J . Phys. Chem. 1984, 88, 2382-2386
2382
a similar trend in the conductivity behavior under isofluidity conditions was noticed. Ingram et a1.I0 gave a mechanistic interpretation to such a conductivity behavior on the assumption that the paired cations form the mobile species in the xK2Si03-(1 - x)Na2Si03-7H20 system. In the light of a similar structural interpretation it is also possible to explain the composition dependence of conductivity of the system under interest. In fact, such an attempt was made by EastealI4 to explain the MAE in Ca(N03)2 (Li,K)N03 hydrate melts. However, any similarity between the MAE in silicate melts and in hydrate melts of the present type is doubtful, since it is difficult to visualize a relatively rigid network structure (which exists in silicate, borate, germanate, and oxide melts and glasses) as existing in hydrate melts.
+
Acknowledgment. S.M. is grateful to the University for the award of a Senior Research Fellowship to him. Registry No. KSCN, 333-20-0;NaSCN, 540-72-7;Ca(NO&, 10124-37-5. Supplementary Material Available: For the 0.3[xKSCN-( 1 - x)NaSCN]-0.7Ca(N03)2.4.06H20 melts least-squares-fitted
values of the parameters of the density equation, p = a - bt(OC), are presented in Table I, the conductivity and the fluidity as functions of temperature and composition are presented in Table 11, and best-fit values of the parameters of eq 1 for the conductivity are presented in Table I11 (4 pages). Ordering information is available on any current masthead page.
Investigation on the Structure of Cadmium Nitrate Aqueous Solutions by X-ray Diffraction and Raman Spectroscopy R. Camhiti,* P. Cucca, Istituto di Chimica Fisica e Industriale, Universitci di Cagliari, 09100 Cagliari, Italy
and T. Radnai Central Research Institute for Chemistry of the Hungarian Academy of Sciences, H-1025 Budapest, Pusztaszeri lit 59-67, Hungary (Received: May 9, 1983; In Final Form: September 26, 1983)
X-ray scattering on a 4.54 M aqueous Cd(N03)2solution and the Raman spectra of five solutions from 1.04 to 4. 4 M have been measured at 25 OC, together with the spectra of hydrated melt and solid. Both the spectral features and the X-ray pair-correlation function suggest the presence of anionic hydration shell and inner-sphere complex. Model interpretations of the X-ray data are discussed. As a result, two hydration shells around the cation and one composed of about nine water molecules around the anion are described. The presence of the complex of the mean formula Cd(H20)50N02+is consistent with the X-ray data.
Introduction The coordination of Cd2+ ions has been the subject of recent investigations in various aqueous solutions by X-ray diffraction. The presented structural models propose two possible coordination states for Cd2+: either it is completely surrounded by six water molecules, as already found by Ohtaki et al.’ in the Cd(C104)2 solution, or the anion enters into the first hydration shell of the cation. This was reported for the chloride, sulfate and phosphate solution^,^-^ where the anions act as monodentate ligands. For the completely hydrated Cd2+ ions, the existence of a second hydration shell was also d e ~ c r i b e d . ~ - ~ As concerns the hydration of NO3- ion, the X-ray diffraction results show greater variety and are more uncertain than for the Cd2+. In fact, sometimes the simple detection of the presence of the hydrating water molecules is difficult, while to assign to them an average geometry is almost hopeless. Here uncertainties arising from the physical nature of nitratewater interactions concur with the difficulties in interpretation, as pointed out elsewhere.6 Although the NO3- ion has a tendency to create ion pairs with cations, no X-ray diffraction work examined this question up to now for the Cd(N03)2solutions. Only a dilute aqueous solution (1) H.Ohtaki, M. Maeda, and S . Ito, Bull. Chem. SOC.Jpn., 47, 2217 (1974). (2) R. Caminiti, G. Licheri, G. Paschina, G. Piccaluga, and G. Pinna, Rend. Semin. Fac. Sci. Univ. Cagliari, 50, 367 (1980). (3) R. Caminiti and G. Johansson, Acta Chem. Scand. Ser. A , 35, 373 (1981). (4) R.Caminiti, 2.Naturforsch. A , 36, 1062 (1981). (5) R. Caminiti, J. Chem. Phys., 77, 5682 (1982). (6) R. Carniniti and T. Radnai, 2.Naturforsch. A , 35, 1368 (1980).
0022-3654/84/2088-2382$01 SO/O
(1 M) was studied by Bo1 et al.,’ and the Cd(H20)62’ complex was found as the only species present. Evidence for complexation in aqueous solutions of cadmium nitrate was found in more recent conductivity, calorimetry, emf, and polarography measurements. These studies indicate the presence of a mononitratocadmium species. A dinitratocadmium species has also been proposed, but no higher complexes.8 Infrared and Raman spectroscopies have been extensively used in the studies of anion-solvent and cation-anion interactions in solutions containing NO3- ion^.^-'^ In fact, the vibrational spectrum of the unperturbed nitrate ion may be altered either by interaction with the solvent or by association. Then, in principle, it is possible to get information on the condition of nitrate ions in aqueous solutions through spectroscopic investigations. The results show that the transition of the NO3- ion from an aqueous environment to the state of an ion in competition with water molecules for sites in the first coordination sphere of the cation should take place gradually, through states where the hydrated cations perturb the hydration sphere of NO3- ions. (7) W.Bol, G.J. Gerrits, and C. L. Van Panthaleon Van Eck, J . Appl. Crystallogr., 3, 486 (1970). ( 8 ) H . E. Hellwege and G. K. Schweitzer, J . Znorg. Nucl. Chem., 27, 99 (1965). (9)D. E. Irish in “Ionic Interactions”, Vol. 11, S. Petrucci, Ed., Academic Press, New York, 1971. (10)A. R. Davies and R. A. Plane, Znorg. Chem., 7 , 2565 (1968). (11) D.E. Irish and A. R. Davies, Can. J. Chem., 46, 943 (1968). (12) D. E.Irish. A. R. Davies, and R. A. Plane, J . Chem. Phys., 50,2262 (19kgj. (13) D. L. Nelson and D. E. Irish, J. Chem. Phys., 54, 4479 (1971).
0 1984 American Chemical Society
Structure of Cadmium Nitrate Aqueous Solutions
The Journal of Physical Chemistry, Vol. 88, No. 11, 1984 2383
TABLE I: Cd2' Concentration of the Studied Solutions (Nl-N5)" soln
[Cd2+],mol/L
soh
N1 N2 N3 N4
1.04 1.94
N5 ME
2.85 3.84
so
[Cd2+],mol/L 4.54 melt solid
a ME and SO are the melted and solid salts of Cd(N0,);4H20 formula, respectively.
Various techniques, including vibrational spectroscopy, render it possible to estimate the equilibrium constants for the outer- or inner-sphere complex formation, from which an average number of nitrate ions bound to the cations can be derived. These techniques, however, did not give direct information about the structural nature of the complexes. These studies do not say how many H,O molecules hydrate the ions and, least of all, if a preferred spatial arrangement of the molecules exists around the central ions. This kind of information, even if sometimes less reliable, can only be concluded from diffraction experiments. In the crystal structure of Cd(N03),.4H20 two nitrate ions are bound to cadmium in the first hydration shell, as determined by X-ray d i f f r a ~ t i 0 n . l ~ For the saturated solution equilibrium constant values were reported, varying from 0.7415 to 1.298 at a temperature of 25 OC, which corresponds to 0.8 d z d 0.9, where z stands for the average number of NO3- ions bound to Cd2+. From vibrational spectroscopy Davies and Planelo give a value of 0.38 for the formation constant at 44 OC, which leads to z = 0.69. A recent ultrasonic study on dilute cadmium nitrate solutions in nonaqueous solvents16resulted in formation constants between CdZ+and NO< without any temperature dependence in the range 15-45 OC when the solvent is methanol and dimethyl sulfoxide. Since here, as also in water, the oxygen is the donor atom involved in the solutesolvent interaction, it is reasonable to check whether significant changes can be observed in the spectra due to the temperature effect. For obtaining direct structural information on the cation-anion interactions, an X-ray diffraction study on the saturated Cd(N03), aqueous solution at 25 OC is reported. The highest available concentration (4.54 M) offers the best possibility for the observation and geometrical description of the complexes present in the solution with the help of X-ray diffraction. For the sake of having the vibrational spectra a t the same temperature, Raman spectroscopy measurements were also carried out on a concentration series of solutions as well as on solid salt, together with one on melted salt at 60 OC.
Experimental Section Preparation and Analysis. The sample solutions were prepared by dissolving Cd(N0,),.4Hz0 (Carlo Erba reagent grade) in water. The concentration of Cd2+ion was determined by EDTA titration. The NO< ion was determined by a method previously de~cribed.'~The density of the saturated solution was 1.7994 g ~ m - The ~ . Cd2+concentration of the sample solutions is given in Table I. X-ray Scattering Measurement and Data Treatment. The 8-8 X-ray diffractometer and technical details of the measurement have previously been described.17 Mo K a radiation was used with wavelength X = 0.71 1 A. The measured intensity was recorded in the s range from 0.6 to 15.5 A-', where s = (4?r/X) sin 8. The applied correction and normalization process was the same as in ref 6. The obtained structure is
(14) B. Matkovic, B. Ribar, B. Zelenko, and S . W. Peterson, Acro Crystallogr., 21, 719 (1966). (15) I. F. Tate and M. M. Jones, J. Phys. Chem., 65, 1661 (1961). (16) S . Yamada and R. E. Verrall, J . Phys- Chem., 85, 3145 (1981). (17) R. Caminiti, G. Licheri, G. Piccaluga, and G . Pinna, J. Chem. Phys., 68, 1967 (1978).
1
1
1
1
1
1
6
1
1
1
1
1
I
I
I
I
15
I
Figure 1. Experimental structure function si(s) for 4.54 M Cd(NO& solution (points) compared with the synthetic structure functions (full line) obtained from the preliminary calculation (model P part a) and from the best fit (model A, part b).
wherefj(s) is the atomic scattering factor, xj is the corresponding stoichiometric coefficient in a structural unit containing m kinds of atoms, and 1," is the intensity in electron units. The experimental correlation function C(r) was computed from si(s) by Fourier transformation according to
G(r) = 1
+ (2?rZpor)-'
si@) sin (sr) ds
(2)
where r is the interatomic distance, smin and,,,s are the lower and upper limits of the experimental data, and po is the bulk number density of the stoichiometric units. After repeated Fourier transformations when the unphysical peaks present in the G ( r ) at small r values were removed, the structure function was corrected for residual systematic errors. In this process the peak due to the intramolecular N - O distance centered at about 1.25 A, was also removed. Although less information can be deduced on the geometry of the NO3- ion in such a way, the removal of the peak ensures that the residual peaks in the G(r) are real, as demonstrated earlier.6J7-19 Raman Spectroscopic Measurements. The Raman apparatus consisted of a CRL-CR2 argon laser (0.4 W, 488 nm), a 25-100 double monochromator from Jarrell Ash, a cooled FW- 100 photomultiplier, and a digital data acquisition system. The solution to be investigated was contained in a Beckman 5-cm3 cylindrical cell and the beam was continuously monitored after a single passage through the cell. In order to avoid local heating and subsequent density and concentration fluctuations, the laser light was defocused to give a beam of about 5-mm radius. The spectra recorded in this way were reproducible in time.
Results X-ray Data. The experimental functions si(s) and G(r) are shown in Figures 1 and 2, respectively, for the 4.54 M solution. In the correlation function some peaks can clearly be. distinguished. From their positions and from earlier results on Cd2+-containing a rough assignment of interactions to the characteristic distances can be made. The first peak at 2.25 A is certainly ascribable to Cd-H201 or Cd-O (0is oxygen from nitrate group) interactions in the first ~
(18) R. Caminiti, G. Licheri, G. Piccaluga, and G. Pinna, Chem. Phys. Leri., 61, 45 (1979). (19) R. Caminiti, G. Licheri, G. Piccaluga, and G. Pinna, J. Chem. Phys., 72, 4522 (1980).
2384 The Journal of Physical Chemistry, Vol. 88, No. 11, 1984
Caminiti et al.
1
I
I
I
I
-I
L
I
1
I
I
I
I
1
I
I
I
I
I
L
I
I
I
I
I
I
I
I
3.0-
2.5-
2.0
-
1.5-
0.0-
r,i I
2
I
3
I
4
I
5
I
6
,
7
Figure 2. Experimental correlation function G(r) for 4.54 M Cd(N03)Z solution (points) compared with that calculated from the structure function for model A. The 0-2-A-I region of the latter one was substituted by the corresponding experimental values.
coordination shell. Contributions to this peak are also due to 0-0 interactions within the anion (at about 2.2 A). The double eak present in the range 2.5-3.3 A has its maximum at 2.85 with a shoulder at 3.15 A. The maximum value is characteristic for the nearest-neighbor water-water interactions such as between hydration water molecules of CdZ+directly bound to second-neighbor water molecules (HZOI-H2011), while contributions can also arise from interactions between the 0 atoms of the NO3- ion and its hydration water molecules. The shoulder, absent in phosphate, sulfate, and perchlorate solution^,^-^ as well as in solutions of N a N 0 3 , NH4N03, and Mg(N03)2,17-19may be ascribed to Cd-N interactions, indicating the presence of complexes in C d ( H 2 0 ) 5 0 N 0 2 +form. Contributions from H201-H201interactions are also expected at about 3.2 A. The small hump at 3.5 A can be, at least partly, due to the N-H20 interactions since its value is not too different from that found earlier for N-H20 pairs assuming that the water molecules occupy positions around the anion directed by tetrahedral angle~.~*'' The large peak centered at 4.35 A is obviously a composite one. It can mainly be attributed to interactions between Cdz+ ions and H20 molecules in the second coordination shell, but minor contributions from interactions between second-neighbor water molecules in the coordination shell around Cd2+also fall into this region. No peaks are discernible at greater distances in the experimental G(r). The observable order phenomena therefore seem to extend up to about 5 8, only. The quantitative description of the possible structuring in the solution is treated with the help of a model hypothesis in a later part of the paper. Raman Data. Spectra obtained for the studied solutions and for the melted and solid salts are shown in Figure 3 in the range from 600 to 850 cm-'. A comparison of the band positions and relative intensities for the 4.54 M solution with those reported by Davies and Planelo for the same solution at 44 "C reveals an excellent agreement. The spectral features of N03--containing solutions have been analyzed extensively in various The splitting of the single v3 mode frequency at 1384 cm-' into two lines even in very
w
t k 1 7 b 1 CM'
9% L
'O0
Figure 3. Raman spectra for aqueous Cd(N03)2solutions and for the melted and solid salts in the range from 600 to 850 cm-I. For the denotations of the samples see Table I.
diluted solutions gave evidence for the presence of hydrated anions. The appearance of a new maximum at 1452 cm-' and the increasing asymmetry of the intense v1 mode vibration band at about 1045 cm-' due to a new component on the low-frequency side with increasing concentration was attributed to the nitrate bound to the cation. The increase in H-bond strength between the first- and second-shell water molecules with respect to the pure water cannot be directly detected by Raman spectroscopy. It was pointed out," however, that the observed increasing half-width of the vl mode band with increasing concentration is, at least partly, diagnostic of increased polarity of the water molecules in the NO3- environment, due to the Coulombic field of the Cd2+ ion. As a consequence, when second-shell water molecules are present instead of the nitrate ions, they must be also strongly bound to the first-shell molecules, with increased Coulombic contribution to the H-bond energy. So the behavior of the above band serves also as an indirect argument for the existence of strong interactions between the two hydrate shells around the cations as was concluded from X-ray studies on solutions containing two- and three-valent cations. The most convincing evidence for the ion-pair formation is the concentration dependence of the v4 mode frequency at 720 cm-I, due to the "free" NO3- ion (Figure 3). In fact, the above band exhibits only a slight asymmetry on the high-frequency side in dilute solutions. For the 4.54 M solution the 740-cm-' band is as intense as the 720-cm-' one, while the latter one disappears completely in the solid, where both nitrate ions of the stoichiometric unit are bound to the cadmium. The position of the new component is continuously shifted toward the higher frequencies with increasing concentration. It is worth noting that in the melted salt, where the chemical composition remains the same as in the solid, the 720-cm-' band is still present. This effect shows that in the liquid phase the number of bound nitrates is less than in solids even at low water content. For the saturated solution a further decrease in number of ion pairs is obvious, which is in
The Journal of Physical
Structure of Cadmium Nitrate Aqueous Solutions
Chemistry,
H O (2 a
TABLE 11: Best Parameter Values and Their Standard Deviationsa for Model Pb ‘Cd-H,OI
2.212 (5)
uCd-H201
nCd-H201
0.10 (1)
5.1 ( 2 )
Vol. 88, No. 11, 1984 2385
For explanation see the text. The distance and its rmsd are given in angstroms. a In parentheses.
qualitative accordance with the result of Davies and Plane.” Model Interpretation of the X-ray Structure Function In order to study the structure of the 4.54 M solution in a more quantitative way, the experimental X-ray structure function i(s) was analyzed with the help of models. As the usual process is, “synthetic” structure functions i*(s) were constructed with adjustable structural parameters. These were then compared with the experimental one by a least-squares fit procedure. The criterium for the best fit was fixed by the condition
u = C w ( s ) [ i ( s )- i*(s)I2= minimum
(3)
S
The weighting function w(s) was chosen as unity in the whole s range. In principle the i*(s) function can be decomposed into
the sum of two contributions i*(s) =
id($)
+ i,(s)
(4)
where d and c stand for the discrete structure and the continuum, respectively, both being the result of the superposition of atom-pair interactions of all possible kinds. The detailed mathematical formulas are given elsewhere.” Models. Five models were constructed: a preliminary calculation for evaluating the cationic hydration only (model P), a complete model which yielded the best fit (model A), and three restricted models for checking the reliability of the complete model (models B-D). Throughout the calculations only the id($)function was applied. In the continuum part, i,(s), the weight of the contribution of a given i j pair interaction would be equal to m
(5)
where i j is Cd, N , 0, or H 2 0 , and 6ij is the Kronecker delta. It is very easy to show that for the solution in question all cijfunctions are almost equal, and introducing them should lead to an unreasonable increase in the number of fitted parameters. On the other hand, if the discrete structure is extended enough, the i,(s) part influences only the low s range of the i*(s) function. It is noteworthy that the usual introduction of the continuum in the form of pair interactions is often questionable and its physical meaning is not cleared up. When the i,(s) function was left out, it was necessary to put the lower s limit for the fitting procedure to s = 2 A-1. This choice proved to be satisfactory, as can be seen from the results. In model P only Cd-H201 interactions were introduced. Three independent parameters were used: the distance rCd-H201, its root mean square deviation (rmsd) aCd-H201, and the coordination number nCd-H201. The final values are reported in Table 11. The obtained structure function is given in Figure l a (solid line). The features of the experimental structure function were very well reproduced for s > 5 AM‘. The Cd-H201 distance is near to the values found in solutions and in solids,20-22in spite of the neglect of the eventual influence of the contribution from i,(s) in the s range 2-5 A-1. The coordination number is very close to 6, and the rmsd is rather small, so the parameters make the assumption (20) R. Caminiti and G. Johansson, Acta Chem. Scand., Ser. A , 35,451 (1981). (21) G. Johansson, M. Sandstrom, and R. Caminiti, (Cd(C104)2.6H20 structure) to be submitted for publication. (22) H. Montgomery and E. C . Lingafelter, Acta Crystallogr.,20, 728 (1966).
Figure 4. Geometrical model assumed for the bonding of the nitrate group to the hydrated cadmium ion. The structural unit has a mirror plane containing the CdZ+ion, the HzO,, the bridging oxygen O, the N atom, and the 0, and O2atoms. The LCd-O,-N angle resulted in 118’.
for an octahedral geometry in the hydration shell rather convincing. Model A was built up on the basis of the qualitative analysis of the experimental G(r) and of Raman spectra, as well as of the result obtained from model P. The model used can be described as follows: (1) The first neighbors of a Cd2+ion occupy octahedral positions in a composition of Cd(H201)6-z0z,where 0 is an oxygen atom of the bound NO3- ion. The interactions within the octahedron were described by four independent parameters: the distance rCd-H201 and the rmsd u1 for the Cd-H201 interaction, uz for the HZO-HZOI cis distances, and u3 for the HzOI-H201 trans distances. (2) Second-neighbor interactions around cadmium were taken into account. The Cd-HzOII interactions were characterized by two new independent parameters, i.e., the distance rCd-H2011 and the coordination number nCd-H2011. The corresponding rmsd is u3. (3) As concerns the HZO-H2OII interactions belonging to two subsequent hydration shells of the cation, the distance rH2OrH2Ol1 was regarded as an independent parameter, while the coordination number fiH2O1-H2OI1is related to ItCd-H2011 by the relationship
- nCd-H20~~/(6 - z , [H2011
(6)
nH201-H20~~
No fixed orientation was chosen for H2011molecules. The rmsd of this distance was ul. (4) For the NO< ion, the usual planar structure was assumed6J3 with the 0-0distance and the corresponding uw as parameters to be refined. ( 5 ) Since the Raman data indicated the presence of hydrated anions, contributions for both 0 - H 2 0 and N-H20 type interactions were also introduced but without any preliminary assumption for the symmetry or the number of interactions. Inn0-H20, rN-H20, nN-H,O. The dependent parameters were rmsd values ul for O-H20 and u2 for N-H20 distance were used. (6) The assumed geometrical form for the cadmium-nitrate complex is shown in Figure 4. The interactions Cd-N, Cd-01, Cd-02, and (H20)i=br(ON02)rwere correlated to the LCd-O-N angle (0being here O3in Figure 4) once the reciprocal orientation between the octahedron and the nitrate plane had been fixed. Only two new independent parameters were introduced, namely, the number z of bound NQ3- groups and the LCd-0-N an le. The rmsd values used here were u1 for the distances G3.0 u2 for the distances between 3 and 4 A, and u3 for distances 24 A. (7) With this model no bulk water was allowed stoichiometrically at the given concentration. In spite of the fairly complicated model construction, the number of fitted parameters was relatively small (14). This is due to, beyond the exclusion of the continuum terms, the choice of the three rmsd values ul, u2, u3 ascribed to different ranges of distances. The results show that this approximation is good enough, in spite of the doubtless simplification involved. In the refinement process the parameters were adjusted gradually, allowing always the less correlated parameters to vary simultaneously. Models B-D served for checking the influence of the complex, anionic and cationic hydration on the complete model A. In model B contributions from the complex Cd(H20)i=6-,(ON02),were omitted (point 6 of model A). In model C the assumption for
f,
2386 The Journal of Physical Chemistry, Vol. 88, No. 11, 1984
Caminiti et al.
TABLE 111: Best-Fit Values for Independent Parameters of Model Aa cation anion 2.284 (5) 2.69 (1) 4.31 (1)
rCd-H 201
YHzOI-H2 0 1 1 ‘Cd-H ,011
yo-0
?O-H,O YN,.H,o
2.215 (5) 2.89 (1) 3.49 (1)
Gtr)
0
r. A I
I
I
I
I
I
I
I
4 5 6 Figure 5. Experimental correlation function for 4.54 M Cd(NO,)* solution (points) compared with those calculated from models A-D (full line).
3
the anionic hydration was dropped (point 5 of model A). Finally, in model D only the cationic hydration was maintained (points 1-4 of model A). The subsequent drastic increase in the leastsquares sum and the worse agreement between the experimental and theoretical functions support the reliability of model A, so the whole refinement process was not repeated for models B-D. Discussion of Model Results. The best theoretical structure function is given in Figure l b (solid line), and its corresponding correlation function in Figures 2 and 5a (solid lines). The agreement with the experimental functions is fairly good. The obtained parameter values are listed in Table 111. Both models P and A confirm that the scattering data are consistent with a regular octahedral coordination of the CdZ+ion in aqueous solution. The rCd-Hlo,and ul parameters (Tables 11 and 111) agree within the precision of the method and are very close to those found in p e r c h l ~ r a t e ,~~u? l~f a t e ,p~h, ~ s p h a t eand ,~ nitrate’ solutions. The distance is also in good agreement with those obtained for crystal structures of Cd(N03)2.4H20,13 3CdSO4.8H2,OZ0Cd(C104)2.6H20,21and (NHz)2Cd(S04)~. 6Hz0.22 As far as second-order interactions around Cd2+are concerned, it is very likely that the nearest-neighbor water molecules are relatively strongly H bonded to outer ones. From eq 6 nHZOrH2011 distance is significantly 2.4 can be calculated. The r shorter than the average 2.85-f%z-?eighbor distance for the pure water. This effect was often found in the presence of twoand three-valent cations. The cationic contributions to the X-ray structure function are definitely predominant compared with the anionic ones. Moreover,
-
00-0 fl1 0 2
0.04 (1) 0.120 ( I ) 0.163 (9) 0.375 (8)
complex 2
LCd-0-N
0.96 (7) 118 (2)
11.9 (7) ~N-H,O 8.8 (6) fl3 The standard deviations are in parentheses. The distances and their rmsd values are given in angstroms, and the LCd-0-N angle in degrees. nCd-H2011
a
rmsd
the contribution due to the first hydration shell is by far the greatest. It almost entirely reproduces the i ( s ) function for values of s > 5 A-l (Figure la). Further on, with the exclusion of contributions from anionic hydration shell and the complex, as in models B-D, the main features of the G(r) still are reproduced. As far as the NO3- ion is concerned, both the intra- and intermolecular distances and u parameters are very similar to those expected from earlier result^.^^^*^^^ From rM and the supposed geometry of NO,- a value of 1.28 A is derived for the distance N-0, in agreement with the literature data. In spite of the minor weight of its contribution, the presence of an anionic hydration shell is quite clear. This is also in agreement with the Raman results. The value of 3.49 A for the N-H20 distance corresponds to the position of the small peak in the experimental G(r). The reasonableness of this identification as well as the significance of the 0-H20 distance may be judged from model C (and D) where the omission of these contributions led to the changes in the G(r) in the given range. An exact geometry for the arrangement of the hydrating water molecules was not a priori assumed (point 5 of model A). A rough calculation for the average LN-O-H~O angle, based on the obtained distances, will result in about 107O, which is in good agreement with the tetrahedral structure reported in a concentrated N H 4 N 0 3 solution.” Moreover, the number of hydrating water molecules per oxygen atom resulted in almost three; therefore, the tetrahedral arrangement is spatially allowed. It seems not to be. very probable, however, that the water molecules occupy these symmetry sites simultaneously, because of the weak interactions between the anion and its hydration shell. Further on, the Raman spectra did not give any obvious indication for this feature; on the contrary, the lowering of the symmetry of the NO3- ion from D3,,to C, suggests the three 0 atoms cannot be treated as equals. Finally, there is evidence for a complex formation of inner type between cation and NO3- ion also from the model parameters. The shoulder appearing at 3.15 A in G(r) could not be fully reproduced without the introduction of a Cd-N distance, corresponding to the LCd-0-N bonding angle of 118’ (see G(r)-s from models B and D, Figure 5). The average number z of nitrate groups bound to each Cd2+proved to be slightly less than 1. This is reasonable, taking into account the above qualitative arguments based on the changes in the 740-cm-‘ band of the Raman spectra. The obtained z values is more than that obtained from data of Davies and Plane, but it is still in good accordance with values which can be calculated from stability constants provided they are assumed to be valid in the concentrated solution used here.23
Acknowledgment. The work has been supported by the Italian National Research Council (CNR). Raman measurements were performed at the Istituto di Fisica G. Marconi, Universitl di Roma. We thank Prof. G. Signorelli for placing the Raman spectrophotometer at our disposal and Dr. G. Ruocco for valuable technical assistance. Discussions with Dr. G. Kabisch (Freiberg, GDR) are kindly acknowledged. The calculations were done at the Computer Center of the University of Cagliari and at the Computer Center of the Hungarian Academy of Sciences. Registry No. Cd(H20)50N02+, 89415-03-2. (23) L. G . Sillln and A. E. Martell, Spec. Pub1.-Chem. SOC.,No. 17, Supplement No. 1 (1964); Spec. Pub1.-Chem. SOC.,No. 25 (1971).
