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X-ray diffraction study of a “three-ion” aqueous solution
Volume 47, number 2
CHEMICAL PHY S:CS LElTERS
15 ApriI L977
X-RAY DIFFRACTION STUDY OF A “THREE-ION” AQUEOUS SOLUTION R. CAMINITI, G. LICHERI, G. PICCALLJGA and G. PINNA Istituto Chimico. Universitridi Cagliari, OSIOO-Cagliari,Italy Received 11 November 1976 Revised manuscript received 12 January 1977 X-ray diffraction data on an aqueous solution 2 M in MgC12and CaCI2 are shown to be consistent with octahedral coordinations for the three ions as already found in solutions of single electrolytes. The rare-gas-like ion hydration thus appears not affected by the presence of other ions independently hydrated.
I_ introduction Interesting information about rare-gas-like ion hydration has been provided in the last few years by diffraction studies [l-4] _Experimental data appeared to be consistent with a simple model describing the ionic coordination only in terms of nearest-neighbour interactions. Such a model presumes that no correlation is present between hydrated ions so that it might be possible to describe the hydration of an ion always in the same way independently from its concentration and/or its counter-ion. An examination of the data so far available seems to confirm such an expectation [5] and suggests the existence of definite hydration shells in all the cases considered. This also suggests that the hydration shell of an ion may be poorly influenced by greater complexity in the chemical composition of the system. To verify this fact in a simple case, we studied an aqueous solution containing three ionic species, about whose hydration concordant information comes from structural investigations on solutions containing only one electrolyte: the hydration of an ionic species should not be affected by the presence of other ions independently hydrated. The ions chosen were Ca2+, Mg2+ and Cl- _In fact, the calcium and the chloride ions have been exhaustively studied by ourselves (solutions of CaBr2 [3], CaC12 [4] and CrCl, [6]) and by Narten et al. (solutions of LiCl Cl]); hydration numbers, geometry and parameters (that is, ionsolvent distances and their standard deviations) came
out almost coincident for the same ion in the different chemical situations. As regards the magnesium ion, the existence of hexa-aqua complexes in aqueous soIutions has been clearly demonstrated by diffractometric studies [7-91, by NMR spectroscopy [10-l l] and by neutron inelastic scattering [ 121. The choice bf these ions was ako suggested by the different vaiues of their ionic radii which will yield to mean distances ionwater of rather different values, thus facilitating the singling-out and quantitative study of the ion-solvent interaciions. It is worth notin that this is the frost X-ray diffraction investigation of a “three-ion” solution.
2. Experimental and data treatment The solution examined was prepared by mixing equal parts of two 2-molar solutions of CaCI, and MgC12 _ The molar salt cpntent can be thus represented as stoichiometric coefficient x in the unit (CaC12)x(MgCl,),(H,0)1_2,
,
where x = 0.038. X-ray scattering measurements were carried out on a 84 diffractometer (G.S.D. Seifert) in a room thermostated at 18 I 1°C. MO Kac radiation (A = 0.7107 A} was diffracted at the horizontal surface of the sample and then monochromatized by reflection from a curved quartz crystal. The sample was kept in a hydrogen atmosphere. 275
CHEMICAL PHYSICS LETTERS
Volume 47, number 2
The observed range of scattering angles (23) was 4” to 120” correspon~g to the range 0.65 Is-’ < s < 15.28 A-’ (s = 4% sinS/X). Times required to accumulate 40000 counts at each angle were recorded; several runs were made in order to collect 200000 counts per point in the range 4” < 20 <; 60” and 360000 in *he range 60’ < 26 < 120°. The measured intensities were corrected for background, polarization and absorption [ 13f. The Compton contribution was then evaluated by a semi-empirical method 1141 in order to account for mono~romator disc~lnation. The corrected in’ tensities were scaled to the independent scattering fattar for the solution using both the analytical method [lSJ and visual comparison. The structure function was then constructed according to
Cl> where fi are the scattering factors corrected foranomaIous dispersion, xi are the stoic~ometric coefficients in a structural unit containing m kinds of atoms, le,u, is the intensity in electron units. The values of the fi used were those proposed by Bol 1161 for the water molecule and those by Cromer and Mann 1171 for the other species. A correction for residual systematic errors in the structure function was also applied [14]_ , The correlation function G(r) was obtained from i(s) by Fourier transfo~ation according to smax
_
G(r) = 1+ (2T+-jr)-’
s i(s) sin (rs) ds , s Smin
I
15 April 1977
s-t k)
-..-observed -
model
I
t
t
r
4
6
8
10
, &A12
14
Fig. I. Observed (0) and model (-) structure functions.
values are very similar to those reported in the references given above. ObvIousIy, contributions to the large peak at 3.20 A, as weIl as to the secondary small peaks at larger distances may derive from water-water cis and tram distances inside the hydration complexes, For a quantitative analysis a theoretical structure function according to the well-known formula proposed by Narten and Levy f143 was evaluated and systematically refmed by least-squares. The calculations are based on the hypothesis that only water molecules nearest-neighbour to ions have a discrete structure described by appropriate hydration models; therefore, no correlation is taken to be present between hydrated ions, and a uniform distribution of distances (continuum) is assumed for distances larger than those characteristic of the hydration shell. In the fitting procedistances dure Mg2+--H20 Ca 2*-H20 and CI--Hz0 and their mean square deviations were refined as inde-
(2)
where r is the interatomic distance, SmIn and smax are the lower and the upper Iimit of the experimental data, and po is the bulk density of stoichiometric units. 3.. Results and discussion The experimentat functions s i(s) and G(r) are shown in figs. I and 2 respectively (circles). The experimental correlation function shows three main peaks centered at 2.05 A, 2.45 A and 3.20 8, which, on the basis of the crystalline radii of the ions and of the water molecule, can be ascribed to the interactions Mgzi-H20, Ca2*-Hz0 and Cl--H20 respectively. Such distance 276
..... observed model
Fig. 2. Observed (a) and model (-) correlation functions.
15 April W?-i
CHEMICAL, PHYSICS LETTERS
Volume 47, number 2
Table 1
Meandistances r(A) and mean squares deviations o (A), with their standard errors, from Icast-squares refinement, are given for nearest-neighbour ion-water interactions. Mean values of the same parameters obtained in other solutions are also given Solutions
%a *+-Hz 0
%a**-Hz0
‘Mg *+-Hz0
aMg2*-H20
*Cl---H20
%--H20
present work CC12 [4]
2.428 rt 0.007 2.42
0.143 f 0.004 0.14
2.044 t 0.005
0.060 f 0.007
3.130 + 0.005 3.14
0.244 L 0.004 0.22
CaBr;! (31 LiCi I1 I
2.42
0.14
3.14
0.20
pendent parameters. H2O--Ii20 distances in the coordination shells are reIated to ion-water distances by the geometries of the hydration models chosen; their mean square deviations were supposed to be equal for all molecules in the same hydration shell; so only three other independent parameters were required. Finally, the four distances of the start of the continuum and their mean square deviations for Mg2+-H20, Ca2+HZO, Cl--H20 and H,O-Hz0 pairs were considered as independent parameters. No bulk water was present at the investigated concentration. The total number of independent parameters thus resulting may appear rather high, but it is not to be forgotten that we did not aim at investigating ex-novo unknown ionic coordinations but rather at confirming results already found in simpler solutions even in the case of the three-ion solution. Therefore only minor variations in the parameters around mean values already known were expected, and the calculations, as we shall see soon, confirmed the expectations. Therefore, coordination numbers ofsix and octahedraI geometries for all the ions were adopted in accordance with the results obtained in the papers quoted and, in the preliminary calculations, parameter values taken frcm results previously obtained by us or found in literature were used. The compatibility of the model with the experimental results came out very good so that few refinement cycles were required to get the best fit, The best function s i(s) is shown in fig_ I as a solid line; its corresponding correlation function is reported in fig. 2. The agreement between theoretical and experimentaI functions can be considered excellent. The final values of the most significant independent parameters are reported in table 1 (first row)_ In table 1 are also reported (when known) the mean values of the same parameters obtained applying the same method to different solutions. From table I clearly
appears the noteworthy agreement between the parameter values obtained in thk present work and those previousIy found. As far as the Mgzf ion is concerned. complete homogeneoufterms of comparison are not available; but our results confirm the data in the Iiterature [7-l 21 for the coordination number (six) and *the mean ion-solvent distance (2-O--2.1 A); moreover the standard deviation of the ion-solvent interaction has a value less than that relative to the Ca2*--if,0 pair, as expected on the basis of their comparative hydration capacity. it can be conctuded that: (a) The hydration of rxregas-like ions does not sigrrificantly change ifmore than two ions are present in the solution. in fact, not oniy hydration numbers and geometries of the ions examined turned out to be coincident with the values found in simpler solutions, but this was found to be true also for ion-solvent mean distances and their standard deviations in cases where the comparison can be made. (b) There is no evidence of the presence of an ordered structure beyond the first hydration sheik. The possibihty of obtaining reliable information about ionic hydration by X-ray diffraction is again clearly confirmed. .
Acknowledgement This work was partially supported by the &onsigIio Nazionale deile Ricerche, Numericat calculations were performed at the Centro di CalcoIo Elettronico, Universits di Caghari.
References [l ] A.H. Narten, F. Vaslow and H.A. Levy, I. Chem Phys. 58 (1973) 5017.
277
Volume 47, number 2
CHEMICAL PHYSICS LETTERS
121 G. Licheri, G. Piccaluga and G. Piina, Cbem. Phys. Letters 35 (197.5) 119. 131 G. Licheri, G. Piccaluga and G. Piia, J. C.hem. Phys. 63 (1975) 4412. [4] G. Licheri, G. piccaluga and G. Pinna, J. Chem. Phys 64 (1976) 2437. (51 R. Caminiti, G. Licheri, G. Piccaluga and G. Pinaa, Ann. Chim. 65 (1975) 695. (61 R. Caminiti, G. Licbeti, G. Piccaluga and G. Ptina, J. Chem. Phys. 65 (1976) 3134. (71 A-K. Dorosh and A.F. Skryshevskii, Zh. Strukt. Mim. .S (1964) 911. (81 IV. Bol, G.J.A. Getrits and C_L. van Panthateon van Eck, 3. Appt. Cry& 3 (1970) 486.
278
15 April 1973
(91 M. AIves Marques and M.I. De Banos Marques. Xonti. Ned. Akad. Wetenschap. Proc. B 77 (1974) 286. [lOj iV.A. ~Matwiyoffand H. Taube, J. Am. Chem. Sot. 90 (1966) 2796. [J I I J.N. A&i& J_Chem. Sot. Dalton (1973) 42. [IZ] G-J. Safford, P.S. Leung, A-W. Naumann and P.C. Schaffer, I. Chem. Phys. 50 (1969) 4444. /f 31 M.E. Milberg, J. Appl. Phys. 29 (1958) 64. [24 i %A. Levy, M.D. Danford and A.H. Narten, Oak Ridge NationaL Laboratory Report No. 3960 (1966). [lS] 1. Krogtt-Moe. Acta Cryst. 9 (1956) 951. [26] W. Bot, 1. AppI. Cryst, I (1968) 234. [J 71 D.T. Cramer and I.B. Mann, Acta Cryst. A24 (1968) 321.
CHEMICAL PHY S:CS LElTERS
15 ApriI L977
X-RAY DIFFRACTION STUDY OF A “THREE-ION” AQUEOUS SOLUTION R. CAMINITI, G. LICHERI, G. PICCALLJGA and G. PINNA Istituto Chimico. Universitridi Cagliari, OSIOO-Cagliari,Italy Received 11 November 1976 Revised manuscript received 12 January 1977 X-ray diffraction data on an aqueous solution 2 M in MgC12and CaCI2 are shown to be consistent with octahedral coordinations for the three ions as already found in solutions of single electrolytes. The rare-gas-like ion hydration thus appears not affected by the presence of other ions independently hydrated.
I_ introduction Interesting information about rare-gas-like ion hydration has been provided in the last few years by diffraction studies [l-4] _Experimental data appeared to be consistent with a simple model describing the ionic coordination only in terms of nearest-neighbour interactions. Such a model presumes that no correlation is present between hydrated ions so that it might be possible to describe the hydration of an ion always in the same way independently from its concentration and/or its counter-ion. An examination of the data so far available seems to confirm such an expectation [5] and suggests the existence of definite hydration shells in all the cases considered. This also suggests that the hydration shell of an ion may be poorly influenced by greater complexity in the chemical composition of the system. To verify this fact in a simple case, we studied an aqueous solution containing three ionic species, about whose hydration concordant information comes from structural investigations on solutions containing only one electrolyte: the hydration of an ionic species should not be affected by the presence of other ions independently hydrated. The ions chosen were Ca2+, Mg2+ and Cl- _In fact, the calcium and the chloride ions have been exhaustively studied by ourselves (solutions of CaBr2 [3], CaC12 [4] and CrCl, [6]) and by Narten et al. (solutions of LiCl Cl]); hydration numbers, geometry and parameters (that is, ionsolvent distances and their standard deviations) came
out almost coincident for the same ion in the different chemical situations. As regards the magnesium ion, the existence of hexa-aqua complexes in aqueous soIutions has been clearly demonstrated by diffractometric studies [7-91, by NMR spectroscopy [10-l l] and by neutron inelastic scattering [ 121. The choice bf these ions was ako suggested by the different vaiues of their ionic radii which will yield to mean distances ionwater of rather different values, thus facilitating the singling-out and quantitative study of the ion-solvent interaciions. It is worth notin that this is the frost X-ray diffraction investigation of a “three-ion” solution.
2. Experimental and data treatment The solution examined was prepared by mixing equal parts of two 2-molar solutions of CaCI, and MgC12 _ The molar salt cpntent can be thus represented as stoichiometric coefficient x in the unit (CaC12)x(MgCl,),(H,0)1_2,
,
where x = 0.038. X-ray scattering measurements were carried out on a 84 diffractometer (G.S.D. Seifert) in a room thermostated at 18 I 1°C. MO Kac radiation (A = 0.7107 A} was diffracted at the horizontal surface of the sample and then monochromatized by reflection from a curved quartz crystal. The sample was kept in a hydrogen atmosphere. 275
CHEMICAL PHYSICS LETTERS
Volume 47, number 2
The observed range of scattering angles (23) was 4” to 120” correspon~g to the range 0.65 Is-’ < s < 15.28 A-’ (s = 4% sinS/X). Times required to accumulate 40000 counts at each angle were recorded; several runs were made in order to collect 200000 counts per point in the range 4” < 20 <; 60” and 360000 in *he range 60’ < 26 < 120°. The measured intensities were corrected for background, polarization and absorption [ 13f. The Compton contribution was then evaluated by a semi-empirical method 1141 in order to account for mono~romator disc~lnation. The corrected in’ tensities were scaled to the independent scattering fattar for the solution using both the analytical method [lSJ and visual comparison. The structure function was then constructed according to
Cl> where fi are the scattering factors corrected foranomaIous dispersion, xi are the stoic~ometric coefficients in a structural unit containing m kinds of atoms, le,u, is the intensity in electron units. The values of the fi used were those proposed by Bol 1161 for the water molecule and those by Cromer and Mann 1171 for the other species. A correction for residual systematic errors in the structure function was also applied [14]_ , The correlation function G(r) was obtained from i(s) by Fourier transfo~ation according to smax
_
G(r) = 1+ (2T+-jr)-’
s i(s) sin (rs) ds , s Smin
I
15 April 1977
s-t k)
-..-observed -
model
I
t
t
r
4
6
8
10
, &A12
14
Fig. I. Observed (0) and model (-) structure functions.
values are very similar to those reported in the references given above. ObvIousIy, contributions to the large peak at 3.20 A, as weIl as to the secondary small peaks at larger distances may derive from water-water cis and tram distances inside the hydration complexes, For a quantitative analysis a theoretical structure function according to the well-known formula proposed by Narten and Levy f143 was evaluated and systematically refmed by least-squares. The calculations are based on the hypothesis that only water molecules nearest-neighbour to ions have a discrete structure described by appropriate hydration models; therefore, no correlation is taken to be present between hydrated ions, and a uniform distribution of distances (continuum) is assumed for distances larger than those characteristic of the hydration shell. In the fitting procedistances dure Mg2+--H20 Ca 2*-H20 and CI--Hz0 and their mean square deviations were refined as inde-
(2)
where r is the interatomic distance, SmIn and smax are the lower and the upper Iimit of the experimental data, and po is the bulk density of stoichiometric units. 3.. Results and discussion The experimentat functions s i(s) and G(r) are shown in figs. I and 2 respectively (circles). The experimental correlation function shows three main peaks centered at 2.05 A, 2.45 A and 3.20 8, which, on the basis of the crystalline radii of the ions and of the water molecule, can be ascribed to the interactions Mgzi-H20, Ca2*-Hz0 and Cl--H20 respectively. Such distance 276
..... observed model
Fig. 2. Observed (a) and model (-) correlation functions.
15 April W?-i
CHEMICAL, PHYSICS LETTERS
Volume 47, number 2
Table 1
Meandistances r(A) and mean squares deviations o (A), with their standard errors, from Icast-squares refinement, are given for nearest-neighbour ion-water interactions. Mean values of the same parameters obtained in other solutions are also given Solutions
%a *+-Hz 0
%a**-Hz0
‘Mg *+-Hz0
aMg2*-H20
*Cl---H20
%--H20
present work CC12 [4]
2.428 rt 0.007 2.42
0.143 f 0.004 0.14
2.044 t 0.005
0.060 f 0.007
3.130 + 0.005 3.14
0.244 L 0.004 0.22
CaBr;! (31 LiCi I1 I
2.42
0.14
3.14
0.20
pendent parameters. H2O--Ii20 distances in the coordination shells are reIated to ion-water distances by the geometries of the hydration models chosen; their mean square deviations were supposed to be equal for all molecules in the same hydration shell; so only three other independent parameters were required. Finally, the four distances of the start of the continuum and their mean square deviations for Mg2+-H20, Ca2+HZO, Cl--H20 and H,O-Hz0 pairs were considered as independent parameters. No bulk water was present at the investigated concentration. The total number of independent parameters thus resulting may appear rather high, but it is not to be forgotten that we did not aim at investigating ex-novo unknown ionic coordinations but rather at confirming results already found in simpler solutions even in the case of the three-ion solution. Therefore only minor variations in the parameters around mean values already known were expected, and the calculations, as we shall see soon, confirmed the expectations. Therefore, coordination numbers ofsix and octahedraI geometries for all the ions were adopted in accordance with the results obtained in the papers quoted and, in the preliminary calculations, parameter values taken frcm results previously obtained by us or found in literature were used. The compatibility of the model with the experimental results came out very good so that few refinement cycles were required to get the best fit, The best function s i(s) is shown in fig_ I as a solid line; its corresponding correlation function is reported in fig. 2. The agreement between theoretical and experimentaI functions can be considered excellent. The final values of the most significant independent parameters are reported in table 1 (first row)_ In table 1 are also reported (when known) the mean values of the same parameters obtained applying the same method to different solutions. From table I clearly
appears the noteworthy agreement between the parameter values obtained in thk present work and those previousIy found. As far as the Mgzf ion is concerned. complete homogeneoufterms of comparison are not available; but our results confirm the data in the Iiterature [7-l 21 for the coordination number (six) and *the mean ion-solvent distance (2-O--2.1 A); moreover the standard deviation of the ion-solvent interaction has a value less than that relative to the Ca2*--if,0 pair, as expected on the basis of their comparative hydration capacity. it can be conctuded that: (a) The hydration of rxregas-like ions does not sigrrificantly change ifmore than two ions are present in the solution. in fact, not oniy hydration numbers and geometries of the ions examined turned out to be coincident with the values found in simpler solutions, but this was found to be true also for ion-solvent mean distances and their standard deviations in cases where the comparison can be made. (b) There is no evidence of the presence of an ordered structure beyond the first hydration sheik. The possibihty of obtaining reliable information about ionic hydration by X-ray diffraction is again clearly confirmed. .
Acknowledgement This work was partially supported by the &onsigIio Nazionale deile Ricerche, Numericat calculations were performed at the Centro di CalcoIo Elettronico, Universits di Caghari.
References [l ] A.H. Narten, F. Vaslow and H.A. Levy, I. Chem Phys. 58 (1973) 5017.
277
Volume 47, number 2
CHEMICAL PHYSICS LETTERS
121 G. Licheri, G. Piccaluga and G. Piina, Cbem. Phys. Letters 35 (197.5) 119. 131 G. Licheri, G. Piccaluga and G. Piia, J. C.hem. Phys. 63 (1975) 4412. [4] G. Licheri, G. piccaluga and G. Pinna, J. Chem. Phys 64 (1976) 2437. (51 R. Caminiti, G. Licheri, G. Piccaluga and G. Pinaa, Ann. Chim. 65 (1975) 695. (61 R. Caminiti, G. Licbeti, G. Piccaluga and G. Ptina, J. Chem. Phys. 65 (1976) 3134. (71 A-K. Dorosh and A.F. Skryshevskii, Zh. Strukt. Mim. .S (1964) 911. (81 IV. Bol, G.J.A. Getrits and C_L. van Panthateon van Eck, 3. Appt. Cry& 3 (1970) 486.
278
15 April 1973
(91 M. AIves Marques and M.I. De Banos Marques. Xonti. Ned. Akad. Wetenschap. Proc. B 77 (1974) 286. [lOj iV.A. ~Matwiyoffand H. Taube, J. Am. Chem. Sot. 90 (1966) 2796. [J I I J.N. A&i& J_Chem. Sot. Dalton (1973) 42. [IZ] G-J. Safford, P.S. Leung, A-W. Naumann and P.C. Schaffer, I. Chem. Phys. 50 (1969) 4444. /f 31 M.E. Milberg, J. Appl. Phys. 29 (1958) 64. [24 i %A. Levy, M.D. Danford and A.H. Narten, Oak Ridge NationaL Laboratory Report No. 3960 (1966). [lS] 1. Krogtt-Moe. Acta Cryst. 9 (1956) 951. [26] W. Bot, 1. AppI. Cryst, I (1968) 234. [J 71 D.T. Cramer and I.B. Mann, Acta Cryst. A24 (1968) 321.