but deviations from linearity occurred a t low light intensities. It is suggested that quadratic chain termination is the predominating contributor to the over-all mechanism of the chain reaction. However some linear termination accounts for the lower intensity exponent under some experimental conditions. I n the case where termination is partly quadratic and partly linear, our generalized treatment of chainexchange reactions' yields an explicit solution for the dependence of 4exon reactant concentrations and I a b s which cannot be cast in a form against which the experimental data can be tested graphically. However, the relative rates of the quadratic to the linear termination reactions, kt[T12+]/kt', can be deduced numerically by the method described in the Appendix. The dashed curve in Figure 4 is based on this procedure and the curve reproduces the experimental points within the experimental error. This numerical analysis shows that the ratio of the rate of the quadratic termination reaction to that of the linear termination reaction varies from 0.26 at the lowest light intensities employed to 5.0 at the highest light intensities. Thus a t the highest light intensities some 10% of all Tl(I1) is being scavenged by the linear termination reaction (s). This analysis shows that under these conditions an
845
CHEMICAL EFFECTS OF CHARGE-TRANSFER ABSORPTION Table 111: Variation of berwith Thallium(II1) Concentration a t 25', 0.050 M Tl(I), and 1.1M HClOd
43ex
1.1 2.1 5.1 l0,l
0.336 0.333 0.330 0.560 0.550 0.691 0 785 0.940
49 47 23 20 17 17 17 21
15.1 20.1 42.4
~
intensity exponent of -0.44 would be exhibited by the chain reaction at the high range of light intensities while this would fall to -0.15 at the lowest range of light intensities. The numerical analysis also confirms that the plateau dependence of deXon [TlI] (Figure 2) could not arise from the increased importance of a linear termination reaction at high [TI']. Any reduction in 4ex from this source is within the experimental uncertainty in This plateau must arise from the balancing effect of the two propagating reactions described by ~ I I and I kI. Attempts were made to determine the rate constant for the quadratic termination reaction kt by rotatingsector techniques. Flashing times down to 5 msec were employed but the reduction in 4exfrom the value for uninterrupted illumination was only of the order of 10%. It was concluded that kt was of the order of diffusion-controlled rate constants (1O'O M-l sec-1). The difficulties of achieving significantly shorter flashing times and of entirely eliminating linear termination reactions precluded further work in this direction. Dependence of 4ex on Thallium(III) Concentration. The variation of +ex with thallium (111) concentrations
l2
t
T
5.18 5.54 12.1 15.6 18.4 20. I 20.7 24.2
2.86 5.14 11.3 18.4 18.4 23.2 26.3 31.5
2.35 4.21 9.28 15.1 15.1 19.1 21.6 25.8
6.30 6.73 14.8 19.0
22.4 24.4 25.2 29.2
ranging from 0.0011 to 0.0424 M was investigated a t a constant thallium(1) concentration of 0.050 Ill. Since thallium (111) is the principal light-absorbing species, variation of [TlIII] involves simultaneous variation of a reactant and absorbed light intensity. Table I11 shows that +lex and 42ex(referring to total thallium(II1) and T10H2+ absorption, respectively) increase with increasing [Tl'II] and approach a limiting plateau value a t high [ T P ] . Equation 4,based on a purely quadratic termination chain mechanism, requires that at constant [TlI], l / ( ~-#&)Iabs1/2 ~~ should be linear in 1/[T1II1]; this is tested in Figure 5 with the reasonable assumption that 41 >~I,
Equation A1 may then be rearranged to the form Iabs
= A4a2
&ex
(A21
where A = kt/&F2 and B = kt'/2&F. The experimental data have been approximated by the empirical expression (e.g., Figure 4) log 4ex= n log Isba
+ constant
(-43)
so that the intensity exponent n is deduced from the relation
where and A x 2 are the limit values of and the and l a b s z . Substicorresponding values of I a b s are tution by means of (A2) in (A3) yields
Hence
where p
4ex 1 = 1On-l 4exa
The ratio of the rates of the quadratic termination reaction to the linear termination reaction is then
Equation A6 may then be curve fitted to the experimental values using known values of 4exand with the ratio 2kt[TP1]/kt' as an adjustable parameter. Within a particular intensity exponent the limits to 4ex2 will therefore be derived for an assumed ratio of the rates of quadratic to linear termination.
where the constant F is given by
F
=
~ ~ ~ I [ T ~ ' ] ~ I I I [ T(k1[T1'] ~'II]/
+~III[TI~~~])
(17) K. G. Ashurst and W. C . E. Higginson, J . Chem. Soc., 3044 (1953).
Volume 7.9, Number 4 April 1869
