1160
DOUGLAS P. FAYAND NEILPURDIE
Ultrasonic Absorption in Aqueous Salts of the Lanthanides. 111. Temperature Dependence of LnSO, Complexation by Douglas P. Fay1and Neil Purdie2 Department of Chemistry, Oklahoma State University, Stillwater, Oklahoma 7407.4 (Received January 89, 1969)
The rates of formation of the trivalent lanthanide monosulfate complexes have been measured as a function of temperature for the ions Ce-Ho. Activation parameters and stepwise enthalpies and entropies in a multistep mechanism are presented and discussed in the light of other available data. Partial molal volume changes are calculated for the slow step of substitution into the cation coordination sphere, and for lanthanum the volume change for the total reaction is calculated and compared with AVT obtained from a study of the pressure dependence of the dissociation constant. There is sufficient contributory evidence to support a multistep mechanism in which the rate-controlling step is dissociative or Sx1.
Introduction I n the continuation of previous studies on complex formation of the trivalent lanthanide the rates of complexation of the monosulfates of the ions Ce-Ho have been measured as a function of temperature. The objectives of this study were to determine the activation parameters from the temperature dependence of the rate constants, which would permit a comparison to be made with the results for the water exchange reaction' and with values for the same cations with other ligands,*r9and to explore the possibility of determining kinetically the thermodynamic parameters for each step in the overall mechanism. A dissociative (SN1) mechanism has been proposed from such observations as similarity in solvent exchange and substitution rates4 and from the linear ~ o r r e l a t i o n ~ ~between ~ o ~ " the free energy of activation, AG*, and the free energy of complexation, AGO. Similar activation energies for exchange and substitution mould be further confirmation of such a mechanism in which the rate of solvent exchange is paramount. Knowledge of the thermodynamic parameters for the individual steps could contribute to the understanding of the structure of complexes if these results could be correlated somehow with the equivalent parameters for the overall process meai sured by classical methods.
Experimental Section The preparation of solutions and sound absorption measurements have been previously described. Solution temperatures were maintained constant to =t0.05".
Results The effect of temperature on the relaxation frequencies and amplitudes at 5 and 45" are shown in Figure 1 for samarium only; the solid lines are calculated single relaxations. Concentrations and relaxation frequencies are given in Table I. (A complete listing of experiThe Journal of Physical Chemistry
mental data has been deposited as Document No 00719 with the ASIS National Auxiliary Publication Service, c/o CCRl Information Corp., Inc., 909 3rd Ave., New York, N. Y. 10022. A copy may be secured by citing the document number and remitting $1.00 for microfiche or $3.00 for photocopies. Advance payment is required. Make checks payable to ASISNAPS.) Not all members of the series could be studied over the entire temperature range, since, even at 2 5 " , the relaxation frequencies for the slower reactions were close to the lower limit of the available frequency range. Pr and Dy are the real limits in the series for study over the entire 40" range, but the results for Ce and Ho at only two temperatures are included. Although the results for these two cations are subject to some skepticism, they are considered to be equally reliable to those for the remainder. The temperature coefficient of the characteristic relaxation frequency is sufficiently small that additional measurements a t intermediate temperatures are unlikely to improve upon the overall accuracy of the calculated values. Assignment of the single relaxation to the third step (1) Taken in part from the Ph.D. Dissertation of D. P . Fay, Brookhaven National Laboratory, Upton, K . Y . 11973. (2) To whom communications should be directed. (3) N. Purdie and C. A. Vincent, Trans. Paraday Soc., 63, 2745 (1967). (4) D. P. Fay, D . Litohinsky, and N. Purdie, J. Phys. Chem., 73,544 (1969). (5) D. P. Fay and N. Purdie, ibid., 73,3462 (1969). (6) V. L. Garza and N. Purdie, ibid., 74, 275 (1970). (7) R. Marianelli, Ph.D. Dissertation, University of California, Berkeley, 1966. (8) A. J. Graffeo and J. L. Bear, J . Inorg. ArucZ. Chem., 30, 1577 (1968). (9) H. B. Silber, R. D . Farina, and J. H. Swinehart, Inorg. Chem., 8, 819 (1969). (10) C. H. Langford and T. R. Sfengle, Ann. Rev. Phys. Chem., 19, 193 (1968). (11) C. H. Langford, Inorg. Chem., 4,265 (1965).
ULTRASONIC ABSORPTIONIN AQUEOUSSALTSOF
THE
1161
LANTHANIDES 23
Table I: Relaxation Frequency Data
3.0 211vmrr1. MHz-... 26"
7
Ion
Ce
Pr
Nd
Sm
Eu
Gd
Tb
C X 102, F
50
1.617 1.078 0.980 0.539 0.490 1.960 1.470 0,980 0.538 0.490 2 034 1.526 1.017 0.961 0.508 1.460 0.976 0.949 0.488 0.474 0.244 0.237 2.002 1.502 1,001 0.980 0.569 0.500 1.528 1.019 0.950 0.510 0.470 1.551 1 500 1.008 0.998 0.543 0.499 0.310 2.023 1.517 1.012 0.970 0.650 0.506 2.048 1.536 1.076 1,024 0.538
... ...
I
I
DY
Ho
114.6
...
...
105.3
...
...
450
4 5"
197.8 182.7 .
I
.
151.3
...
I..
92.5
74.7 71.0 67.8
...
...
141.9 130.9 120.0
234.2 212.9
...
...
...
...
182.7
82.9 77.2 72.8
...
...
160.1
265.6 240.5
...
147.6 129.4
...
...
,..
...
...
239.3
157.0
...
...
208.5
138.8
...
..,
177.7
118.7 147.0 139.4 127.5
... . . *
... 151.3 140.7
* . .
... 265.6
...
248.4
...
218.5 222.9
...
...
... ...
..* 364.9 341.6
105 5 I
. . #
92.3
...
...
348.5 314.0
... ,..
*.. *.. * , .
... ... .,.
...
*..
248.7
157.0
...
...
233.0
...
...
116.0
203.5 186.5
104.2 92.9
...
..,
166.4 138.8 128.7
... 72.0 66.6
...
55.9
step over a two-step mechanism. The rate constants are determined from a graphical solution of the equation4 2 7 r V m I I I = IC43
...
...
... ...
Figure 1. Excess sound absorption vs. frequency for F; (b) 9.7 x 10-8 F ; Sm2(SOn)a: at 45O, (a) 1.46 X F; (e) 4.74 x 10-8 F; (c) 4.88 X loU8F ; at So, (d) 9.49 X (f) 2.37 x F.
...
280.2
172.7
133.1
80.0 73.5 69.1 61.5
E 0.4
...
...
..,
m
304.0
297.0
...
d v
c
...
... 171.0
e !
270.0
121 2
...
10.3 4.0
0
...
207.0
...
c
h
215.4 331.0 305.0
... I
6
...
...
123.1
...
@(C)IC34
(2)
where V ~ I I Iis the characteristic relaxation frequency, O(C) is given by the expression O(C) = O(C)/{Klz-'Kz3-I (1 KZ3-')O(C)where O(C) = TI#{ 5 - 4p (3 - 20) (bIn TIf/d In ,L?)~; Klz and are the association constants for the first and second steps in the consecutive mechanism, and C is the analytical salt concentration. 0, the degree of association of the salt, and IIf,the activity coefficient quotient, were evaluated by a standard reiteration procedure using the Davies equation
+ +
+
i
+ BdI1l2))- 0.311 (3) and the ionic strength expression1 3C + 12(1 - p)C. - log Ti
in the multistep mechanism of Deibler and Eigen,12 that of substitution into the coordination sphere of the cation according to the equilibrium
+
=
Azi2{ (1'"/(1
=
(1)
The parameters A andB were corrected for temperature, and the distance of closest approach d was taken as the sum of the Pauling ionic radii plus two water molecule diameters.
has been made on the basis of previous e v i d e n ~ e . ~ , ~ Reference is made later to the preference of a three-
(12) H.Deibler and M. Eigen, 2.Phys. Chem. (Frankfurt am Main), 20, 229 (1969).
k*
M3+(HzO)S0d2-
+ HzO
M*S04+ kk8
Volume 74, Number 6 March 19, 1070
DOUGLAS P. FAYAND NEILPURDIE and Stepwise Association Constants
Table I1 : Rate
k84
Temp, OC
8ec -1
Ce
25 45 5 25 45 *5 25 45 5 25 45 5 25 45 5 25 45 5 25 45 5 25 45 25 45
2.7 (2.0) 6.3 (5.0) 1 . 5 (0.94) 3.1 (2.5) 6 . 7 (5.6) 2 . 3 (1.3) 3.9 (3.1) 6 . 7 (5.9) 4 . 3 (2.7) 5.9 (4.7) 8 . 2 (7.4) 4 . 4 (2.5) 6 . 5 (4.9) 9 . 4 (8.4) 4 . 1 (2.6) 6.4 (4.9) 7 . 8 (7.1) 4 . 1 (2.2) 5.2 (3.8) 7 . 1 (6.1) 3 . 5 (1.4) 4.0 (2.9) 5 . 0 (4.3) 2.5 (1.6) 3.7 (3.0)
Pr Nd Sm Eu
Gd Tb
DY Ho a
x
Ion
Estimated error &lo%.
IC43
X 10-8, nec -1
0.68 1.20 0.58 1.o 1.3 0.57 1.1 1.8 1.o 1.5 2.3 1.o 1.9 2.5 1.1 1.5 2.5 0.74 1.1 1.7 0.39 0.85 1.4 0.38 0.97
Rar
K23
3.9 (2.9) 5 . 4 (4.3) 2.5 (1.6) 3.0 (2.4) 5 . 1 (4.2) 4.0 (2.3) 3.7 (2.9) 3.8 (3.4) 4.2 (2.6) 4 . 0 (3.1) 3.6 (3.3) 4 . 4 (2.5) 3.5 (2.6) 3 . 8 (3.4) 3.9 (2.4) 4 . 3 (3.3) 3 . 1 (2.8) 5.6 (3.0) 4.9 (3.5) 4.2 (3.6) 8.8 (3.6) 4 . 8 (3.4) 3.7 (3.2) 6.6 (4.2) 3.8 (3.0)
1.62 1.67 1.6 2.2 2.0 1.1 1.9 2.6 1.1 1.9 3.0 1.1
1.8 2.8 1.2 1.8 3.2 0.86 1.5 2.4 0.58 1.4 2.4 1.0 2.1
Kiz X 10-2, l./mol
4.31 (9.97) 4.88 (10.8) 3.92 (9.83) 4.32 (12.3) 4.90 (12.1) 3.93 (8.06) 4.33 (11.2) 4.90 (15.5) 3.96 (7.42) 4.36 (11.0) 4.93 (17.0) 3.96 (7.90) 4.37 (12.6) 4.94 (16.1) 3.97 (8.11) 4.37 (10.6) 4.95 (18.4) 3.98 (6.68) 4.39 (9.54) 4.96 (14.4) 3.99 (5.77) 4.40 (9.32) 4.97 (14.2) 4.41 (7.43) 4.99 (13.8)
Values in parentheses are calculated from the two-step model.
I n the solution of eq 2 , the unknowns are the overall association constant KT (required to calculate p), K I Z , and K23. Values of KT at 5 and 45' were calculated from the van't Hoff isochore equation d log KT/d(l/T) = - A H ~ ' / 2 . 3 0 3 R
(4)
using the known KT values'3 at 25" and the enthalpies of complexation, measured calorimetrically under conditions similar to the kinetic experiments. The results and their interpretation are consequently subject to the assumption that AHT is constant over the entire temperature range, an assumption very often accepted in the determination of heats of complexation from the temperature dependence of the stability constant. Curvature in the plots has been reported for the CrNCS2+ 14 and Co(NH3)&12+ complexes. However, both are outer-sphere complexes, and there is good reason t o believe that it is a consequence of purely long-range electrostatic intera~ti0n.l~Moreover, it has been shown that AHT is insensitive to KT, if KT is .sufficiently large,16which it is for the present system.6~17 This method of extrapolation, therefore, might well make the difference between a calculated KT and an experimentally measured KT inconsequential, regardless of the possibility of a nonconstant AHT. K12 was calculated at each temperature using the Bjerrum equation's in which the 12 value ww taken equal to that in the Davies equation. This leaves only K23 The Journal of Physical Chmiatry
as an adjustable parameter which was calculated by iteration around eq 2 and the expression for KT in terms of the individual association constants (5)
where Kat = k34/kd3. Iteration was continued until the difference between successive values of K23-I was less than 0.0001 and required, on the average, five cycles. The procedure involved the calculation of a leastsquares line through the data in the solution of eq 2. The relevant rate constants, together with the corresponding equilibrium constants, are given in Table 11. Although there is experimental evidence t o support the proposed three-step m e ~ h a n i s m for ' ~ a sulfate system, results are frequently analyzed in terms of a twostep mechanism in which the first two steps are combined and defined by a single association constant, K I 3 . This model permits the direct calculation of Kl3 (13) F.H.Spedding and 8.Jaffe, J.Amer. Chem. Soc., 76,882 (1954). (14) C. Postmus and E. L. King, J. Phys. Chem., 59, 1208 (1955). (15) C. H.Langford and W. R. Muir, ibid., 71,2602 (1967). (16) J. J. Christensen, D. P. Wrathall, J. 0. Oscarson, and R. M. Izatt, Anal. Chem., 40,1713 (1968). (17) R.M . Ieatt, D. Eatough, J. J. Christensen, and C. H. Bartholemew, J . Chem. SOC., A , 47 (1969). (18) R.A. Robinson and R. H. Stokes, "Electrolyte Solutions," 2nd ed, Butterworth and Co.,Ltd., London, 1959,p 392. (19) K. Tamm, 6th International Congress on Acoustics, Tokyo, Japan, 1968,p GP-25.
ULTRASONIC ABSORPTION IN AQUEOUSSALTS OF THE LANTHANIDES
+
Table 111: Activation Parametersa at 25" for the Reaction Ln*+(HzO)S02- Ln.SOaf Ion
K * X 1OSb
Ce forward reverse Pr forward reverse Nd forward reverse Sm forward reverse Eu forward reverse Gd forward reverse T b forward reverse Dy forward reverse Ho forward reverse
4 . 3 (3.1) 1.1 5 . 0 (3.9) 1.7 6 . 3 (4.9) 1.7 9.6 (7.5) 2.4 10.4 (7.9) 3.0 10.3 (7.8) 2.4 8 . 4 (6.1) 1.7 6 . 5 (4.6) 1.4 4.0 (2.5) 0.6
Ea, kcal/molo
8.1 (8.8) 5.0 6.7 (7.8) 3.7 4.8 (6.7) 5.0 2.9 (4.5) 3.6 3.4 (4.4) 4.0 2 . 8 (4.4) 3.7 2.4 (4.5) 3.7 1 . 6 (4.9) 5.4 3.9 (6.0) 8.9
AH
1163
+ HzO
*,
kcal/mol
AU
7.5 (8.2) 4.4 6 . 1 (7.2) 3.1 4.2 (6.1) 4.4 2 . 3 (3.9) 3.0 2.8 (4.8) 3.4 2.2 (3.8) 3.1 1 . 8 (3.9) 3.1 1 . 0 (4.3) 4.8 3 . 3 (5.4) 8.3
Error in values &lo%. a Values in parentheses are calculated for the two-step model. Error estimated to be 4ZO.l kcal/mol. e Error estimated to be 4Z3.0 eu.
*,
kcal/mold
6.0 (6.2) 6.8 5.9 (6.0) 6.5 5.7 (5.9) 6.5 5.5 (5.6) 6.3 5.5 (5.6) 6.2 5 . 4 (5.6) 6.3 5.6 (5.8) 6.5 5.7 (5.9) 6.6 6.0 (6.3) 7.1
AS+! eue
5.2 (7.0) -8.0 0.77 (4.1) -11.6 -5.1 (0.8) -7.2 -10.7 (-5.7) -11.2 -8.9 (-5.9) -9.2 -10.9 (-5.9) -10.6 -12.6 (-6.1) -11.5 -15.8 (-5.4) -6.1 -9.2 (-3.0) 4.0
Error estimated to be 1 0 . 9 kcal/mol.
Table IV : Stepwise Thermodynamic Parameters a t 25" Ion
Ce
Functionn
AH
- AG AS
Pr Nd
AH
- AG Ai3 AH - AG
AS
Sm
AH - AG
AS Eu Gd
AH
- AG AS AH - AG
Tb
AS AH
- AG AS
DY
Ho
AH
- AG AS AH
- AG AS
a
Step 3 4
8 tep 2-3b
s t e p 1-2'~
Total (kinetic)
Total (calorimetric)
3 . 1 (3.8) 0.8 (0.6) 13.2 (15.0) 3.0 (4.1) 0.65 (0.5) 12.4 (15.7) -0.2 (1.7) 0.8 (0.6) 2.1 (8.0) -0.7 (0.9) 0 . 8 (0.7) 0 . 5 (5.5) -0.6 (1.4) 0 . 7 (0.6) 0 . 3 (3.3) -0.9 (0.7) 0.9 (0.7) -0.3 (4.7) -1.3 (0.8) 0.9 (0.7) -1.1 (5.4) -3.8 (-0.5) 0.9 (0.7) -9.7 (0.7) -5.0 (-2.9) 1.1 (0.8) -13.2 (-7.0)
0.31 0.29 2.0 0.96 0.46 4.8 3.7 0.39 13.7 4.3 0.38 15.7 4.0 0.36 14.7 4.2 0.34 15.3 4.5 0.24 15.8 6.2 0.21 21.4 6.8 0.01 22.9
0.97 (0.75) 3.6 (4.1) 15.3 (16.2) 0.97 (0.92) 3.6 (4.2) 15.3 (17.2) 0.97 (2.9) 3.6 (4.2) 15.3 (26.3) 0.97 (3.6) 3.6 (4.2) 15.3 (26.1) 0.97 (3.1) 3.6 (4.2) 15.3 (24.7) 0.97 (3.6) 3.6 (4.1) 15.3 (25.9) 0.97 (3.4) 3.6 (4.1) 15.3 (24.9) 0.97 (4.0) 3.6 (4.1) 15.3 (26.9) 0.97 ( 5 - 8 ) 3 . 6 (3.9) 15.3 (32.7)
3.41 (4.21) 4.89 (4.89) 27.9 (30.5) 3.99 (4.69) 4.94 (4.94) 30.0 (32.3) 4.66 (4.46) 4.96 (4.96) 31.7 (31.6) 4.79 (4.43) 4.99 (4.99) 32.8 (31.6) 4.56 (4.40) 4.99 (4.99) 32.0 (31.5) 4.55 (4.24) 4.99 (4.99) 32.0 (31.0) 4.58 (4.12) 4.96 (4.96) 32.0 (30.5) 4.56 (3.55) 4.92 (4.92) 31.8 (28.4) 4.33 (3.25) 4.89 (4.89) 30.9 (27.3)
3.78 4.89 29.1 3.92 4.94 29.7 4.15 4.96 30.6 4.34 4.99 31.3 4.13 4.99 30.6 4.10 4.99 30.5 4.02 4.96 30.1 3.58 4.92 28.5 3.54 4.89 28.3
AH and AG are in kcal/mol and A S in eu.
Errors defined in the footnote to Table 111.
from the Bjerrum equation if an appropriately smaller value of it is chosen, and reduces, by K23, the number of parameters needed for the kinetic solution, although it does not change the degrees of freedom in the calcula-
tion. Iteration is still necessary using the @(C>function for a two-step mechanismS and KT = KI3(1 K84). In this treatment it is the adjustable parameter, and the value is chosen which gives the best comparison
+
Volume 74, Number 6 March 19, 1970
1164
DOUGLAS P. FAYAND NEIL PURDIE sure change is not accompanied by an appreciable temperature change, owing to the small value of the coefficient of expansion. Relaxation amplitudes can therefore be used to determine the partial molal volume changesz1between reactants and products in the individual steps. Because of coupling between the steps in the successive equilibria mechanism, the volume change for the slow step AV34 is not directly obtained from the amplitude of the observed relaxation unless previous steps relax at a much higher frequency. Instead a weighting factor must be introducedz2according to
A V I = AViz
5
E
AVIII
AV34
+ IC’ + h3’
(6)
IC32
AVII
(8)
where IClz‘ and ICz3’ have their usual ~ignificance.~The equation (9) which relates AVIII to the maximum amplitude is readily derivedz2
3.I
3.3
3.5
EEf] u blna (9)
Figure 2. Plot of log k ~ log , k43, log Kn3,and log Karus. I / T x 103.
between KT calculated and observed. Typically an 8. value of 5.5 A is obtained at 2 5 ” . It mill be seen from Table I1 that the values of k34 are lowered slightly from the three-step model while the kd3 values are unchanged and are not given. Preference for the three-step model is based entirely upon Tamm’s experiment^'^ at very high frequencies on MnS04 and JlgSOa. The excellent correspondence between the calculated rate constants from both models gives us confidence in the method used to evaluate K Z 3 . Activation parameters, applicable at 2 5 ” , are given in Table 111. The activation energies and changes in enthalpy accompanying each step were calculated from the slopes of the plots of log k i f , log k j l , and log K f f11s. 1/T, respectively. Typical of the results is the plot for samarium, Figure 2. The value of AH12 is constant throughout the series at 0.97 kcal/mol. In Table IV the individual A.Gf3, AH,,, and AXij values are given for a temperature of 25”, and their sums are compared with the results obtained calorimetrically.20 AH34 and AX3? as calculated from the two-step model are slightly more positive, but a similar dependence with atomic number is observed. The excess sound absorption in aqueous systems, which is a result of chemical relaxation, is primarily determined by a finite A V T for the reaction; the presThe Journal of Physical Chemistry
where PO is the adiabatic compressibility of the solvent and n is the degree of dissociation. To a close approximation /30 = ( p c 2 ) - I where p is the density and c is the velocity of sound. At 25’ the value of Po is 4.4G X lo-” ml/erg. The calculated AVB4values are given in Table V. Compared to divalent metal sulfates the AVa4 values, and consequently the absorption amplitudes, are much greater.
Discussion The error limits on the activation and thermodynamic parameters are based on a 10% experimental error on the measured rate constants and overall associalion cons t a n t ~ .It ~ ~should be reemphasized that the interpretation is subject to constancy in AHT so that a similar error was assumed in the KT values at 5 and 46’. The same criticism pertains to the method used to determine the stepwise thermodynamic parameters and the (20) The thermodynamic parameters from calorimetry describe the equilibrium reaction between the free ions and all forms of the ion pairs in solution. I n comparing the total kinetic parameters a weighted sum must be calculated in a manner analogous to the d e t e r mination of AVT. AGT kinetic is always equal to AGT calorimetric, a consequence of the method used to calculate K23 in the threestep mechanism or ri in the two-step mechanism. (21) Molar concentrations were used in this study, but since the Solutions were very dilute the differencehas been ignored. (22) K. Tamm, “Handbuch der Physik,” Band XI, Altustic 1, Springer-Verlag, Berlin, 1961, p 129.
ULTRASONIC ABSORPTION IN AQUEOUS SALTSOF
Ion
C X 105, F
d
La
8.80 9.80 9.80 9.61 9.76 9.80 9.50 9.98 9.70 10.76
0.0987 0.1002 0.0936 0.0912 0.0873 0.0871 0.0886 0,0909 0.0971 0.0963
Ce Pr Nd Sm Eu Gd Tb
DY Ha
THE
LANTHANIDES
- a In nf a In ,,
- AVIII,
- hV84,
ml/mol
ml/mol
0 * 1119 0.1107 0.1062 0.1051 0.1021 0.1020 0.1040 0.1048 0.1104 0.1069
19.1 19.6 20.4 22.1 22.3 23.7 19.5 20.3 18.9 20.2
20.7 21.6 22.7 26.5 26.7 28.1 23.9 24.8 23.8 25.0
activation parameters in that a linear Arrhenius plot was assumed. Error limitations alone, however, do not account for the observed trends in the values of the significant parameters with atomic number which must be considered real, if only relative. The present results are augmentative to previous convictions that the mechanism is multistep in which the transition state is formed with a reduced coordination number by the elimination of a water molecule. Very good agreement is obtained in E, and AS* for complexation with the energy and entropy of activation for water exchange on trivalent gadolinium,' 3.2 A= 0.3 4 eu, respectively, measured by kcal/mol and -7 l7O nmr line broadening, and the only value yet available. Because of this comparison and the agreement between for GdS04+and the rate of water exchange on Gd,7 IC,, = 9.0 X 108 or 8.0 X lo8 sec-l, for 9 and 8 coordination, respectively, the mechanism may be concluded to be dissociative with little or no steric requirement involved in the substitution. Energies of activation pass through a minimum around the ions in the middle of the series consistent with the trend in rate constants, so that a steric requirement is probably absent for all systems. I n a previous test for a dissociative mechanism a linear plot of AG* vs. A G O was de~ c r i b e d . ~Contrary to the suggestion presented in that study, the dependence of AS* on A S o is not linear. Besides water exchange, a temperature dependence study has been made on two other rare earth systems, anthranilateg and oxalate.* I n both of these systems the bimolecular rate constants were measured, and a direct comparison with the sulfates is not totally justifiedeZ3To complete the comparison for Gd3+ion, the corresponding activation energies and entropies are 8.5 kcal/mol; +9 eu, and 6.5 kcal/mol; -5.2 eu for anthranilate and oxalate, respectively. Some steric requirements may be in operation or else the values are representative of the process in which a further water molecule is lost in ring fusione6 In this regard higher substitution into the metal coordination sphere has been observed to proceed with progressively decreasing rates, at least for ions with inert gas configuration^.^^
1165
The irregular trend in AS* with atomic number for the anthranilates, in which only Gd3+ and Lu3+ have positive values, is not reproduced in the sulfate system. Nonlinear variations in AGT, AHT, and AST with atomic number or with inverse cation radius,25it has frequently been inferred, result from a coordination number change somewhere in the series. The same effect might account for the variation in AV34. In the calculation of AV34 from AVII1, values for AB12 and AV23 were not available for the rare earth sulfates since measurements have not as yet been made in the GHz range. Fisher26 has indicated from a comparison of volume changes obtained from sound absorption me& surements and pressure dependence measurements of the dissociation equilibrium constant for lanthanum sulfate that a multistep mechanism exists. Sufficient kinetic evidence is now available to corroborate this conviction. From an entirely pragmatic point of view, we have used the values AV12 = - 18.0 ml/mol and AV23 = +13.2 ml/mol calculated by TammI9 for MgS04. The assumption is made, perhaps with some justification, that AV12and AV23 are independent of the cation. The difference in AVa4 for LaSO4+ and MgS04 is basically one of the difference in AVIII observed. Summation of the individual volume changes gives AVT = -25.6 ml/mol for 8.80 X M La2(S0&. In view of the necessary assumptions in this calculation the comparison with the value of Fisher, AVT = -25.7 ml/ is ~remarkably )~ good. mol for 8.20 X 10-3 M L S L ~ ( S O The values of AV12 and AB23 cannot be too critical and probably are illustrative of little coupling between the third step and previous steps, in that using earlier values27of AV12 = 0 ml/mol and A1123 = -14 ml/mol, a value of AVT = -27.7 ml/mol is obtained, which is still in excellent agreement with the value from pressure studies. To substantiate this proposition recent studies at high frequencies locate the relaxation frequency for sulfate desolvation in the range 300-400 A/IHz.l9 Probably the most important observations to be made on the variations of AH,, and AS,, for the second and third steps with atomic number are that the breaks occur where it has been proposedz8that there is a coordination number change and that the trends in these values do not follow the trends in ANT and AST obtained calorimetrically.6 It is possible to divide the series into (23) The comparison is not strictly correct since the T-jump and P-jump activation parameters include the contribution from faster preequilibrium steps. The results are included only for completeness. (24) M. Eigen and G. Maass, 2.Phys. Chem. (Frankfurt am Main), 49,163 (1966). (25) The two are comparable because the variation in ionic radius with atomic number is almost linear. (26) F. H. Fisher and D. F. Davis, J.Phys. Chem., 71,819 (1967). (27) M. Eigen and K. Tamm, Z . Elektrochem, 66,93, 107 (1962). (28) F. H. Spedding, M. J. Pikal, and B. 0. Ayers, J . Phys. Chem., 70, 2440 (1966).
Volume 74, Number 6 March 19,1970
R. E. JAMESAND F. SICILIO
1166 three groups, La-Pr, Nd-Tb, and Dy-Lu, in which AH34and ASa4are reasonably constant. The dependences of AHz3and AS23,the values for anion desolvation, apparently indicate that the ligand contribution is not constant across the series as has often been assumed. Reverting to the argument29that if bonding is electrostatic and if there is no coordination number change in a series of similar cations, e.g., the alkaline earths, a linear plot of AHT of complexation with inverse cation radius would be observed, it seems natural to expect that as the radius decreases across the rare earth series the value of AHT should increase. The increase would not be monotonic because of the change in coordination number. The fact that AHT passes through a maximum and a later minimum might be explained by a nonconstant contribution from the ligand interaction. 30 implication is being made, nor can it be made on the basis of a single observation, that this is a general phenomenon. An apparent test for this proposition would be a corresponding study of the
temperature dependence of the rates of formation of some alkaline earth or divalent transition metal complexes of both inner- and outer-sphere types. Although perhaps a little premature, in view of the present remarks, the common practice of using the sign and magnitude of the overall thermodynamic parameters, with the added constraint of a constant contribution from the ligand, to distinguish the structure of a complex species in solution30mould seem to warrant some reconsideration.
Acknowledgment. We wish to acknowledge the financial assistance of the Research Corporation and the Research Foundation, Oklahoma State University. We are also grateful to the National Aeronautics and Space Administration for providing a fellowship to (D. P. F.). (29) J. F. Duncan, Aust. J . Chem., 12,356 (1959). (30) T.Moeller, E. R. Birnbaum, J. H. Forsberg, and R. B. Gayhart, Progr. Sci. Tech. Rare Earths, 3,61 (1968).
Kinetics of Isopropyl Alcohol Radicals by Electron Spin Resonance-Flow Techniques by R. E. James and F. Sicilio Department of Chemistry, Texas A & M University, College Station, Texas 77843 (Received September 11, 1969)
Detailed kinetic studies on the Ti (111)-Hz02-2-propanol system have supplied evidence for decay modes of radicals from 2-propanol. With [HzOzlo> 2[TiCla]o, the empirical rate law for these radicals is d[R]/dt = -IC [R][H20z]. This is supported by dependency studies, invariance of rate constants, values of the Arrhenius parameters, and product analysis. Average second-order rate constants for this case are 4.0 X loz Jf-l sec-1 for (CH&&OH, Rl, and 2.5 X 102 M-1 sec-l for .CH2CH(CH3)OH, Rz. With [HzOz]o= [TiCls]~, combination of radicals appears to predominate; k (second order) = 1.6 X 107 M-’ sec-1 for the reaction R1 R1. The ratio of observed concentrations of substrate radicals depends on time after mixing and initial concentrations of TiC13and H20z. The kinetic results and stoichiometry indicate that the ‘‘ OH” product from the reactions of R1and Rzwith HzOz is relatively unreactive towards this substrate. A reactive “‘OH” would not be in accord with the disappearance of R1 and Rz at high [Hz02], since a concurrent increase in [Rl] and [R2]would be developed by abstraction reactions. A cyclic reaction sequence is thus ostensively not perpetuated by radical-HzOz reactions. Refined values of isotropic hyperfine coupling coiistants are ~ H ( C H ~=) 20 1 0 . 1 Gfor (CH&COH; uH(CH2) = 22.4 & O 2G,andaH(CH) = 2 3 . 8 & 0 0 . 2 G f o r ~ C H 2 C H ( C H , ) O H .
+
*
Introduction Rapid flow mixing of aqueous solutions of titanium(111) ion and hydrogen peroxide produces two freeIt radical species observable by esr spe~troscopy.~-~ is now generally agreed that these radicals are forms Of ‘OH Or ‘OzH complexed Ti(1V)*3-7 In this paper we shall refer to these radicals nnd their associated The Journal of Physical Chemistry
esr signals as Sf (g = 2.0132) and Sz (q = 2.0118). When an alcohol is included ‘as a substrate in one or (1) F. Sicilio, R. E. Florin, and L. A. Wall, J. Phys. Chem., 70, 47 (1966). (2) W. T.Dixon and R. 0. C. Norman, J. Chem. SOC.,3119 (1963). (3) Y. 8. Chiang, J. Craddock, D. Miokewich, and J . Turkevich, J . Phus. Chem., 70,3509 (1966).
