J. Phys. Chem. 1982, 86, 140-144
140
Ultrasonic Absorption Study of Ion Associatlon in Aqueous Copper( I I ) Formate, Acetate, and Propionate Slmeen
Sattar and Don Eden'
Lbparhnent of Chemistry, Yale University, New Haven, Connectlcut 0651 1 (Received: Aprll 14, 1981; In Final Form: July 20, 1981)
The ultrasonic absorption of aqueous copper(I1)formate at 20,35, and 50 "C and copper(I1)propionate at 20 "C was measured in the concentration range 0.0062-0.1 M with a pulsed, variable-path-lengthapparatus over the frequency range 10-143 MHz. The ultrasonic absorption of 0.0016-0.025 M copper(I1) acetate at 20 "C was measured from 1to 21 MHz in a differential cell. The single relaxation observed in all cases was attributed to ion association. The steady-state approximation was applied to the concentration of the solvent-separated ion pairs. The rate constant at 20 "C for the substitution of water by a carboxylate ion around Cu2+is (3.4 f 1.2) x IO8 s-l. The enthalpy of activation for the substitution process is 10 f 1kcal/mol for copper formate. The overall volume change due to ion association is 13-17 cm3/mol.
Introduction Ever since Eigen and Ta"' presented a detailed analysis of the ultrasonic absorption of electrolyte solutions, the mechanism of ion association has been probed extensively. Eigen and T a " proposed a multistep process to account for the observed relaxations. A metal ion and ligand approach each other at a diffusion-limited rate to form a solvent-separated pair. Next, one or two solvent molecules are removed from the space between the ions, leading to the formation of a contact pair. Numerous investigations of a variety of electrolytes in both aqueous and nonaqueous solvents have upheld the validity of the original analysis. Research in this area continues to be interesting because each system points out features peculiar to the ions and solvents involved. A number of metal acetates have been studied by ultrasonics including alkali earthsF3 transition metals,4Psand lanthanides.6 Generally, attention has focussed upon the metal ions. The relaxation of aqueous copper acetate at 20 "C was characterized by Maass. He attributed the relaxation to the formation of contact pairs from the separated Cu2+and acetate ions and reported net forward and reverse rate constants for the process. The purpose of this work is to determine whether Maass' interpretation can be extended to copper formate and propionate. In addition to a kinetic analysis of the relaxations, we shall calculate the volume changes accompanying ion association and relaxation parameters. The relaxations of copper formate and propionate are reported for the first time. Since more accurate values of the rate constants for copper acetate are available from previous experiments in this laboratory,' they are used instead of the ones obtained by Maass. Experimental Apparatus The absorption measurements were made with an improved pulse amplitude comparison technique which is both accurate and precise. A schematic of the electronics (1) M. Eigen and K. Ta", 2.Elektrochem., 66, 93, 107 (1962). (2) N. Purdie and A. J. Barlow, J. Chem. SOC.,Faraday T r a m . 2,68, 33 (1972). (3) G. Atkinson, M. M. Emma, and R. Fernandez-Prini, J. Phys. Chem., 78, 1913 (1974). (4) G. M u . 2.Phvs. Chem. (Frankfurt am Main). 60. 138 (1968). (5) S. Harada, T. Ybunaga, K.'Tam&a, and N. Tat&moto, J..Phys. Chem.. 80. 313 (1976). (6) N. Purdie and 'M. M. Farrow, Coord. Chem. Reu., 11,189 (1973). (7) D. Eden and J. G. Elias, J. Acoust. SOC.Am., 65, 548 (1979).
is shown in Figure 1. A frequency-stabilized continuous-wave signal generator is the source for the gated transmitter whose output is split to both the exciting transducer and a continuously variable waveguide beyond cutoff piston attenuatora8 The acoustic signal is detected by a second transducer and combined with the output of the reference attenuator. The radio-frequency pulses are amplified in the receiver, square law detected, and applied to the input of the gated differential integrator. The gates for the integrator are positioned so that the first coincides with the attenuated, exciting pulse and the second with the acoustically delayed pulse. The signal-averagedoutput of the gated integrator is monitored with a voltmeter. For each data point, the reference attenuator is adjusted until the amplitude of the reference pulse is the same as that of the received acoustic pulse as indicated by a null on the voltmeter. Because the reference and acoustic signals are derived from the same radio-frequency pulse and because they pass through the same receiving and detecting electronics, the pulse stability and the gain stability and flatness do not limit the accuracy of the measurement. It is therefore possible to determine the amplitude of the acoustic signal within 0.01 dB, which is the resolution of the reference attenuator (specified accuracy 0.01 dB/20 dB). The signal enhancement derived from the presence of the gated integratorg facilitates accurate measurements in solutions with large attenuations. Preliminary measurements on copper acetate have been reported previous1 and were obtained with a Carstensen differential celllo dIer the frequency range of 1-21 MHz. The absorption coefficient arising from the chemical relaxation is observed directly, since the solvent absorption is directly removed. The accuracy of the measurements was 2 X dB cm-'. The measurements on copper formate and copper propionate were made with a pulsed variable-path-length interferometer over a frequency range of 10-143 MHz. The gated transmitter was implemented by amplifying in an EN1 406L the radio-frequency pulses which were generated s from by a Watkins S6C RF switch driven by a 3 - ~ pulses an EH 171 pulse generator. The variable-path-length interferometer uses a glass cell which is hermetically sealed and totally immersed in a (8) F. Eggers and Th. Funck, Rev. Sci. Instrum., 44, 969 (1973). (9) R. C. Williamson and D. Eden, J. Acoust. SOC.Am., 47, 1278 (1970). (10) J. G. Elias and D. Eden, Reu. Sci. Instrum., 50, 1299 (1979).
0 1982 American Chemical Society
Ultrasonic Absorption Study of Ion Association
The Journal of Physical Chemistry, Vol. 86, No. 1, 1982
141
TABLE I: Relaxation Parameters electrolyte
T, "C
CuPr,
20.0
CuAc,
20.0
CuFo,
20.0
CuFo,
35.0
CuFo,
50.0
103c,M 6.2 12.5 25.0 50.0 75.0 1.6 3.2 6.2 25.0 12.5 25.0 50.0 75.0 100.0 12.5 25.0 50.0 75.0 100.0 12.5 25.0 50.0 75.0 100.0
f R , MHz
1017A, sz cm-'
8.00 i 0.98 9.29 i 0.38 12.73 t 0.59 15.24 t 0.49 16.75 t 0.42 6.15 i 0.60 7.01 i 0.92 7.86 i 0.35 9.85 t 0.49 35.92 i 5.29 40.96 i 3.70 41.09 t 3.76 42.86 t 1.28 47.43 i 2.34
54.04 t 8.23 113.34 t 5.01 155.04 t 4.91 231.81 t 4.24 309.22 t 4.68 15.14 i 0.49 33.16 t 1.48 63.44 i 1.13 122.69 t 2.74 17.36 i 1.85 35.37 i 2.10 54.74 i 4.30 73.20 t 1.36 92.78 i 3.72
58.51 71.59 71.48 81.82 76.33 72.90 62.24 74.30 97.14 141.14
5.01 10.69 t 7.32 i 9.61 i 4.83 i
i
t
t i i i
GENERATOR
Flgure 1. Pulse amplitude comparison electronics: Signal generator (Wavetek Model 3000); reference attenuator (Ailtech Model 323 1); detector (Hewlett-Packard Model 423A); gated differential integrator (Molectron Model 112); transducers (2 MHz, 36" Y t u t lithium niobate); gated transmttter and receiver (see text).
12.28 5.45 8.54 11.78 36.39
12.79 28.74 47.73 57.97 61.90
i t i i i
10.94 t 18.45 t 33.69 t 34.98 i 64.84 i
Solutions Copper(I1) formate was prepared by the addition of an excess of 90% formic acid to copper carbonate" (Fisher certified). Light blue crystals of copper formate-tetraformic acid were filtered from the solution. After allowing (11)R. L. Martin and H. Waterman, J. Chem. SOC.,1359 (1959).
26.12 26.78 28.36 30.71 28.06 -0.22 -0.98 -1.44 14.03
i i i
t i i
t i t
0.3% 0.42 1.47 2.14 1.80 0.55 1.62 1.44 3.05
23.00 t 2.02 21.49 i 2.39 23.42 i 4.65 23.74 i 1.54 21.46 t 3.94 13.09 i 0.96 9.26 * 4.02 5.34 t 5.20 3.45 t 7.43 9.51 i 3.41
0.90 3.78 4.96 7.18 3.20 1.98 0.94 3.60 3.91 23.83
9.07 i 2.06 10.47 r 1.14 8.07 i 3.81 9.29 i 4.10 -14.87 i 24.03
to stand overnight in a desiccator the crystals converted to royal-blue anhydrous copper formate. Copper(I1) propionate monohydrate was obtained similarly from copper carbonate and propionic acid.12 The dark, blue-green crystals separated from solution were recrystallized from hot, dilute propionic acid. Solutions of copper formate and copper propionate in the concentration range 0.0062-0.1 M were prepared by the dilution of stock solutions with doubly deionized water. Copper(I1) acetate monohydrate was purchased from Mallinckrodt (AR) and dissolved without further purification in doubly deionized water. Measurements were made on 0.0016-0.025 M solutions.
Results and Discussion The ultrasonic absorption spectra of aqueous copper formate at 20,35, and 50 "C and copper acetate and copper propionate at 20 "C,shown in Figures 2-4, can be described by eq l for a single relaxation, where a is the LY
thermostated bath. Displacement of 4 cm is possible and the liquid volume is 30 cm3. The support for the top transducer has been coupled to the top of the glass cell with a very flexible welded stainless steel bellows. The pressure changes, which are concomitant with the volume changes as the bellows is compressed or extended, are moderated by a ballast volume attached to the cell. The transducer drive is a Gaertner M303A micrometer stage with a specified accuracy of 0.0002 in. The accuracy of the attenuation measurements is determined principally by the resolution of and total range of attenuation and displacement. Least-squares fits to the data typically result in attenuation uncertainties of 0.005,0.01, and 0.9 dB cm-' at frequencies of 10, 32, and 143 MHz, respectively.
lO"B, s2 cm-'
A
+B
= + f2/fR2 absorption coefficient, fR is the relaxation frequency, A is the relaxation amplitude, and B is the background absorption. In the cases of copper formate and copper propionate, at frequencies below 32 MHz, a was corrected for diffraction effects by using Benson's tables.13 Diffraction corrections were unnecessary in the differential cell measurements of copper acetate. The weighted experimental data were fitted to eq 1by the method of least squares.14 The calculated values of fR, A , and B are given in Table I. Some features of Table I require comment. In the case of copper acetate, only the excess absorption is measured. In fact, except for the most concentrated solution, B is determined to be zero within the uncertainty of the fit. The relaxation frequencies of copper formate approach the (12) R. L. Martin and H. Waterman, J. Chem. SOC.,2545 (1957). (13)(a) G. Benson and 0. Kioyhara, J. Acoust. SOC.Am. 56, 184 (1974);(b) "Table of Integral Functions Describing Diffraction Effects in the Ultraeonic Field of a Circular Piston source", cited in ref 13a. (14)H. Margenau and G. Murphy, "The Mathematics of Physics and Chemistry", Van Nostrand, Princeton, NJ, 1965,p 517-9.
142
Sattar and Eden
The Journal of Physical Chemistry, Vol. 86, No. 1, 1982 I
I
I
I
C U F O ~35C ,
b
6
\
I
0
'
I
CuFo2 ,50C
i
50t
i
---%
40 -
30 -
55
20 IO -
25
20 50 f (MM)
IO
u
100
IO
20 50 f (MHz)
Figure 2. a l f 2vs. the frequency, f , for copper formate at 20 (a),35 (b), and 50 (+) 0.0125 M. The vertical bars denote the relaxation frequency.
100
IO
20
50
100
f (MHz)
"C (c): (0) 0.1 M; (A)0.075 M; (W) 0.05 M; (V)0.025 M; I
CuPr2 , 2I 0 4'
2 7 0 K 230
'i 1
I
10
Figwe 3. aIf2vs. the frequency, f , for copper acetate at 20 "C: (V) 0.0016 M; (W) 0.0032M; (A)0.0062 M; (0) 0.025 M.
20 50 f (MHz)
I00
Flgure 4. aIf2vs. the frequency, f , for copper propionate at 20 'C: (0) 0.075 M; (A)0.05 M; (M) 0.025 M; (V)0.0125 M; (+) 0.0062
M.
high-frequency limit of the apparatus at 35 and 50 "C. Therefore, the accuracy of the relaxation parameters at these temperatures is poorer than that at 20 "C. Only one measurement was possible above the calculated relaxation frequency for the 0.1 M solution at 50 "C. The increase in the relaxation frequency with concentration, evident from Figures 2-4 and Table I, suggests that a bimolecular reaction is involved. Also, note that at any given concentration, copper formate has the highest relaxation frequency of the three electrolytes. The relaxation can be ascribed to the reaction cu2+ + L-
=CuL+ kf
(2)
kr
The rate constants for the forward and reverse steps are given by the expression (3) 2nf, = k&C) + k , where O(c) is a function of the equilibrium ionic activities d In ny
(2a
+ 1) + (a + 1)-d In a
ryis the activity coefficient product, c is the stoichiometric
concentration, and
u
is the degree of dissociation.
O(c) was calculated following the method developed by is obtained from DebyePetrucci.15 ny = ycuztyL-/y~uLt Hiickel theory. u is numerically calculated from
(5) where KA is the overall association constant. The association constants of all three electrolytes are known from solubility measurements at 25 "C and equal 95.2,175, and 167, respectively,for copper formate, acetate, and propionate.16 While it is acceptable to employ these association constants at 20 "C, we shall use them at 35 and 50 "C as well. It has been demonstrated that kf and k, are remarkably insensitive to the value of KA chosen to calculate O(c).15 Even if the KA of copper formate is increased by a factor of five, kf and k , at 50 "C will remain within the estimated limits. k f and k , are obtained from a weighted, least-squares fit to eq 3, as shown in Figures 5 and 6, and are reported in Table 11. (15) A. Diamond, A. Fanelli, and S. Petrucci, Inorg. Chem., 12, 611 (1973). (16) M. Lloyd, V. Wycherley, and C. B. Monk, J. Chem. SOC.II, 1786 (1951).
The Journal of Physical Chemisrry, Vol. 86, No. 1, 1982 143
Ultrasonic Absorption Study of Ion Association
TABLE 11: Rate Constants
10-7kr,
10-9k f , electrolvte
2'. "C
M-1
CuPr, CuAc, CuFo, CuFo, CuFo,
20.0 20.0 20.0 35.0 50.0
1.4 i 1.8 * 3.8 * 9.9 *
L
140,
M-l s-
6-l
s-l
1.9 f 0.1
0.3 0.9 1.4 3.7
~
io-lOkll,
3.8 * 0.3 3.8 0.3 21 * 3 33 f 4 23 * 8
1.73 1.81 1.98 2.85 4.12
10-9k,,,
----
lO-*k,,,
10-7k,,
6-'
6-l
S-l
3.04 3.27 3.68 5.17 6.83
3.8 * 0.3 2.7 f 0.8 3.7 * 2.6 8.0 * 4.1 21 f 11
4.3 f 0.5 4.1 f 1.3 23 * 16 38k 20 30 * 19
CuFo2
I
90
-
.01
.02
.03
e(c) Flgure 6. The relaxation frequency, f R , vs. &c) for copper acetate and copper propionate at 20 O C .
lowing equations for the net forward and reverse rate constants:l .01
.02
.04
.03
ew
Flgure 5. The relaxation frequency, f,, vs. 8(c) for copper formate at 20, 35, and 50 O C .
The rate constant for the diffusion-controlledformation of an ion pair may be independently estimated from the Debye-Smoluchowski expression' 1212
8NkT 0 =30007 1 - e - @ ~
The reverse rate constant is given by (7)
where 0= Iz,z-le2/aDkT, a is the interionic distance in cm, D is the solvent dielectric constant, and N is Avogadro's number. a is calculated by summing the hydrated Stokes radii and equals 4.92 X 5.49 X and 5.81 X cm, respectively, for copper formate, acetate, and propionate. From Table I1 it is clear that the experimental rate constants, kf and k,, are one to two orders of magnitude smaller than the rate constants predicted by a purely diffusion-controlled model. Hence, a slower rate-limiting process must be included in eq 2 to account for the observed relaxations. The Eigen-Tamm mechanism is
__
CU2+(H@)6+ L- ECu2+(H20)8LktZ
k21
k2.3
ha2
hlk32
k, =
(10) + k23 The results of this analysis are reported in Table 11. It may be noted that k23 does not vary greatly among the three copper carboxylates. This is reasonable, since the rate at which the coordinate bond between Cu2+and the water molecule is broken should not depend significantly upon the incoming ligand. The average value of k23is 3.4 X los s-l. This agrees well with the value of 2.5 X lo8 s-l observed by Eigen and Maass for copper acetate" and with the rate constant for water exchange by Cu2+,reported as 3 X lo8 s-l a t 25 "C by using NMR.lB An examination of Table I1 reveals that the rate constant which most differentiates the three electrolytes is k,. The k, of copper formate is five times that of copper acetate or propionate. Since k, k#(c), it is apparent from eq 3 that the size of k, (or k32) causes copper formate to have a higher relaxation frequency than the other two electrolytes. The stabilities of the copper carboxylates parallel those of the corresponding carboxylic acids. The K , of formic acid is ten times greater than the K,s of acetic and propionic acids, which have similar values. For copper formate, the entropy and enthalpy of activation of the second step in eq 8 are found by using the Eyring equation, shown in Figure 7 k21
-
Cu2+(H20)6L(8)
For carboxylates,the equilibrium in the second step favors the contact pairs; the concentration of the solvent-separated pairs is small. Therefore, the steady-state approximation can be applied to the intermediate, i.e., d[ c ~ ~ + ( H ~ o ) ~ L=- ]0./ dThis t condition leads to the fol-
An unweighted least-squares fit of the data to eq 11 gives 10 f 1 kcal/mol and 20 f 1 cal/(K mol) for AH*23 and AS'23, respectively. Values of 5.6-12 kcal/mol and -4-6 .-
(17) R. Wilkins and M. Eigen, Adu. Chem. Ser., No. 49,Chapter 3
(1965). (18)T.J. Swift and R. E.Connick, J. Chem. Phys., 37,307 (1962).
144
The Journal of Physical Chemistry, Vol. 86, No. 1, 1982
I
231-
I
I
1
I
I
’\
Sattar and Eden I
I
I
I
I
I
i
\
i
1 002
005
.01
02
05
.I
CONC (MI
Flgure 8. The overall volume change AV,,, at 20 OC vs. the concentratbn of copper propbnate,).( copper acetate, )(. (0represents Maass’ data), and copper formate (A). 3.1 Figure 7. In k, and In k,,lTvs.
3.2
3.3 I/Tx IO 3
3.4
T-‘ for copper formate.
cal/(K mol) have been reported for m * e x c h and AS*exch from NMR s t ~ d i e s . ~ ~The J ~ discrepancy between the entropies of activation is disconcerting, although the agreement between the enthalpies of activation is good. The Arrhenius activation energy for the overall process is 11 f 1 kcal/mol. Apart from the kinetic information contained in f R , the volume change for the overall reaction, AVI,, can be determined from A in eq l. According to Tamm20
where /3, is the solvent compressibility and u is the sound velocity. G+II is a function related to 6(c)
where
GD =
+
(-1 + -+ -)l -1u 1
u
l + u
-l
(14)
u, 1 u, and 1 - u are the fractions of Cu2+,L-, and CuL+ present at equilibrium. While only the absolute value of AVn can be determined from eq 12, it is assigned a positive value. First, ion association reduces the total number of charged species in solution. Therefore, electrostriction of the solvent is lessened. Second, a water molecule severely compressed by Cu2+is released into the bulk solution. AVII is related to the volume change of each step in eq 8 by
(19) G.W.Meridith and R. E. Connick, Abstracts of the 149th National Meeting of the American Chemical Society, Detroit, April 1965, paper 106M H. P. Bennett0 and E. F. Caldin, J. Chem. SOC.A , 2198 (1971). (20) K.Tamm in “Handbuch der Physik”, S. Flugge, Ed.,Vol. XI/l, Springer-Verlag, Berlin, 1961, pp 202-74.
Despite what one might intuitively suppose, AV12 is not necessarily zero. In fact, it has been shown by dilatometryz1and ultrasonicsB that AV12and AVB may have similar values.23 A plot of AVn vs. c for the three copper carboxylates at 20 “C is shown in Figure 8. (In order to present results over as wide a concentration range as possible, Maass’ ultrasonic relaxation data for 0.0125-0.1 M copper acetate was analyzed to obtain AVII). AVII remains relatively constant between 13 and 15 cm3/mol for copper formate and acetate. However, AVn appears to increase with the copper propionate concentration. Such a trend has been observed before.24 In this calculation of AVII the choice of KAis crucial. G+II is a sensitive function of u, a,, and 6(q), which are all derived from Kk Therefore, it is possible that the dependence of AVII upon concentration is artificial. We note that our AVII’Sare larger than the values for the alkali earth acetates (3.5-9 ~ m ~ / m o l ) . ~ %
Conclusion We have measured the ultrasonic absorption of dilute solutions of copper carboxylates using an improved absorption technique. We determined that Maass’ treatment of the acoustic relaxation in copper acetate can be applied to copper formate and propionate. The kinetic analysis was extended by using the steady-state approximation to calculate the rate constants for the individual steps leading to ion association. We observed that the ligand derived from the strongest acid forms the weakest complexes with the metal Acknowledgment. We are grateful to one of the reviewers for his helpful comments on the manuscript. We also thank Derek G. Leaist for writing the computer program which was used to calculate the relaxation parameters. (21) T. G.Spiro, A. Revesz, and J. Lee, J. Am. Chem. SOC.,SO, 4000 (1968). (22) L. G.Jackopin and E. Yeager, J. Phys. Chem., 74,3766 (1970). (23) P. Hemmes, J.Phys. Chem., 76,895 (1972). (24) A. Elder and S. Petrucci, Inorg. Chem., 9, 19 (1970). (25)F. J. C. Rossotti in “Modern Coordination Chemistry”, J. Lewis and R. G. Wilkins, Ed., Interscience, New York, 1964, Chapter 1, p 51.
