2649
OUTER-SPHERE ASSOCIATION KINETICS an increase in kea, or else inhibit the rate of removal and decrease Iceo. The above considerations, of course, apply in the absence of adsorption phenomena and in the absence of any specific interaction of the complex or ligand with the mercury electrode. The changes in k2, in the absence of the above phenomena, appear in general to be fairly small, so that changes in E,,, for irreversible electrode processes of this type can in most cases be used, at least in a qualitative sense, to determine whether complexes are “nonexistent,” weak, or strong. Such was the case for some Co(II), IVIn(II), and Fe(I1) complexes
considered in this work. In cases where k,O does not alter significantly on addition of ligand, use of the simple method of calcuIation proposed previously by the author can be employed by the author to give data on the stability and nature of the complexes formed, such as for the fluoride, chloride, and nitrate complexes of nickel(II), and presumably for other species with slow removal of coordinated water.
Acknowledgment. The author wishes to acknowledge helpful discussions with Mr. E(. A. Phillips during the course of this work.
Outer-Sphere Association Kinetics of Magnesium(II), Manganese(II), Cobalt (II), Nickel( II), Copper(I1) , and Zinc(I1) rn-Benzenedisulfonates in Methanol1 by Anthony Fanelli and Sergio Petrucci* Polytechnic Institute of Brooklyn, Brooklyn, N e w York
11!201
(Received December 29, 1970)
Publication costs borne completely by The Journal of Physical Chemistry
Measurements of the relaxation of ultrasonic absorption of Mgz+,Mn2+,Co2+, Ni2+,Cu2+,and Zn2+ m-benzenedisulfonates in methanol at 2 5 O , in the frequency range 15-185 MHz, have been interpreted as being due to the outer-sphere process of association between the solvated cations and BDS2- anion. The forward and reverse rate constants are comparable with the calculated diffusion controlled rate constants according to the Smoluchowski-Debye-Eigen theories. The volume changes of reaction can be interpreted as being due to the elimination of one molecule of methanol from either the second coordination sphere of the cations or from the anion. The process has a barrier of energy equal to the one of viscous flow. This has been proven by measurements of the activation parameters, AH and AS *, by measuring the ultrasonic relaxation of MgBDS in methanol at - 15 and -50”. Corresponding electrical conductance results in a comparable temperature range are reported for MgBDS in methanol in order to calculate the necessary association constants. The Fuoss-Kraus method has been employed for this purpose.
*
Introduction The problem of the mechanism of ionic association and complexation in nonaqueous solvents is presently receiving much attention, after the corresponding study in aqueous media has provided a rather complete picture . 2 One of the first queries to be answered is whether the complexation process involves ion pairs or outer-sphere intermediates as found for complexation involving divalent metal cations in water.2 According to Eigen2 the process starts with a diff usion-controlled approach of solvated ions. This is followed by stepwise elimination of molecules of solvent from between the ions. The second question is whether the collapse of the outer-sphere complex with the penetration of the ligand into the first coordination sphere of the metal cation,
in the case of octahedrally coordinated systems, occurs with a dissociative, D (SN1 lim), or with an interchange dissociative (Id) m e c h a n i ~ m . ~In the D mechanism an intermediate of reduced coordination is predicted in the transition state. The rate constant for solvent exchange, as determined by nmr, should correspond to the first-order rate constant of ligand p e n e t r a t i ~ n . ~ In the Id mechanism an interchange of ligands, solvent, (1) This work is part of a thesis of A. Fanelli in partial fulfillment for the requirements of the degree of Doctor of Philosophy (Chemistry), Polytechnic Institute of Brooklyn, 1971. (2) M . Eigen and L. DeMaeyer in “Investigation of Rates and Mechanism of Reactions,” Val. 8, A. Weissberger, Ed., Wiley, New York, N. Y . , 1963, Part 11. (3) C. H. Langford and H. B. Gray, “Ligand Substitution Processes,” U‘.A. Benjamin, New York, K. Y., 1965; T. R. Stengle and C. H. Langford, Coord. Chem. Rev., 2 , 349 (1967). The Journal of Physical Chemistry, Vol. 76, A‘o. 17, 1971
2650
and anion occurs in the transition state without formation of an intermediate of reduced coordination. The first-order constant of ligand penetration should differ by a statistical factor from the rate constant of solvent exchange. This factor should correspond to the solvation number of the cation in the second coordination sphere. 3 , 4 Recent evidence4t5shows that some first-order rate constants of solvent substitution are 1 / 2 0 times the rate of solvent exchange as determined by nmr. I n other cases6 an equality between the two rate constants has been reported for similar systems. While this problem is currently under experimental investigation in this laboratory the first equation, namely, the problem of the outer-sphere kinetics in nonaqueous solvents, has not been widely studied. It is particularly important to perform such a study whenever possible to ascertain that the use of theoretically calculated outer-sphere association constants is justified. If one takes a two-step mechanism as the simplest scheme of a multistep reaction and assumes a preequilibration condition for the first step, the observed second-order rate constant, is related to the outer-sphere association constant KI2-l, and to the first-order rate constant of ligand penetration, k23, by the expression k f = K12-lk23. Much of the discrepancy between the substitution rate constants, k23, and the rate constant of solvent exchange might arise from the use of incorrect outer-sphere association constants. This is an uncertainty to be clarified before speculating between the relative virtues of the D or I d mechanisms of solvent substitution in the first coordination sphere of metal cations. Recently,' the electrical conductance of several 11(11) m-benzenedisulfonates in methanol at 25" has been measured, providing useful parameters like association constants, collision diameters, and hydrodynamic radii. The pressure-jump relaxation kinetics of the same systems have been p e r f ~ r r n e d providing ,~ rate constants for inner-sphere complex formation. I n order to extend this research, in the light of the above discussion, it was necessary to perform the study of the outer-sphere ion-pair formation. Ultrasonic relaxation has proved to be a suitable tool for such a study.
ANTHONY FANELLI AND SERGIO PETRUCCI
Experimental Part
cryostat with a cold finger immersed in the liquid. A Bayley proportional thermoregulator was used to maintain the desired temperature. The temperature was measured within *0.001" with a Pt thermometer (calibrated by the National Bureau of Standards) connected to a Leeds and Korthrup Mueller bridge. Both the ultrasonic and the conductance cell were opened to be filled only when at room temperature in order to avoid moisture condensation. The ultrasonic measurements were performed at low temperatures after the cell had remained immersed in the bath already at the desired temperature for at least 1 hr. Measurements were repeated at the same frequency with time to assure reproducibility. Eventually several solutions were reanalyzed4 after the measurements in the ultrasonic cell to ensure that no significant condensation of water or change in composition occurred. Water content was checked by Karl Fischer reagent and was always found to be below 0.05%. The sound absorption of the solvent was measured to -78.5". This last temperature was achieved by Dry Ice-acetone slush. A relaxation started to appear as shown below. Corrections of the concentrations for the density of the solvent at various temperatures were done in the calculations. The conductance measurements were performed at low temperatures also in the constructed thermostat. n-Hexane proved to be a suitable bath fluid. No abnormal frequency dependence of the resistance was observed. On the contrary when acetone or methanol were first tried as bath liquids capacitance losses between the glass sealed-in leads of the conductance cell caused unreliable data even at the frequency of 1000 He, the frequency dependence becoming several per cent of the measured resistance at higher frequencies in the audio region. The liquid n-hexane was changed after each run to avoid capacitance leaks due to humidity condensation in the thermostat liquid. The temperature of the bath was held constant within =kO.Ol" at - 15 and -45") the lowest temperature obtainable with this precision. Therefore, conducatance data were performed at - 15 and -45", whereas the ultrasonic runs were preformed at -15 and -50". At this last temperature a precision of *0.05" was obtained. The association constant was extraplolated to - 50" for the ultrasonic calculations.
The ultrasonic equipment and procedure for the work at 25" have been described elsewhere.E-10 The conductance apparatus and technique have also been previously de~cribed.','~ For the work a t -15 and -46 or -50" special precautions and additional equipment have been used. A thermostat was built capable to perform within &0.01" to -50". This was built by surrounding a 2.5-gal. stainless steel beaker with 5-in. thick asbestos insulation. As the thermostat liquid stirred n-hexane was used. Cooling was done by a Cryo-cool C60
(4) G. Macri and S. Petrucci, Inorg. Chem., 9, 1009 (1970). (5) C. H. Langford and H. G. Tsiang, ibid., 9, 2346 (1970). (6) R. G. Pearson and P. Ellgen, ibid., 6 , 1379 (1967). (7) R. Lovas, G. Macri, and S. Petrucci, J . A m e r . Chem. Soc., 9 2 , 6502 (1970). (8) S. Petrucci, J . Phys. Chem., 71, 1174 (1967). (9) 9 . Petrucci and M. Battistini, ibid., 71, 1181 (1967). (10) G. S. Darbari, M. R. Richelson, and 8. Petrucci, J . Chem. Phys., 53, 859 (1970); G. S. Darbari and 9 . Petrucci, J . Phys. Chem., 73, 921 (1969). (11) S. Petrucci, P. Hemmes, and M . Battistini, J . A m e r . Chem. Soc., 89, 5552 (1967).
The Journal of Physical Chemistry, Vol. 75, N o . 17, 1971
265 1
OUTER-SPHERE ASSOCIATIOK KINETICS Addition of further stock solution to the conductance cell was done in a drybox under a dry Nz atmosphere after the cell had returned to room temperature. The cell constant was measured at 25O.' Corrections for the temperature change for the geometrical characteristic of the cell were done by calculation from the literature.12 They were less than 0.05% of the cell constant value.
Results The data for the sound absorption coefficient a (neper cm-') at the frequencies and temperatures investigated have been deposited in the microfilm edition of this j0urna1.l~ The solvent properties pertinent to this work are density p (g/cc), dielectric constant e, viscosity, 7 (P), longitudinal ultrasonic ve1oc:ty Vo (m/ sec), and sound absorption coefficiency, expressed as a o / f 2 (neper cm-I secz). These constants are: at 25" p = 0.7866, E = 32.66, = 0.00547, Vo = 1100, (a0/f2)= 30 X lo-''; at -15" p = 0.8249, E = 39.1, 11 = 0.0105, V O= 1230, (a0/fz) = 35 X 1O-l'; at -50" 4 6 . 3 , ~= 0.0237, T i 0 = 1372, ( o ~ o / f ~ ) = p = 0.8583, E 49 X 10-17. I n the above f is the frequency (Ha). The data of density, dielectric constant, and viscosity have been taken from the 1 i t e r a t ~ r e . I The ~ sound velocities and attenuation, ao, have been measured in this laboratory. I n Table I values of the equivalent electrical conductance d (mhos cm2 equiv-') at the concentrations c (mol/l.) investigated for PtlgBDS at -15 and -45" are reported. ~
O
T
,
Table I : Equivalent Conductance A (mhos cmz equiv-1) and Concentration c (mol/l.) for MgBDS i n Methanol at - 15 and -45" __o.
c
x
.
104,
IM
2.211 3,798 7.355 10.844 13.331 16.693 2,288 3,929 7.609 11.219 13.791 17.270
A
32.092 27,618 22,730 20,217 18,987 17.844 20.856 18.486 15.707 14,180 13.424 12.669
t,
oc
- 15.
-45O
Calculations and Discussion I . Isothermal Study. The value of the solvent sound absorption has been measured as a function of the frequency at 25, - 15, and -50". I n the range of frequency investigated (15-185 MHz) no relaxation of the solvent is present. At -50" however, an onset of a
relaxation process at the highest frequency started to appear. I n order to confirm this observation, the temperature of -78.5" was investigated. Here a relaxation was clearly visible starting at about 100 RIHz. This relaxation is probably connected with a thermal and/or structural relaxation of the liquid. For the purpose of this work, however, namely in the temperature and frequency range where measurements were performed for the electrolyte solutions, the solvent absorption may be taken safely as constant. I n Figure 1 the ultrasonic results at 25" for the n l I 1 BDS in methanol a t 25" are reported in the form of ( a e x c X ) V S . f, where aexc= LY - a0 is the excess sound absorption coefficient with respect to the s o l v h t value, cyo, a t each frequency f; X is the sound wavelength, X = u/f, and u is the sound velocity that has been approximated to the solvent sound velocity. The solid lines in Figure 1 have been calculated for the theoretical function for a single relaxation
where is the relaxation time (T-' = 2TfR), f~ the relaxation frequency, and (/J,exc)max the maximum value of the excess sound absorption at f = f R . Equation 1 has been fitted as a two-parameter equation to the data (Figure 1). The results of these calculations are reported in Table 11. An error of =k5% may be associated with these results. It may be noticed that the values of the relaxation frequency are concentration dependent, an indication that the process observed is not a first-order transformation but a bimolecular (or more complex) one. Ultrasonic data on Ni(C104)2,0.09 M , in methanol at 25" show no relaxation and an insignificant excess sound absorption ( A a / f 2 GZ. 1 X 10-l') with respect to the solvent. Further, the relaxation frequency seems to be dependent on the charge of the cation. Indeed in Figure 2 data for KzBDS and CszBDS in the form of (aexcX)os. f are reported. It may be seen that the relaxation frequencies are higher than the corresponding ones at the same concentration for the 2: 2 salts. The above proves the involvement of both R!P+ and BDS2- in the observed relaxation process. The hypothesis is advanced that the process is due to ionic association. On the other hand the elimination of methanol from the first coordination sphere of the (12) R. A. Robinson and R. Stokes, "Zlectrolyte Solutions," Butterworths, Washington, D. C., 1965, p 97. (13) Data for the sound absorption coefficient a (neper cm-1) will appear following these pages in the microfilm edition of this volume of the journal. Single copies may be obtained from the Reprint Department, ACS Publications, 1155 Sixteenth St., N.W., Washington D. C. 20036, by referring to author, title of article, volume, and page number. Remit $4.00 for photocopy or $2.00 for microfiche. (14) "International Critical Tables," and "Handbook of Chemistry and Physics," 48th ed, Weast, Ed., Chemical Rubber Publishing Co., Cleveland, Ohio, 1967. The Journal of Physical Chemistry, Vol. '76,h'o. 1'7, 1071
ANTHONYFANELLI AND SERGIO PETRUCCI
2652 where
s
=
P
=
+ kzl + + kl2e(kZ3+ ka2) + k12e
k23
k32
kZlk32
T ~ corresponds - ~ to the fast relaxation time with the positive sign before the square-root term.
Table I1 : Maximum Excess Sound Absorption (poxc)max, Relaxation Frequency f~ (MHz) and Isoentropic Volume Change AV, for MI1 BDS, KzBDS, and CszBDS in Methanol a t 25"
Electrolyte t = 25'C
MgBDS
.0497M .0326M .0243M
'
100
MnBDS
NIBDS IN MeOH
CoBDS
0421M 20
NiBDS
0284M 0106M
CuBDS
50
0437M 0 2 70M
"1
.00860M
ZnBDS
A I
KiBDS CszBDS
c,
M
0.0412 0.0257 0.0142 0.0542 0.0402 0.0257 0.0497 0.0326 0.0243 0.0421 0,0284 0,0106 0.0437 0.0270 0.0086 0.0488 0.0223 0.0113 0.0177 0.0182
75 44 28 83 65 34 98 65 41 108 52 25 138 88 27 97 49 22 28 34
85 65 50 90 80 70 85 75 60 90 70 50 75 65 38 85 65 40 85 100
55.9 49.3 47.5 54.2 52.5 46.0 60.5 55.9 48.5 66.8 52.0 49.2 74.8 69.0 55.0 60.5 54.5 45.2
t = 25°C
If k12, kzl one has2
20 .0113M "1
2
5
>> k23, k32 as it should be in our case t'hen TI-l
10
20 5 0 100 200 f (MHZ) -D
500
=
klze
+ kZl
(3)
with
Figure 1. (CY&) us. f (MHa) for MI'BDS in methanol a t 25".
divalent metal cations studied in this work occurs in 10-3 t o 10-4 sec,16therefore several orders of magnitude slower than the process observed here. The hypothesis of ionic association must therefore correspond t o outer-sphere complex formation, namely to the first step of the Eigen scheme2 M,2+
+ BDSS2-
k1z
k28
n12+Ss,BDS2ksz
kZl
RISaBDS ( 2 ) with S a solvent molecule. The general solution of this mechanism in terms of the relaxation times is2 ~ 1 , ~ l -= l '/2[X
f
d S z - 4P]
The Journal of Physical Chemistry, Vol. 76, N o . 17, 1971
and
I n previous work4 TII was measured for the same systems by pressure-jump relaxation kinetics. If the present hypothesis concerning the identification of the observed ultrasonic relaxation time with the first step of eq 2 is correct, then eq 3 should apply to the ultrasonic data. I n the above u is the overall degree of
(15) C.H. Langford and T.H. Stengle, Annu. Reu. Phys. Chem., 19, 193 (1968); R. G.Pearson, J. Palmer, M. M. Anderson, and A. L. Allred, 2.Elektrochem., 68, 110 (1960).
OUTER-SPHERE ASSOCIATIONKINETICS
2653
1, (b lnfit2)/(d In u ) = 0, and Q
