Complexation of Metal Ions with Crown Ethers
parameter at each temperature. When further studies are available, it may be possible to make an a priori prediction of that parameter based on the physical properties of the system.
Acknowledgment. Discussions with Dr. D. G. Hendry
(SRI International) concerning the pertinence of this work to atmospheric modeling were very helpful. We also thank C. J. Howard, R. A. Graham, A. M. Winer, and J. N. Pitts, Jr., for allowing us to quote their experimental results prior to publication.
References and Notes (1) H. Niki, P. D. Maker, C. M. Savage, and L. P. Breitenbach, Chem. Phys. Left., 45, 564 (1977). (2) R. Simonaitis and J. Heicklen, J . Phys. Chem., 80, 1 (1976). (3) C. J. Howard, J . Chem. Phys., in press. (4) R. A. Graham, A. M. Winer, and J. N. Pitts, Jr., Chem. Phys. Lett., 51, 215 (1977).
The Journal of Physical Chemistry, Vol. 82, No. 6, 1978 647
(5) S. W. Benson and D M. Golden in "Physical Chemistry; An Advanced Treatise", Vol. VII, H. Eyring, D. Hendersen, and W. Jost, Ed., Academic Press, New York, N.Y., 1975. 161 D. M. Golden and G. P. Smith. Int. J . Chem. Kinet.. in Dress. (7j C. Anastasi and I. W. M. Smith, J . Chem. Soc., Faraday trans. 2 , 72, 1459 (1976). (8) C. J. Howard and K. M. Evenson, GeoDhys. Res. Lett., 4.437 (1977). (9) L. Batt, R. T. Milne, and R. D. McCuliough, Int. J. Chem. Kinet., 9, 567 (1977). (10) D. R. Stull, E. F. Westrum, and G. C. Sinke, "The Chemical Thermodynamics of Organic Compounds", Wiley, New York, N.Y., 1969. (1 1) S. W. Benson, "Thermochemical Kinetics", Wiley, New York, N.Y., 1976. (12) D. G. Hendry and R. Kenley, J. Am. Chem. Soc., 99, 3198 (1977). (13) R. A. Cox and M. J. Roffey, Environ. Sci. Techno/.,11, 900 (1977). (14) E. V. Waage and B. S. Rabinovitch, Chem. Rev., 70, 377 (1974). (15) S. E. Stein and B. S. Rabinovitch, J . Chem. Phys., 58, 2438 (1972). (16) "JANAF Thermochemical Tables", Natl. Stand. Ref. Dah Ser., Natl. Bur. Stand., No. 37 (1970). (17) This, in fact, violates the principal of conservation of angular momentum. Calculations in which the rotation was adiabatic change the final results by less than a factor of 2. (18) J. Troe, J. Chem. Phys., 66, 4745 (1977).
Kinetic Studies of Complexation of Divalent Strontium, Barium, Lead, and Mercury Cations by Aqueous 15-Crown-5 and 18-Crown-6 Gerard W. Liesegang,lb Michael M. Farrow,lb Neil Purdie,lc Liceslo J. and Edward M. Eyring"lb Department of Chemistry, University of Utah, Salt Lake City, Utah 84 112 (Received June 24, 1977; Revised Manuscript Received October 27, 1977) Publication costs assisted by the Office of Naval Research and the Air Force Offlce of Scientific Research
The rates of complexation-decomplexation of the 15-crown-5 [1,4,7,10,13-pentaoxacyclopentadecane] and complexes of the aqueous cations Sr2+,Ba2+,Pb2+,and Hg2+ 18-crown-6[1,4,7,10,13,16-hexaoxacyclooctadecane] have been determined from ultrasonic absorption measurements covering the 15-205-MHz frequency range at 25 "C. As in the case of previously reported studies of complexation of monovalent cations by these crown ethers, the data have been fitted to a two-step mechanism. Diffusion has been ruled out as the rate-limiting step in the complexation. Loss of the coordinated water from the ions is proposed as the rate-determining step.
Introduction Interest in the solution chemistry of the synthetic macrocyclic polyethers has increased greatly since their introduction by Pedersen,' stimulated by the many chemical and biological applications of these ligands as complexing and transport agents for metal ions. In a previous kinetic investigation3 of the complexation equilibria between monovalent metal ions and the crown ethers Chock proposed a mechanistic scheme involving a ligand conformational rearrangement followed by the stepwise substitution of the coordinated solvent molecules by the ligand. Kinetic studies in this lab~ratory"~of aqueous monovalent metal ion and ammonium ion complexation by 18-crown-6 and 15-crown-5 have confirmed the existence of at least one conformational rearrangement equilibrium for each of the ligands. Furthermore, one conformer strongly predominates in each such conformational equilibrium; the predominant form is involved in the metal ion complexation equilibrium; and complexation is not diffusion controlled. The kinetics of the complexation equilibria involving these same crown ethers with some divalent metal ions is considered here. If loss of coordinated water is rate limiting then complexation rates should be slower for 0022-365417812082-0647$01 .OO/O
divalent ions compared to monovalent ions. In making our choice of divalent ions, two with inert gas configurations, Sr2+ and Ba2+, and two ions with nonspherical coordinations, Pb2+and Hg2+,were selected. By analogy with the results for monovalent ions where faster complexation rates were observed for nonspherically coordinated Ag+ and T1+ ions, the rates of complexation of Pb2+and Hg2+ by the polyethers might be anticipated to be greater than those for Sr2+and Ba2+. If such were the case, we would have additional evidence for water loss as the rate-limiting step in the mechanism.
Experimental Section Ultrasonic absorption measurements were made at 25.0 f 0.1 "C over an acoustic frequency range from 15 to 205 MHz, using a computer-controlled laser acoustooptic t e ~ h n i q u e . ~The argon ion laser was operated at the 514.5-nm green line and the piezoelectric acoustic transducer element was a gold-plated, 5-MHz frequency, X-cut quartz crystal which was driven at odd harmonics over the frequency range. Additional low-frequency measurements were made on aqueous solutions of BaClz with 15-crown-5 using resonance ultrasonic absorption techniques. 0 1978 American Chemical Society
The Journal of Physical Chemistry, Vol. 82, No. 6, 1978
648
Eyring et al.
TABLE I: Relaxation Parameters from Computer Analysis for Complexation by 15-Crown-5O Strontium 1017~. [ S ~ C I , ] , , ~ [15-Crown-5],,~ M M 1.00 1.51 1.82
0.0877 0.0877 0.0797
Mkz
cmNysa
10l8 rmsc
9.95 14.09 18.33
157.9 82.37 48.89
1.3 1.0
f R 11,
-----%
1.0
fr
Bariumd 1017~, [BaCl,],, M
[15-Crown-510, M
0.756 0.886 1.01
0.0640 0.0864 0.0860
Mkz
c,"-Psz
1Ol8 rms
12.15 15.92 19.64
144 126.7 84.5
1.5 2.5 2.3
10'7~, Np 10" cm-'s2 rms
f R 11,
Lead( 11) [Pb(C104),],, M
[15-Crown-5l0, M
f~ 11,
0.413 0.516 0.688
0.0783 0.130 0.0877
19.72 20.80 31.19
Mkz
69.17 83.87 32.92
1.2 1.8 0.9
Mercury(I1) [Hg(C104),]0, M
[15-Crown-5l0, M
f~ 11, Mkz
1017~, NP 10" cm-'s2 rrns
0.590 0.871 1.15
0.114 0.111 0.107
14.97 18.91 26.20
759.3 572.1 287.1
2.3 2.3 1.9
The subscript a All symbols as defined in the text. zero on concentration denotes total concentration. Barium results based on Root mean square deviation, resonance ultrasonic absorption measurements in the 0.9to 4-MHz frequency range as well as on higher frequency acoustooptic data.
I I
I
f
IO
50
I
I
100
250
f [MHz]
Flgure 1. Plot of ultrasonic absorption, expressed as a / P ,vs. logarithm of the experimental frequency for aqueous solutions of BaCI, plus 15-crown-5. Experimental points are as follows: A for [Ba*+], = 0.756 M, [15-crown-5], = 0.064 M; 0 for [Ba2+], = 0.886 M, [15-crown-5], = 0.0864 M; H for [Ba2+], = 1.01 M, [15-crown-5], = 0.0860 M. The curves are computer calculated, nonlinear, least-squares fits of the experimental data. For clarity, the curves are arbitrarily displaced vertically; all have the same high-frequency asymptote of 21.7 X lo-'' Np cm-' s-'. The vertical amplitudes are as given in Table I. Data points at f < 10 MHz were obtained by a resonance technique.
TABLE 11: Relaxation Parameters from Computer Analysis for Complexation by 18-Crown-6a Strontium
1.00 1.40 1.89
0.100 0.100 0.0920
10.82 17.12 20.97
89.00 64.70 46.25
2.1 1.4 1.1
19.19 39.48 24.76 (b) 25.14 28.10 (c) 21.99
1.7 1.2 1.1
Barium
-
-
1.00
1.30 Solutions were prepared using deionized redistilled 1.50 water. The 15-crown-5 and 18-crown-6 (Parish Chemical Co., Provo, Utah) were purified as described previou~ly.~,~ The inorganic ions were all analytical reagent grade. Strontium and barium ions were in the form of chloride [Pb(CIO,),lo, M salts and stock solutions were prepared by weight. The lead and mercury ions were introduced as perchlorates. 0.24 2 These latter stock solutions were standardized either 0.323 gravimetrically (PbSOJB or titrimetrically (Hg(CNS)Ja9 0.430
Results Total sound absorption data, expressed as ( a / f ) T Np cm-l s2 (see paragraph at end of text regarding supplementary material), were analyzed in terms of relaxational and nonrelaxational contributions to the ultrasonic absorptions. In all cases only one relaxational process was detected. The best fit was obtained using the following one-relaxation equation: + ( f / f R ) ' ] - l -k where A is the relaxation amplitude, f and f R are respectively the experimental ultrasonic and relaxational frequencies, and B is the solvent absorption, which was varied in the fitting process around the pure water value to take account of the structural changes in the solvent brought about by the added electrolyte. However, if the final best B value was in the range 21.7 f 0.5 X Np cm-l s2, that of the pure water obtained on the present equipment, the central value 21.7 X 1O-l' Np cm-l s2 was used in the fit as a fixed parameter. Representative plots of experimental data for Ba2+and 15-crown-5 are shown
(a/fz)T
I
5
= A[1
0.100 0.100 0.100
Lead(I1) [18-Crown-610, f~ 11, M Mkz 0.0134 0.0179 0.0238
11.50(d) 16.37 ( d ) 21.69 (e)
1017~,
czPs2
10l8 rrns
45.94 30.92 23.43
0.9 0.5 0.5
Mercury (11)
0.354 0.47 2 0.590
0.0400 0.0450 0.0500
21.80 28.51 32.55
71.28 58.39 55.76
1.0 1.1 1.2
a A background of ( b ) 23.0 x 10-17,( c ) 22.7 x 10-17, ( d ) 20.6 X lo-", ( e ) 2 0 . 2 x lo-'' Np cm-' s2 give the best
fit to the experimental data.
in Figure 1. For clarity the data sets have been displaced vertically relative to each other; all have the same a / f in the limit of high frequencies (>250 MHz). Tables I and I1 show the parameters calculated at different concentrations of crowns and metal ions which give the best fit of the experimental data. The resulting values of the relaxation frequencies, f R , are in some cases below the lower limit of the experimental frequency range scanned with the present equipment. For several of these sample solutions complementary measurements were madelo on resonance ultrasonic spectrometers in the -0.5-
The Journal of Physical Chemistry, Vol. 82, No. 6, 1978 649
Complexation of Metal Ions with Crown Ethers
TABLE 111: Rate Constants for Complexation by 15-Crown-5 and 18-Crown-6 in Aqueous Solution at 25 C Calculated from Ultrasonic Absorption Data 15-Crown-5 18-Crown-6 O
Cation
k Z 3 M-' , s-'
k,,, s-'
K T M-' ~
k,,, M-l s-l
k32,
Sr2+ BaZ
6.5 x 107 1.2 x l o 8 3.2 X 10' 1.6 X 10'
7.3 x 105 2.3 X l o 6 4.6 X lo6 3.3 x lo6
89.1 51.3 70.8 47.9
7.7 x 107 1.3 X l o 8 3.3 x lo8 4.0 X 10'
1.5 x 1.7 x 1.8 x 1.5 X
+
PbZ+ Hg2+ a
KT,a M-I
105 104 104 10'
5.25 X 7.41 X 1.86 x 2.63 X
10,
lo3 104 10'
Izatt et al., ref 11.
to 5-MHz frequency range. Discrepancies greater than a factor of 2 were noted in the absorption amplitudes for some of the strontium-15-crown-5 solutions. Other solutions gave generally better agreement between the two methods. Practically the same relaxation frequencies, f ~ , were found from the composite ultrasonic data as were found originally in the laser acoustooptic measurements a t Utah. By comparing the analysis of only the higher frequency acoustooptic data with the analysis of the composite data including the low frequency resonance results, an average maximum error of f14% in f~ was established for the three Ba2+and 15-crown-5 data sets (Figure 1). Since these three data sets show relaxation frequencies which might be considered to be at the lower analysis limit of the equipment in this laboratory, the value of -14% error in fR was used to estimate errors in the computed rate constants. This -14% error in fR gives rise to an uncertainty in the complexation rate constant h23 (determined graphically from a plot of eq 6) of the same magnitude. Since none of the calculations or conclusions in this paper are based on the ultrasonic absorption amplitudes, uncertainties in their magnitudes are irrelevant to the present discussion. Earlier studies in this laboratory of the complexation kinetics of monovalent metal ions by 15-crown-5 and 18-crown-6 were i n t e r ~ r e t e d ~in- ~terms of a two-step mechanism (eq 1 and 2) previously suggested by Chock3 N
for the case of metal ion complexation by dibenzo-30crown-10 in methanol. Although the relaxation time of the conformational step was not measured in Chock's study, a concentration independent relaxation frequency for pure crown in aqueous solutions has been reported for both 15-crown-56(fR,I = 22.9 MHz) and 18-crown-64(fR,I = 101 MHz). Accordingly it seems reasonable to expect that a two relaxation process should be observed when complexing electrolytes are present. The above reaction scheme is mathematically described by the secular de~ ,the extent of terminant in eq 3 where Xi = l / ~and
0 Ti+
1
1
I
I 2
ionic chargelradius
Figure 2. Plof of the logarithm of the rate constant for complexation, k,,, vs. the ratio of ionic charge to ionic radius (arbitrary units) for complexation by 18-crown-6, 0, and by 15-crown-5, 0 . The straight diagonal line is a least-squares fit of the alkali and alkaline earth metal data.
one relaxation is observed when electrolytes are p r e ~ e n t . ~ For the divalent ions, therefore, an analogous two-step mechanism is to be expected with the second step having the larger amplitude and thus giving rise to the detected relaxation. Consequently, the analysis of the kinetic data is made in terms of contributions from only this step, i.e.
(4) The experimental equilibrium concentrations can be calculated from the equilibrium constants for the overall complexation KT, reported by Izatt et al.ll in the form
(5) Taking into account the fact that [CR,] >> [CR,] since we have found12 for both 15-crown-5 and 18-crown-6 K2,
