J . Phys. Chem. 1989, 93, 1182-1184
1182
Hydration of Compiexed Chloride Ions in Aqueous Zinc( II ) Chloride Solution P.S . Salmon School of Physics, University of East Anglia, Norwich NR4 7TJ, United Kingdom (Received: August 2, 1988)
The chloride ion coordination numbers, obtained from the neutron diffraction experiments of Powell et al.' on aqueous ZnClz solutions, are analyzed assuming inner-sphere complexing of the chloride ion by zinc. Several of the different published sets of stability constants, which describe the equilibria between the various zinc complexes present in solution, are used to determine the mean number of water molecules, R, in the complex C1Zn(H20),+. It is shown that, irrespective of the set of stability constants used, ,t is independent of concentration, within the experimental uncertainty of the neutron data, and takes a value in the range from 3.2 to 3.6. This result implies that the mean number of water molecules displaced from free chloride ions on complexing with Zn2+is constant and independent of whether the chloride ion is incorporated in the species ZnCl+, ZnCl,, ZnCl,-, or ZnC1,2-.
Introduction It has long been an aim to identify the degree of complexing and type of complexed species formed in aqueous ZnC12 solution. Although information has been gained from many different sources, including X-ray diffraction,2 Raman s ~ a t t e r i n g , ~ . ~ transport and dielectric relaxation8 measurements, no clear picture has emerged. There is, however, strong evidence for inner-sphere complexing of the chloride ion by ZnZ+,especially at higher solution concentrations. In this Letter we focus on the recent first order difference neutron diffraction experiments of Powell et al.' in which the local environment of the chloride ion was investigated as a function of ZnC12 solution concentration. A sufficiently large concentration range was covered to suggest an attempt at deducing the individual hydration numbers of the different types of complexed chloride ion. This can be achieved by an analysis of the neutron data using a suitable set of stability constants for the equilibria that describe complex formation. Theoretical Background Powell et al.' measured the first order difference function AGcl(r) in several heavy water-ZnC12 solutions, by using the method of isotopic substitution in neutron diffraction. AGcl(r) describes the correlations involving the chloride ion in solution and is given by the expression
where the gcv(r) are the chlorine partial pair distribution functions and the coefficients A , B, C, and D depend on the concentration and coherent scattering lengths of the species present. Its measurement enabled the determination of the coordination number BE, where
fig =
4T7
-s," dr PIAGcl(r)- AGa(0)]
(2)
r,,, is the position of the first minimum in AGcl(r),cDis the atomic
TABLE I: Chloride Ion Coordination Number i$ at =23 O C Expressed as a Function of ZnCI, Solution Concentration" c/M i# (10.2) c/M i # (10.2) 0.27
5.6
0.52
5.1
1.07
4.5
2.03 3.83
4.5 4.4
"The values were obtained from the neutron diffraction work of Powell et ai.' The concentrations, c, refer to light water solutions that have a ratio of ZnCl2:H20that is the same as the ratio of ZnC12:D20 in the solutions of the neutron diffraction work (see text). M refers to the molarity scale of concentration (Le., mol L-I). fraction of deuterium in solution, p is the atomic number density of the solution, and AGcl(0) = - ( A B + C + D ) . The results that were obtained for @ are presented in Table I; r,, was found 7 in each of the solutions that were studied. to be ~ 2 . 8, The observed reduction of iit; with increase in solution concentration suggests that there is a significant degree of inner-sphere is in the range from complexing of the chloride ion by zinc: iznCI 2.25 to 2.60 8, in the crystal hydrate ZnC1z.11/3H209 and it is unlikely that ?clcl< 2.7 8, (in an aqueous 14.9 m LiCl solution, for example, gclc,(r) = 0 for r 5 3.0 AI0). It follows that
+
where iiD is the mean number of deuteriums and AZn the mean number of zinc ions at a distance 0 < r < rminfrom the chloride ion. 6, is the coherent scattering length of species a,and i i ~is, often identified with the chloride ion hydration number.' Further progress can be made if it is assumed that there is no polymerization at the concentrations used in the Powell et al.' study. In this case the chloride ion species that contribute to At; are either free or ion paired with a single zinc ion. A hydration number of 4 . 6 has been measured for the chloride ion in solutions where the degree of ion pqiring is negligible." The chloride ion species in ZnC12 solution can therefore be written as Cl(H20)5,, and CIZn(HzO),+ where ,t is the mean hydration number. Thus, if we let c- be the equilibrium concentration of free chloride ions and c the total concentration of zinc in the ZnClz solution, then iiZn = (1 - c 4 2 c ) and (3) becomes
(1) Powell, D. H.; Barnes, A. C.; Enderby, J. E.; Neilson, G. W.; Salmon, P. S . Faraday Discuss. Chem. SOC.,in press. (2) Paschina, G.; Piccaluga, G.; Pinna, G.; Magini, M. J . Chem. Phys. 1983, 78, 5745. ( 3 ) Irish, D. E.; McCarroll, B.; Young, T. F. J . Chem. Phys. 1963, 39, 3436. (4) Shurvell, H. F.; Dunham, A. Can. J . Spectrosc. 1978, 23, 160. (5) Agnew, A.; Paterson, R.J . Chem. SOC.,Faraday Trans. 1 1978, 7 4 , 2896. (6) Easteal, A. J.; Giaquinta, P. V.; March, N. H., Tosi, M. P. Chem. Phys. 1983, 76, 125.
(7) WeingPrtner, H.; Muller, K. J.; Hertz, H. G.; Edge, A. V. J.; Mills, R.J . Phys. Chem. 1984,88, 2173.
(8) Kaatze, U.; Lonnecke, V.; Pottel, R. J . Phys. Chem. 1987, 91, 2206.
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Powell et al.' analyzed their data using (4) with c- taken from the Raman scattering results of Irish et aL3 in which a negligible concentration of the species ZnC13- was assumed. The existence (9) Follner, V. H.; Brehler, B. Acta Crystallog. 1970, 826, 1679. (10) Copestake, A. P.; Neilson, G. W.; Enderby, J. E. J . Phys. C: Solid Stale Phys. 1985, 18, 4211. (11) Enderby, J. E.; Cummings, S.; Herdman, G. J.; Neilson, G. W.; Salmon, P. S.; Skipper, N. J . Phys. Chem. 1987, 91, 5851.
0 1989 American Chemical Society
The Journal of Physical Chemistry, Vol. 93, No. 4, 1989 1183
Letters
TABLE 11: Mean Hydration Number, R, of the CIZn(H20),+ Complex Calculated from (4) Using Different Ki
c - ~ K I K ~ K+~ ~Kj (~K l K z K 3+ 2cKiK2K3K.J + c - ~ ( K I K ~ c K ~ K ~ K ~C_'KI ) ~ - ( l- cK1) - 2~ = 0 (7)
+
+
+
and the ci (i = 1, 2, 3, 4) follow from the expression
and (6). If we denote by xi ( i = 1,2, 3,4) the hydration number of the chloride ion when it is incorporated in, respectively, the species ZnCP, ZnC12, ZnC13-, and ZnC142-, then it follows that, at each solution concentration (2c - c-)-I(qx,
+ 2c2x2 + 3c3x3 + 4c4x4) = R
(9)
The individual xi can be found by solving the set of linear equations thus generated which, in matrix notation, are given by
cx = !i
(10)
where !iis a column vector whose elements are obtained from the neutron diffraction experiments using (4) and Cis a matrix having the property that its row elements sum to unity, Le., cjCij= 1.
Results and Discussion Owing to the lack of self-consistency between the published sets of stability constants and the different ionic strengths of the solutions used in the neutron diffraction work, R was evaluated using (4) for each set of four Ki given in references 12-15. Errors on X were calculated by assuming that the only significant uncertainty arises from fig. The ratio bz,/bD was fixed at 0.85,16 (12) SilEn, L. G.; Martell, A. E. Stability Constants of Metal-Ion Complexes; Chemical Society: London, 1964. (1 3) Sillen, L. G.; Martell, A. E. Stability Constants of Metal-Ion Complexes; Chemical Society: London, 1971; Suppl. 1. (14) HBgfeldt, E. Stability Constants of Metal-Ion Complexes Part A: Inorganic Ligands; IUPAC Chemical Data Series 21; Pergamon: Oxford, 1982. (15) Smith, R. M.; Martell, A. E. Critical Stability Constants. Vol 4: Inorganic Complexes; Plenum: New York, 1976.
Figure 1. Experimental coordination numbers obtained by Powell et al.' in aqueous ZnClz solution (shown as dots with error bars) plotted as a function of the zinc concentration, c, and compared with (4) which was calculated using several different models for c-. Full line, c- calculated from the Ki given by set A and X fixed at 3.3; dotted line, c- calculated from the Ki given by set B and X fixed at 3.3; dashed line, c- calculated from the Ki given by set C and X fixed at 3.6; dot-dashed line, c- taken from Figure 9b of Irish et al.' and f fixed at 3.0 (these are the results obtained by Powell et al.'); squares, c- taken from Table I11 of Irish et ai.' and X fixed at 3.0.
and the concentrations used in the diffraction work were first converted, on the molality scale, to give the same ratio of ZnCl2:HZ0as ZnC12:D20used in the diffraction experiments and subsequently converted to the molarity scale using the density data in ref 5. The results are given in Table 11. It should be noted that the x value obtained at the lowest concentration is independent of the set of Ki chosen because fig is equal to 5.6, the hydration number of free chloride ions. This value for fib seems to be too large since, from (4), fig is only expected to equal 5.6 in the limit when c2c whereas the maximum value of c-/2c a t 0.27 M, calculated using the Ki, is ~ 0 . 8 . It was not found possible, in view of the large errors on the .f, to obtain reliable xi from solving (10). However, with the exception of the lowest concentration data, the R values for any given set of stability constants are in agreement, within experimental error, across the concentration range covered in the neutron diffraction experiments. The values of 2 for each set of Ki, averaged over the four highest concentrations, are given in Table I1 where they are denoted ( 3 ) . It is found that (n) falls in the range from 3.2 t o 3.6. The assumption that x is independent of concentration was made by Powell et a1.l in their data analysis wherein they obtained, using
-
~
~
~
~
(16) Sears, V. F.Thermal-NeutronScattering Lengths and Cross Sections for Condensed-Matter Research; Atomic Energy of Canada Limited Report AECL-8490; 1984.
J. Phys. Chem. 1989, 93, 1184-1187
1184 c- taken from Irish et aL3, x
3. The present analysis supports this approach as illustrated in Figure 1 where the fig from the neutron diffraction experiments are compared with (4) which was evaluated using several different models for c-. The three sets of Ki used to obtain the curves based on the present analysis are given, on the molarity scale, by K1 = K2 = 0.32, K3 = 10, K4 = 0.1 (set A); K, = 0.48, K2 = 1.86, K3 = 0.56, K4 = 1.41 (set B); and K1 = 2.0, K2 = 1.0, K3 = 10, K4 = 0.1 (set C). Set A has previously been used to interpret 67ZnN M R chemical shift data,I7 set B has been compared with dielectric spectroscopy data with some measure of success,8 and set C has been recommended by Smith and MartellI5 for ZnC12 solutions of ionic strength Z = 4. The R value for each Ki set used in (4) was fixed at the corresponding (2)value given in Table 11. The agreement between the measured and calculated fig is much better when c- is taken (17) Marciel, G. E.; Simeral, L.; Ackerman, J. J. H. J. Phys. Chem. 1977, 81, 263.
from the present model than when, like Powell et aI.,l c- is taken from Figure 9b in the paper of Irish et aL3 The agreement is, however, improved by taking the tabulated values given by Irish et aL3 (see Figure 1). The implication of 3 values that are independent of concentration and equal to a constant value (x) is that the individual xi (i = 1 , 2 , 3 , 4 ) are all equal to the same constant. This follows from (10) since IC1 # 0 for any set of Ki used in the present work and G C i j = 1. Thus the mean number of water molecules displaced from free chloride ions on complexing with Zn2+ is, within the experimental uncertainty on the neutron diffraction data, independent of the type of complex species. It would be of interest to test this result by repeating the neutron diffraction experiments at the same values of c but in solutions of constant ionic strength. Acknowledgment. I thank Hugh Powell and Roderick Cannon for several useful discussions. The financial assistance of the UK Science and Engineering Research Council is gratefully acknowledged.
First Observation of Carbon Aggregate Ions >C,,,+ Transform Mass Spectrometry
by Laser Desorption Fourier
Hun Young So and Charles L. Wilkins* Department of Chemistry, University of California, Riverside, Riverside, California 92521 (Received: September 22, 1988)
Pulsed carbon dioxide laser desorption Fourier transform mass spectra (LD/FTMS) of benzene soot samples, deposited upon a stainless steel probe tip and a potassium chloride coated stainless steel probe tip, are reported. Under both conditions, polyaromatic hydrocarbon ions with m / z below 1000 and a series of even-numbered carbon aggregate positive ions extending above m / z 7200 are observed. Enhanced relative abundance of Cso+is found for soot deposited upon stainless steel, but not on KC1-coated stainless steel. In the high mass region above m / z 1O00, it appears that two distinct distributions of carbon aggregate positive ions can be detected. One distribution appears to be centered around c154+and a second, much broader, distribution extends from ca. C300+to above Cm+.
Formation of neutral and ionic aggregates exclusively containing carbon, via laser ablation processes from graphite,’-I0 has inspired a good deal of dialogue regarding the structures of these species. Because no direct structural information is available, various structural proposals including both spherical3 and linear crosslinked polymeric speciesI0 are rationalized in terms of mass spectrometric ion abundance measurements. One particular aggregate, Ca+, and its metal-attach,ed derivatives have been the subject of much discussion, primarily because of Smalley’s im(1) Rohlfing, E. A.; Cox, D. M.; Kaldor, A. J. J. Chem. Phys. 1984,81, 3322-3330. (2) Heath, J. R.; O’Brien, S.C.; Zhang, Q.; Liu, Y.; Curl,R. F.; Kroto, H. W.; Tittel, F. K.; Smalley, R. E. J. Am. Chem. Soc. 1985.107, 7719-7780. (3) Kroto, H. W.; Heath, J. R.; O’Brien, S.C.; Curl, R. F.; Smalley, R. E. Nature 1985, 162-163. (4) Bloomfield, L. A.; Geusic, M. E.; Freeman, R. R.; Brown, W. L. Chem. Phys. Lett. 1985, 121, 33-37. ( 5 ) OKeefe, A.; Ross, M. M.; Baronavski, A. P. Chem. Phys. Lett. 1986, 130, 17-19. (6) OBrien, S.C.;Heath, J. R.; Kroto, H. W.; Curl, R. F.; Smalley, R. E. Chem. Phys. Lett. 1986, 132,99-102. (7) Hahn, M. Y.; Honea, E. C.; Paguia, A. J.; Schriver, K. E.; Camarena, A. M.; Whetten, R. L. Chem. Phys. Leu. 1986, 130, 12-16. (8) McElvaney, S.W.; Nelson, H. H.; Baronavski, A. P.; Watson, C. H.; Eyler, J. R. Chem. Phys. Lett. 1987, 134, 214-219. (9) Knight, R. D.; Walch, R. A.; Foster, S.C.; Miller, T. A.; Mullen, S. L.; Marshall, A. G. Chem. Phys. Lett. 1986, 129, 331-335. (10) Cox,D.M.; Reichmann, K. C.; Kaldor, A. J. Chem. Phys. 1988,88, 1588-1597.
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aginative nomenclature (which describes the parent species as “buckminsterfullerene” or “ b ~ c k y b a l l ” and ) ~ ~the ~ ~ ingenious experimental evidence he and his co-workers adduce for their thesis regarding its special geometry and ~ t a b i l i t y . ~ - ’However, ~ ~ ’ ~ it is by no means established that the claimed special stability exi s t ~ ~ , ’or, ~ ,indeed, ’~ that the stability, if it does exist, cannot be explained equally well by structural alternatives, including those advanced by Kaldorlvloand others.15 Ultraviolet lasers were used in most prior studies of carbon aggregate formation, both in the aggregate formation step and to photoionize the resulting species for subsequent mass spectral analysis. Here, we report a number of interesting new observations regarding direct observations of carbon aggregates formed from benzene soot, using a pulsed infrared (C02) laser, with Fourier transform mass spectrometric detection (LD/FTMS).16 Although these new data do not resolve the structural questions, they may assist in evaluating the validity (11) O’Brien, S. C.; Heath, J. R.; Curl,R. F.; Smalley, R. E. J. Chem. Phys. 1988,88, 220-230. (12) Weiss, F. D.; Elkind, J. L.; O’Brien, S. C.; Curl, R. F.; Smalley, R. E. J. Am. Chem. SOC.1988, 110, 4464-4465. (13) O’Brien, S. C.; Heath, J. R.;Kroto, H. W.; Curl, R. F.; Smalley, R. E. Chem. Phys. Lett. 1986, 132, 99-102. (14) Cox,D. M.; Trevor, D. J.; Reichmann, K. C.; Kaldor, A. J. Am. Chem. SOC.1986, 108, 2457-2458. ( 1 5 ) Frenklach, M.; Ebert, L. B. J. Phys. Chem. 1988, 92, 561-563. (16) Ijames, C. F.; Wilkins, C. L. J. Am. Chem. SOC.1988, 110, 2681-2688.
0 1989 American Chemical Society
