966
M. TAMRES, W. K. DUERKSEN, AND J. M. GOODENOW
tively at least by the different moments of inertia for the different axes of the methyl iodide molecule.
Calculation of Moments
Approximate calculation showed that this contribution could be greater than the value of the moment itself, in some cases. This line of approach was therefore abandoned.
An attempt was made to calculate momentss from these results. The calculated errors, however, we found to be very large (50-100%). Moreover, these errors did not include a contribution due to the physical necessity of truncating the integrals to reaaonable limits.
Acknowledgment. We wish to acknowledge the help of Dr. W. C. Krueger and others in this laboratory and also the Kational Science Foundation for financial help under Grant GP-3411. C. E. F. wishes to thank the Argentine Government for financial support.
Vapor-Phase Charge-Transfer Complexes. 11. The 21,
I, System'
by Milton Tamres, Walter K. Duerksen, and John M. Goodenow Chemistry Department, University of Michigan, Ann Arbor, Michigan
481 04 (Received August 69,1967)
The 21z Q 1 4 equilibrium has been investigated in the vapor phase a t 110-140" by analysis of the ultraviolet absorption band. The extinction coefficient of Iz and the product of the extinction coefficient and constant of dimerization of 1 4 have been determined as a function of wavelength. The band maxima for 1 4 and Iz,at -2450 and 2700 A, respectively, show blue shifts relative to those observed in nonpolar solvents, with the shift for 14 being much larger. Thermodynamic constants for 1 4 formation were not obtained, but it is concluded that AE must be quite small.
Introduction Iodine is known to have a weak absorption in the ultraviolet that fails to obey Beer's law.2 The observed dependence of absorbance on concentration has been attributed to a monomer-dimer e q ~ i l i b r i u m . ~ - ~ Quantitative studies of the spectral and thermodynamic properties of this system have been made in cc14,4v6 and the solvent effect on the system also has been investigated.5 Analysis of the data is based on the assumption that the complex is very weak, so that, for the concentrations used at room temperature, the dimer concentration is negligibly small compared to that of monomer. Nevertheless, the dimer species contributes significantly to the total absorption because its extinction coefficient must be several orders of magnitude larger than that for the monomer.6 The observation that the enthalpy of dimerization is low, ~ accord with the between - 1 and -2 k c a l / m ~ l , ~is- in assumed weak nature of the complex. Information about the monomer-dimer equilibrium in the vapor phase is very limited. Apparently, the only work in this area is that of Kortum and Friedheim,3 who studied the system quaIitatively at 340". Their absorption curves are those for the composite contribuThe Journal of Physical Chemistry
tion of both monomer and dimer, but the study was not carried to the point which allowed separation into contribution from each species. The present investigation was undertaken for two reasons. First, it was hoped to obtain spectral and thermodynamic properties of the system in the vapor state for comparison with the properties in solution. Second, it was thought essential to establish the extent to which the formation of dimer could interfere in interpreting data on charge-transfer studies in the ultraviolet region where iodine is used as the acceptor. In the latter case, for example, the composite monomerdimer band maximum at 2670 A (for an iodine conM at 340°)3 is very close to centration of 9.238 X
(1) Taken in part from the Ph.D. Thesis of W. K. Duerksen, University of Michigan, Ann Arbor, Mich., Aug 1967. (2) J. Groh and S. Papp, 2. Phyaik. Chem. (Frankfurt), 149, 153 (1930). (3) V. G. Kortum and G . Friedheim, 2. Naturforsh., 2A, 20 (1947).
(4) (a) P. A. D. De Maine, J . Chem. Phya., 24, 1091 (1956); (b) Can. J . Chem., 3 5 , 573 (1957). (5) M. M. De Maine, P. A. D. De Maine, and G. E. McAlonie, J . Mol. Spectry., 4, 271 (1960). (6) R. M. Keefer and T. L. Allen, J . Chem. Phys., 2 5 , 1059 (1950).
VAPOR-PHASE CHARGE-TRANSFER COMPLEXES
967
t
recently reported for the the maximum of 2680 benzene-iodine complex in the vapor phase.' Experimental Section Apparatus and Procedure. Spectrophotometric measurements were made on samples of iodine vapor of varying concentration. For the higher concentrations, a 10.0-crn cell was used. The cell, cell housing, and temperature control unit have been described elsewhere,* For the lower concentrations, a multireflection unit (White cell) was used, with the mirrors placed outside the 25.0-cm cell to avoid attack by the iodine. Four passes were used to give an effective path length of 100.0 cm. The design of the cell housing and temperature control for the multireflection unit was rather similar to that for the smaller cell.'Zab For both cells, data were taken using a Beckman DU spectrophotometer, Model 2400. The cells were filled by metering out and transferring the iodine using a Pyrex vacuum line.8b The amount of iodine actually in the cell was determined after the spectrometric measurements were completed. After having cooled to room temperature, the iodine was dissolved in n-heptane. An aliquot of the resulting solution was diluted, and the concentration of the second solution was found from a spectrophotometric measurement at the maximum of the visible iodine absorption band (5250 A). Reagent. Iodine (Baker Analyzed reagent) was purified by twice subliming it from a finely pulverized mixture with potassium iodide. Results In the 10.0-cm cell, spectrophotometric measurements were made on eight samples of iodine vapor at four temperatures and eight wavelengths. One of the samples was measured over a much wider spectral range, and the data obtained at two temperatures are shown in Figure 1. There is an apparent m!ximum at 2660 8, which is quite close to that of 2670 A observed by Kortum and Friedheim3 at 340" for the lowest of their iodine concentrations. It had been shown4t6that, for the case where dimerization is weak, the apparent extinction coefficient, eaPp, is expected to be given by an equation of the type
where A is the absorbance, b is the cell path, [IZl0is the initial concentration of iodine, e~~ and are the extinction coefficients of iodine monomer and dimer, respectively, and KD is the equilibrium constant for dimer formation. The plot of tappvs. [ I 2 1 0 should give a straight line .whose intercept is equal to E I and ~ whose Plots at two temperatures are slope is equal tto &€I4. shown in Figure 2. The intercepts and slopes, determined by the inethod of least squares, are compiled in
0.5
!
g 0023 t
OIt
I 1
I
I
I
2800
3000
3200
I
2400
2200
2600
3400
x (A1 Figure 1. Iodine vapor-phase absorption spectra: [I210 = 2.28 X 10-8 M , cell length = 10.0 cm.
20
10 5
10
20
15
25
[12Iox lo4
Figure 2. The apparent extinction coefficient, eapp in 1. mole-' cm-', us. initial iodine concentration, [I210 in mol l.-l, at 2640 A.
Tables I and 11, with the probable errors calculated at the 50% confidence level. Within the wavelength region in Table I, it is to be noted that there is a systematic decrease in eIa with increasing temperature. However, as seen in Table 11, no systematic change with temperature is found for the product KDar,. ~~
Table I: The I1 $ IC System. Least-Squares Analysis for Plots of eapp us. [Iz]o: Best Intercepts"
2500 2540 2580 2600 2620 2640 2660 2700 a
9 . 6 f0.5 12.0 2C 0 . 5 14.2 f 0 . 5 15.3f 0 . 5 16.0 f 0.5 16.6 i 0 . 4 17.1 f 0 . 5 17.5 i 0 . 4
9.2 f0.6 11.610.5 13.9 f 0 . 5 15.010.5 15.82C0.4 16.5f0.4 16.9i0.4 17.350.4
8 . 5 f 0.6 11.0f0.6 13.3f0.6 14.5f0.5 15.0f0.4 15.8f0.4 16.4f0.3 16.82C0.4
7 . 1 f 0.6 9.4A0.6 11.9f0.6 13.1*0.5 13.8f0.4 14.8f0.4 15.6f0.4 15.92C0.4
Probable errors calculated at the 50% confidence level.
(7) F.T. Lang and R. L. Strong, J . A m . Chem. Soc., 87,2345 (1965). (8) (a) J. M. Goodenow and M. Tamres, J . Chem. Phya., 43, 3393 (1965); (b) M.Tamres and J. M. Goodenow, J. Phya. Chem., 71, 1982 (1967).
Volume 79,Number 3 March 1068
M. TAMRES, W. K. DUERKSEN, AND J. M. GOODENOW
968
Table I1 : The IZe 1 4 System. Least-Squares Analysis for Plots of eapp us. [I&: Best Slopes X lo-@ l5
2500 2540 2580 2600 2620 2640 2660 2700
2.67zkO.25 2 . 6 2 r t 0 . 2 6 2 . 6 7 r t O . 2 5 2.62 f 0 . 2 4 2.701t0.25 2 . 5 5 f 0 . 2 6 2.62zk0.23 2.47rt0.22 2 . 6 1 1 0 . 2 2 2.38rtO.20 2.50?cOO.21 2.29 f 0 . 1 9 2 . 4 0 z k 0 . 2 3 2.19 f 0 . 1 8 2.16 r t 0 . 2 1 1.95 & 0 0 . 1 7
2.68rt0.29 2.64-1: 0.26 2.54i0.28 2.39i0.22 2.42f0.19 2.27f0.19 2.13f0.17 1 . 9 1 k 0.18
2.95-1: 0.30 2.921t0.29 2.741t0.29 2.6OIt0.23 2.56rtO.20 2.391t0.19 2.12 1 0 . 1 8 1.96-1: 0.17
5
A - ~1~b[I210 = K D ~ I ~ ~ [ I Z ] O ~ (2)
The Journal of Physical Chemistry
I
w g2500 l ,
,
0 ~
~
,
3500
3000
(AI
Figure 3. The pure 1 2 extinction coefficient (in 1. mol-! cm-1) as a function of wavelength (A): A, extrapolated value a t 110" from data in 10.0-cm light path; ,. direct measurement at 100' for [I210 = 7.16 X 10-6 M in 100.0-cm light path; and 0, ref 9 at 101' for [Iz],,= 3.09 X 10-4 M.
The relative contribution of the I4 complex is obtained directly from the relation
Discussion It does not seem possible to separate the product KDQ, into its components in order to compare the effect of solvent on each term. If instead of using the approximation KD = [I4]/[Iz]02r as was done in deriving
I;
2000
Probable errors calculated a t the 50% confidence level.
A plot of the left side of equation 2, where €Izis determined by extrapolation using eq 1, os. the square of the initial iodine concentration gave a straight line passing through the origin. The I4 contribution becomes appreciable for iodine vapor above 10-3 M , but at conM , as indicated by the centrations of the order of arrows in Figure 2, ea,,, 'v €I2, within experimental error limits, and the vapor in this spectral region can be considered to behave essentially as iodine monomer. By using a path length of 1 m, it, is possible to work M and with iodine concentrations of the order of hence obtain q2 directly. Two such studies were made: (1) four passes through a 25.0-cm multireflection cell of total volume 240 ml, where the Iz concentration was determined spectrophotometrically (see the Experimental Section), and ( 2 ) a 91.3-cm cell of total volume 1.56 l., where the Izwas weighed directly into a breakseal tube.9 Comparison of the various studies of E I is shown in Figure 3. The extrapolated values for t12as a function of X are in good agreement with those measured directly, and this gives support to the validity of eq 1. The good agreement also supports the validity of the independent analytical methods used to determine iodine concentration. It was o b ~ e r v e d for , ~ an M , that E I ~deiodine concentration of 3.09 X creased with increasing temperature in the region 2440-2880 A and increased outside this region on either side, which is indicative of temperature broadening. The extrapolated values for B I ~actually follow this trend (Table I). Similar observations have been reported for the vapor Iz band in the visible regionlo and for the solution I2band in the ultraviolet region.6
t
eq 2,4t6one used KD = [ L ] / ( [ I Z ]-~ becomes
KD(eI4 - 2~12)b[I2]0~ = (A - Ao)
where €1,
A0
[&I2),
then eq 2
+
= e ~ ~ b [ I ~ ] oOn . rearranging and considering
>> €I,, this becomes
In this study, b is large, as is the product KmI, (Table 11). Since [ I 2 3 0 is quite low and, undoubtedly, KD is small, it follows that
~
Dropping the last term in eq 4 results in an expression similar to the Scott" modification of the BenesiHildebrand12 equation. Person13 already has discussed in detail the difficulty of trying to obtain separate values for the equilibrium constant and the exbinction coefficient when
Separation of the terms in KD€14could be achieved by using very narrow cells and high iodine concentrations (and assuming unit activity coefficients). These are impractical conditions to attain in the vapor phase. They also are not attainable in solution because of the (9) This study was done a t the University of Chicago, Chicago, Ill.; M. Kroll and M. Tamres, unpublished work. (10) P. Sulzer and K. Wieland, Helv. Phys. Acta, 2 5 , 653 (1952). (11) R.L. Scott, Rec. Trau. Chim., 7 5 , 787 (1966). (12) H. A. Benesi and J. H. Hildebrand, J . A m . Chem. Soc., 71, 2703 (1949). (13) W. B. Person, ibid., 87, 167 (1965).
VAPOR-PHASE CHARGE-TRANSFER COMPLEXES
969
limited solubility of iodine. Therefore, the attempt4b to separate terms from data of iodine in CC1, at 17" into KD (2.28 l./mol, which seems high) and €1, (389 I l./mol cm, which seems low) probably is not correct. 16A better procedure is that of Keefer and Allen,6 who b estimated that, in CC14, K D lies between 0.5 and 0.05 2 12rt l./mol and €1, < 40,000 l./mol cm. From a general w relation of enthalpy and free energy for weak iodine x" 8 complexes, they calculated, at 25.5", that K D 'v 0.13 4, 16 X lo3 l./mol cm. l./mol and e ~ PV It is possible, however, to compare the KD~I,product l l J 1 l l l ' l l ' l l 0 in the different studies. In the vapor phase, at 3000 3500 2500 2500 (around A,), and 110" is 2.67 X 10 1 / mol2 (AI cm (Table 11), while in CC1, solution at 2880 8 and Figure 4. Comparison of the shape of the 1 4 absorption band: 25.5", Keefer and Allen6 found a rather comparable A, CCla solution at 8" (ref 4 ) ; and B, vapor phase at 1 1 0 O . value of 2.04 X l o 3 1.2/mo12cm. De Maine4 reports similar figures in CC14,but there is a small dependence within experimental limits, between 100 and 12Q0, exof K D E I , on the nature of the ~ o l v e n t . ~It should be cept at low wavelengths (below 2300 &. noted in Table I1 that, even for the 50% confidence The shape of the 1 4 bands in solution and in the vapor level, the error is of the order of 10%. are compared in Figure 4. Because of the different In solution, the KDtr, product shows a small but procedure used here to calculate KDEI,,as compared to nevertheless systematic temperature dependence which the least-squares method used to calculate the data in permits e v a h t i o n of A H , assuming temperature inI and 11, the results in Figure 4 and in Table I1 Tables dependence of eI4. The values reported in CC14 are not the same. In the figure, the result for &I4 at solution, -1.96 f 0.15, -1.52 A 0.29, and -1.0 -I: 110" and A , is only 2.16 X lo3 1.2/mo1z cm. Consider0.2 kcal/mol, re~pectively,~-~ show that A H is low ing the error limits, the values obtained by the two pro(and also show that experimental variation probabIy cedures cannot be considered to be significantly different does not permit determination to much better than from each other or from the solution value. 3~0.5 kcal/mol). The AH'S in several nonpolar The band maximum in cc14has been reported at hydrocarbon solvents lie in about the same range.5 28806 and at 2935 & 4 , 5 and in n-hexane it is around 2775 In the absence of specific heat data, it is not possible to In the vapor, the band maximum is approximately estimate the change in AH with temperature, but 2450 8. This is a relatively large blue shift, and is assuming temperature independence in A H and simitypical of the large effects observed for weak CT comlarity in results between vapor and solution, A E near plexes.' Caution should be given that the true magni110" would be less negative than the above quoted tude of the shift may be in considerable error. It values by -0.8 kcal/mol. Thus, A E may be too small should be noted that there already is some variation in to be determined within the experimental limits of the 1 4 band maximum in CC14.4-6 This arises the reported method, as is suggested by the random variation in because the shape of the band is determined from the KDCI, with temperature (Table 11). Another reason for absorption data by subtracting the IZ contribution, and suspecting that A E may be quite small is the fact that, it is sensitive to small variations in a,. The same situafor only a slightly higher concentration range, contribution applies in the vapor phase, so that the magnitude of tion of dimer t o the absorption is observed even at 340°n3 the shift may not be reliable to better than 100 8. The shape of the 1 4 band can be obtained by plotting By contrast, the shift in the band maximum of the the slopes in eq 1 us. wavelength, as was done in the soluiodine monomer is much smaller, from 2800 1 in CC1, tion ~ t u d i e s . ~ -In ~ the present case, because of the ~ o l u t i o n ~ to 2700 ~ 8 in the vapor (Figure 3). Maxima random temperature variation of the slope, it was for in hydrocarbon solvents are difficult to obtain bethought preferable to use the absorbance data taken on cause of the onset of contact charge transfer (CT).5 At a single iodine sample and subtract out the contribution the maximum, €1, in the vapor phase at 110" is 18 l./mol of monomer at each wavelength. As seen from eq 2, cm. From the Kortum and Friedheim3 data for iodine dividing the data in Figure 1 by b[IzJO2and that in M , at which vapor at 340" and [I2],, = 9.238 X Figure 3 by [IzIO, and subtracting, gives KDEI,as a funcconcentration eapp and (1% should not be too different, an tion of wavelength. The data in Figure 4 used for the upper limit of 14 l./mol cm is set,', which is in reasoncalculation were those which correspond to [I& = 7.16 ably good agreement with that of the present study, X M and 100" in a path length of 100.0 cm. This concentration ii3 well below that where any significant I4 contribution occurs (Figure 2). At this concentration, (14) L. Mathieson and A. L. G. Rees, J. C h e m Phys., 25, 753 no temperature dependence of absorption was observed, (1956),estimate a value of -16 l./mol om from these data, N
H
.
Volume 72, Number 8 March 1968
S. BJORKLUND, N. FILIPESCU, N. MCAVOY,AND J. DEGNAN
970
considering the error limits of the methods used and the difference in temperature. Although the thermodynamics of the equilibrium could not be established, complications in future vaporphase uv studies of iodine complexes do not seem serious. First, by using iodine concentrations of 2 M , the formation of 1 4 can be completely ignored. Second, for larger concentrations, in those cases where the complexes are weak so that the per cent of iodine complexed is small, valid correction of the total ab-
sorbance can be made by subtracting the absorbance curve of iodine of the same concentration as is used in complex formation. For these reasons, the analysis of Lang and Strong' on the benzene-iodine system is valid. Only in the case of high iodine concentration and strong complexation would special consideration be necessary.
Acknowledgment. This work was supported by grants from the National Science Foundation, NSF GP3691 and GP-6429 Research.
Correlation of Molecular Structure with Fluorescence Spectra in Rare Earth Chelates. I.
Internal Stark Splitting in Tetraethylammonium
Tetrakis(dibenzoylmethido) europate(111) by Sven Bjorklund, Department of Physics, The George Washington University, Washington, D.C.
Nicolae Filipescu, Department of Chemistry, The George washington University, Washington, D . C.
N. McAvoy, and J. Degnan Goddard Space Flight Center, N A S A , Greenbelt, Maryland
(Receioed August bo, 1967)
The internal Stark splitting in the emission spectrum of tetraethylammonium tetrakis(dibenzoylmethido)europate(III) in microcrystals at 77'K was analyzed in detail treating the ligand field as a perturbation on the free ion levels. The complete equivalence between crystalline field and a molecular (ligand) field in chelates with respect to the splitting of the intra-4f levels allows the use of equivalent operator techniques in the calculation of ligand field parameters. These parameters were derived from the splitting in the 'F1 and 'F2 levels of the Euaf ion without assuming a known molecular geometry, and their values establish the configuration of the emitting species. In addition, the ligand field parameters are used to calculate interatomic distances and bond angles. The method developed for deriving and verifying the geometrical arrangement, interatomic distances, and bond angles from fluorescence spectra proves to be a powerful tool.
Introduction Narrow-line fluorescence is observed in certain Eu complexes when excited with light absorbed by the organic ligand as a result of intramolecular energy transfer. The absence of broad-line fluorescence characteristic of rare earth ions incorporated in nonhomogeneous surroundings (e.g., glasses) indicates the presence of the same environment for all Eu ions similar to that present in doped single crystals. The Journal o j Physical Chemistry
The present work shows that the splitting of the 'F levels of Eu3+ ion observed in the fluorescence spectra of organic chelates can be effectively explained in terms of a first-order perturbation produced by the electrostatic effect of the ligand field on the complexed europium ion. Furthermore, we propose to determine the ligand field parameters in tetrakis-p-ketoenolate chelates from experimental data without assuming any one of the possible octacoordinated models as being
