The Journal of Physical Chemistry, Vol. 82, No. 21, 1978 2335
X04"- Ion Hydration
X04"- Ion Hydration. The Crystal Structure of Mg3(P04),*22H20 L. W. Schroeder,+ M. Mathew," and W. E. Brown American Dental Association Health Foundation Research Unit, National Bureau of Standards, Washington, D.C. 20234 (Received May 5, 1978) Publication costs assisted by the American Dental Association Health Foundation Research Unit
Mg,(P04)2.22H20is triclinic, space group Pi, with a = 6.902(2), b = 6.961(2),c = 15.982(4)8, cy = 87.66(2), /3 = 85.22(2),and y = 60.81(2)'. The structure was refined to R, = 0.033, R = 0.058 for 1317 observed reflections. The most interesting feature of the structure is that all cations and anions are completely surrounded by water molecules. The Mg(H20),octahedra and PO4 tetrahedra form a layer structure with the stacking sequence BAABAA .... Each Mg(H,O), octahedron in an A layer shares three faces with tetrahedra, and each tetrahedron shares faces with three octahedra in a pseudotrigonal arrangement. The immediate environment of the PO4 ion consists of 12 water molecules, all of which are hydrogen bonded to PO4 oxygens. The water molecules are arranged approximately at the vertices of a cuboctahedron. The pair distances associated with this environment may be used to aid in investigations of the structure of phosphate solutions.
Introduction Although some values of the hydration numbers for X04n-ions in aqueous solutions are available,' the geometrical details of the hydration are not clear. The most direct information comes from radial distribution functions obtained from diffraction studies of aqueous solutions. A few such studies have been carried out; the most detailed is on aqueous HC1 solutions.2 Studies of M2+ (ref 3) and Cr3+ (ref 4) ions in aqueous solutions show that the Mn+-H20 distances in solutions are very nearly those found in the corresponding crystalline hydrates. This implies that some details of the hydration of X04n-ions in solution can also be found from the structures of crystalline hydrates. As part of a study of high hydrates we have determined the crystal structure of Mg3(P04)222H20. In this paper we will show how models for the hydration of PO>-, S042-,and AsO>-, as obtained from crystalline hydrates, might aid in the interpretation of radial distribution functions. These models also provide configurations that can be used in theoretical calculations of the stability of X04.nH20 complexes. Such calculations have been made for M"+.nH20 c o m p l e x e ~ . ~ Experimental Section Data Collection and Structure Solution. Crystals of Mg3(PO4),.22Hz0 were prepared following the method of Ahmed., MgCl2.6H20 (1.1g) was dissolved in 25 mL of HzO and 3.1 g of Na2HPO4-7H20was dissolved in 30 mL of H 2 0 . The two solutions were added drop-by-drop to 50 mL of H 2 0 with just enough stirring to clear the solution. Addition of the reactants was stopped when the solution remained cloudy. Suitable crystals appeared overnight. A crystal of dimensions 0.24 X 0.13 X 0.044 mm, whose refractive indices agreed with reported value^,^ was used for data collection. The crystals are triclinic, with cell parameters a = 6.902(2), b = 6.961(2), c = 15.982(4) A, cy = 87.66(2), /3 = 85.22(2), and y = 60.81(2)'. These values of the reduced and their estimated standard deviations were obtained by a least-squares fit of 30 f 20 values measured on a four-circle diffractometer with graphite monochromatized Mo K a l radiation (A 0.70930 A). The diffractometer controlling programs were those of Lenhert.g The space group was assumed to be Pi with Z = 1;this choice 'Division of Chemistry and Physics, Food and Drug Administration,
Washington, D.C.
This article not subject to
was confirmed by the successful structure analysis. All reflections in the hemisphere (h f h f 1) with 20 I 50" were measured using the 8-20 scan technique. The scan rate was 0.5' min-l and backgrounds were counted for 40 s at both ends of the scan range. Reflections in the range 50 < 20 I60' were measured only if a precheck at the calculated positions produced at least 20 counts in 10 s. Three standard reflections were measured every 30 reflections and revealed negligible variations during the data collection. These were merged into a set of 1613 independent reflections of which 1317 with intensity I 2 3r(O and were considered observed and used in the structure analysis. No absorption corrections were applied. The positions of Mg and P atoms were deduced from a sharpened three-dimensional Patterson synthesis. A Fourier synthesis, based on these three atoms, indicated the positions of all the remaining atoms except hydrogens. Refinement was carried out by full matrix least-squares using the program RFINE4." The quantity minimized was Cw(Fo- Fc)2where w = [ c ( F , ) ~+ 0.0004(F0)2]-1. The scattering factors used were those for the neutral atoms, taken from the "International Tables for X-ray Crystallography".ll Refinement of all Mg, P, and 0 atoms with anisotropic thermal parameters gave R (= CllFolIFcII/CFo) = 0.077. The positions of all the hydrogen atoms were obtained from a difference Fourier synthesis. The R factor was reduced to 0.062 when the hydrogen atoms were included. The positional parameters of the hydrogen atoms were also refined in batches (with fixed isotropic B = 3.0 A2) in subsequent least-squares calculations. The refinement converged to R = 0.058 and R, = [Ew(lF,I - IFc1)2/Cw(Fo)2]1'2 = 0.033 for the 1317 observed reflections. The corresponding values were 0.077 and 0.034 for all reflections. The final atomic parameters are listed in Tables I and 11.
Description of Structure The structure consists of Mg(H20), octahedra, PO4 tetrahedra, and two "loose" water molecules, O(w8) and O(wll), all linked together by a three-dimensional network of hydrogen bonds (Figure 1). All cations and anions are completely surrounded by water molecules; thus, there are no direct contacts between cations and anions. Mg(H20)6 octahedra and PO4 tetrahedra form a layer structure with the stacking sequence BAABAA.... The layers are approximately perpendicular to the c axis (Figure 1). Inversion centers occur within the B layers and
U S . Copyright. Published 1978 by the American Chemical Society
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The Journal of Physical Chemistry, Vol. 82, No. 21, 1978
L. W. Schroeder, M. Mathew, and W. E. Brown
G
W6
C
T
c
Figure 1. A stereoscopic illustration of the unit cell of Mg3(P04)2.22H20. The origin is labeled with a star (”).
TABLE I: Final Parameters of Non-Hydrogen Atoms in Mg,(PO,), .22H,0a atom
Y
X
z
UI 1
U’2
u33
U,’
’ 1
3
‘23
Mg(1) O(0) O(0) O(0) 30(2) 23(2) 16(2) -15(2) -1(2) 2(1) Mg(2) 2168(4) 8871(4) 3431(1) l8(l) 17(1) 22(1) -7(1) -1(1) -1(1) P 953(3) 4470(3) 7592(1) 16(1) 16(1) -8(1) 1(1) 18(1) -3(1) 4481(7) O(11) 995(7) 6622(2) 24(3) 12(2) -13(2) 24(3) -1(2) O(2) 2060(6) 2136(7) O(2) 7898(2) 29(3) 17(3) 24(3) -11(2) -4(2) 1(2) 5696(7) O(3) 2149(6) 7861(2) 20(3) 27(3) -14(2) O(2) 22(3) -5(2) 4359(7) O(4) 1492(6) 2040(2) 12(2) 5(2) -11(2) 29(3) 23(3) -8(2) 7476(8) O(W1) 744(7) 4261(2) 21(3) 47(3) -36(3) 1(2) 51(4) -5(2) 1745(6) O(W2) 1272(6) 4110(2) 25(3) 17(3) -8(2) -6(2) 22(3) -4(2) 9560(8) O(W3) 903(7) 7080(3) -14(2) 26(3) 23(3) 36(3) -14(2) 3(2) 8651(8) 1823(8) O(W4) 1050(3) -22(3) 63(4) 31(3) 29(3) -21(3) 1(2) O(w5) 1937(8) 6977(7) 9423(2) 61(4) 24(3) 18(3) -13(3) -2(2) -6(2) 960(8) O(w6) 2232(8) 9504(3) 57(3) 50(3) 17(3) -40(3) -2(2) 5(2) O(w7) 12(7) 3447(7) 2405(2) 23(3) 20(3) 30(3) -9(2) 4(2) 4(2) 3383(8) O(w8) 3330(8) 460(3) 31(3) 47(4) 26(3) -19(3) 4(3) 1(3) 5924(7) O(W9) 3661(7) 2799(3) 23(3) lO(2) -22(2) 45(3) -14(2) 27(3) O(W10) 4944(8) 7634(8) 4098(3) 23(3) 50(4) 15(3) -4(3) -4(2) -1(2) O(wl1) 5050(8) 2496(7) 4163(3) 45(3) 30(3) 31(3) -15(3) 2(2) 6(2) a All positional parameters are multiplied by l o 4 and thermal parameters by lo3. The thermal parameters are of the form e ~ p [ - 2 n ’ ( U , , h ’ a *+~ U,,k’b*2 t U3,Zzc*2-t 2Ul,hka*b* t 2U,,hla*c* t 2UZ3klb*c*)]. Estimated standard deviations are given in parentheses. TABLE 11: Final Parameters in Mg,(PO,),. 22H,0a atom ~
X
(X
l o 3 )of Hydrogen Y
Atoms
2
~~
32(10) 666(11) 388(4) H(1) -7(11) 205(11) 517(4) H(2) 382(4) 47(11) 296(11) H(3) 421(4) 269(11) 184(10) H(4) 737(4) 155(10) 822(10) H(5) 17(10) 740(4) 129(10) H(6) 142(3) 205(9) 930(10) H(7) 714(10) 117(3) 232(9) H(8) 898(4) 208(11) 632(11) H(9) 589(11) 989(4) 242(10) H(10) 133(10) 898(3) H(11) 236(9) 246(9) H(12) 149(9) - 5(4) 775(4) 475(12) 69(10) H(13) 225(4) 289(11) 141(12) H(14) 275(10) H(15) 357(10) 98(4) 464(10) H(16) 287(10) 55(3) 255(4) 298(11) 533(11) H(17) 536(11) 248(4) H(18) 510(11) 232(10) 610(4) 375(10) H(19) 537(4) 483(10) 258(10) H(20) 377(11) 399(4) H(21) 482(10) 605(4) 372(11) 844(11) H(22) a A fixed isotropic temperature factor (3.0 A’) was used.
between the A layers. Layer A consists of Mg(2)(H20)6 octahedra and PO4tetrahedra linked together by hydrogen bonds (Figure 2). Hydrogen bonds between water molecules belonging to Mg(2) octahedra and the “loose” water O(wl1) link pairs of A layers across a center of symmetry. Layer B consists of Mg(l)(H,O), octahedra and water molecule O(w8). O(w8) is an important link between layers A and B as well as in layer B itself. Layer A can be visualized as consisting of Mg(2)(H20)6 octahedra coordinated to PO4 tetrahedra in a pseudotrigonal arrangement (Figure 2). The lengths of a and b and the angles of the unit cell are in accord with pseudotrigonal symmetry of the layers. As shown in Figure 2, a face of an Mg(2)(H20),octahedron normal to c has its three adjacent faces linked to the faces of three PO4 groups through three hydrogen bonds per pair of faces. Each PO4 group is similarly coordinated to three Mg(2) (HzO)6 octahedra. It is suggested that association of Mg(H20)6and PO4 groups in an aqueous solution may take place through such a configuration. Pseudotrigonal axes pass through the Mg(2) atoms, the P-00) axes, and the centers of the (P04-Mg(H20),), rings of a given layer. The absence of a simple translational relationship between the centers of symmetry and the pseudotrigonal axes indicates that the
The Journal of Physical Chemistty, Vol. 82, No. 21, 1978 2337
X04”- Ion Hydration
TABLE 111: Bond Lengths and Bond Angles in Mg,(P0,),.22H,0a bond D ,A bonds Mg(l)-O(w4) Mg(1 )-0(w5 1 Mg(l)-O(w6)
2.086(5) 2.068(4) 2.050(6)
Mg(P)-O(wl)
2.068( 5)
Mg(2)-0(~2) Mg(2)-0(w3) Mg(2)-0(~7) Mg( 2 ) - 0 ( ~ 9 ) Mg(B)-O(wlO) P-O( 1) P-O(2) P-O( 3) P-O( 4)
2.103(5) 2.075(6) 2.106(5) 2.056(5) 2.052(6) 1.549(4) 1.544(4) 1.539(5 ) 1.546(5 )
0 ( ~ 4 ) - M g1( ) - 0 ( ~ 5 ) O( w 4)-Mg( 1)-O( w 6) O(~ 4 ) - M g1 ( )-O( ~5 ) 0(~4)-Mg(l)-0(~6’) 0 ( ~ 5 ) - M g1( ) - 0 ( ~ 6 ) 0 ( ~ 5 ) - M g1( ) - 0 ( ~ 6 ’ ) O(wl)-Mg( 2 ) - 0 ( ~ 2 ) O(wl)-Mg( 2)-O( w 3) O(w1 )-Mg( 2)-O( ~ 7 ) O(wl)-Mg(2)-0(~9) O(W1)-Mg( 2 ) - 0 ( ~ 1 0 ) O( w 2)-Mg( 2)-0 (W 3) 0(~2)-Mg(2)-0(~7) O(w2)-Mg( 2 ) - 0 ( ~ 9 ) 0 (w 2)-Mg( 2)-O( w 10) O(W3)-Mg( 2)-O( ~ 7 ) 0(~3)-Mg(2)-0(~9) O(w 3)-Mg( 2)-O( w 1 0 ) O(W7)-Mg( 2)-0 (w 9 ) O(w7)-Mg( 2 ) - 0 ( ~ 1 0 ) 0(~9)-Mg(2)-0(~10) O(1)-P-O( 2) O(1)-P-O( 3) 0(1)-P-0(4) O(2)-P-0(3) 0(2 )-P-0 (4 ) 0(3)-P-0(4)
angle, deg
D(O.-O), a
87.5(2) 91.4(2) 92.5(2) 88.6(2) 89.0(2) 91.0(2) 98.7(2) 85.4( 2) 168.8(2) 86.5(2) 91.2(2) 89.4(2) 90.6( 2) 168.9(2) 82.7(2) 88.5( 2) 100.8(2) 170.9(2) 85.5(2) 96.1(2) 87.4(2) 108.6(3) 109.1(3) 109.0(3) 110.5(3) 109.7(3) 109.8(3)
2.872(6) 2.960(7) 2.999(7) 2.887(9) 2.885(7) 2.936(8) 3.163(7) 2.809(6) 2.824( 6) 2.943(8) 2.938( 7) 2.991( 6) 2.917(8) 2.917(8) 3.181(7) 2.823(6) 3.092( 6 ) 2.837(7) 2.511( 6) 2.515(6) 2.518(6) 2.533(6) 2.525(6) 2.523(7)
a Estimated standard deviations are given in parentheses.
rb 02
a
Figure 2. A stereoscopic illustration of the packing of Mg(HpO)eoctahedra and PO4tetrahedra via face sharing in a layer type A in Mg3(P04)2.22H,0.
space group of this compound is not a subgroup (Le., a simple distortion) of the space group of a truly trigonal, centrosymmetric structure. Moreover, the pseudotrigonal symmetry is not present in layer B. Each Mg ion is coordinated to six water molecules forming a distorted octahedron; Mg-O(w) distances vary from 2.050 to 2.106 A, with a mean value of 2.080 A in excellent agreement with those found in other hydrates.12 The “right angles” for Mg(1) and Mg(2) octahedra range from 87.5 to 92.5’ and 82.7 to 100.8’, respectively. The differences in the distortion of the two Mg(H20), octahedra can be explained as follows: (a) Mg(1) is in a more symmetrical environment (at a crystallographic center of symmetry). (b) All water molecules coordinated to Mg(1) are of class 1 (coordination along the bisector of the lone-pair orbitals, as defined by Ferraris and Fran~hini-Angela’~)and therefore do not act as acceptors in hydrogen bonds. In contrast, water molecules coordinated to Mg(2) are of mixed types, classes 1 and 1’ (class 1’ represents coordination along a lone-pair orbital) and hence act as acceptors in hydrogen bonds. (c) Mg(2) octahedra have three faces that are shared by faces of PO, groups linked through strong hydrogen bonding, which induces distortion, whereas linkage of
Mg(1) octahedra occurs with four vertices of different PO4 ions. All P-0 distances (1.539-1.549 A) are equal within two standard deviations, in good agreement with the value 1.536 8, calculated for 64 orthophosphate groups.14 The 0-P-0 angles (108.6-1 10.5’) show only slight variations from ideal tetrahedral angles. This reflects the fact that there is no coordination of a PO4 edge by a cation which distorts the group (Table 111). Three of the four PO4faces (01,02,0,; 01,02,0,; and 01,03,0,) are linked to the faces of Mg(2)(H20), octahedra via three hydrogen bonds per pair of faces (Figure 2). Additional hydrogen bonds are to Mg(l)(H,O), octahedra through vertices and to water molecule O(w8). The immediate environment of the PO4 ion consists of 12 water molecules, arranged approximately at the vertices of a cuboctahedron (Figure 3). This may be the first reported example of complete hydration of the Po43ion in the solid state, although complete hydTation of As04,( C ~ K A S O ~ ~ J Hand ~ OSO?) ’ ~ (MgSO4.6Hz0,MgSO4-7H20, NazS04~10H20)16~17~1s is known. Of the 11water molecules in the asymmetric unit, nine are strongly coordinated to the Mg ions. All but two of the 22 available hydrogen atoms, H(8) and H(16), are involved in hydrogen bond formation, 12 of them to PO4
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The Journal of Physical Chemistry, Vol. 82, No. 21, 1978
Figure 3.
The configuration of water molecules around the
PO-:
L. W.
Schroeder, M. Mathew, and W. E. Brown
ion.
TABLE IV: Probable Hydrogen Bonds in Mg,(P0,),.22H,0a Db-H ...A O(w1)-H( 1)...0( 1) -H( 2 ) . . . 0 ( ~ 2 ) 0(~2)-H(3)***0(1) -H( 4 ) * . . 0 ( ~ l l ) O(w3)-H( 5)-0( 3 ) -H(6)..*0(2) 0(~4)-H(7).**0(~7) -H(8 1 0(~5)-H(9)..*0(3) -H( 1 0 ) - . 0 ( ~ 8 ) O(w6)-H( l l ) s . * O (2) -H( 1 2 ) - 0 ( ~ 8 ) O(w7)-H( 1 3 ) - . 0 ( 2) -H( 14)-0(4) O(w8)-H( 1 5 ) * * *4) 0( -H(16)..#0(~5)' O(w6)' O(w9)-H( 1 7 ) - 0 ( 4 ) -H( 18)*-0(3) O( w 10 )-H( 19)..#O( 1) -H(20).**0(~11) O ( w l 1 )-H( 2 1 ) . - 0 ( ~ 9 ) -H( 2 2 ) * - 0 ( ~ 3 )
D-H, A
H...A, A
D***A, A
D-H...A, deg
l.OO(7) 0.98(7) 0.89(7) 1.04(8) 0.94(6) 0.8217) 0.83(6) 0.95(6) 0.83(7) l.OO(8) 0.88( 6 )
1.73(7) 1.83(7) 1.72(7) 1.89(8) 1.76(6) 1.90(7) 2.10( 6 )
2.705(7) 2.790( 6 ) 2.600(6) 2.907(8) 2.679(6) 2.698(7) 2.907(7)
166(6) 166(6) 171(7) 166(6) 165( 6) 165(7) 163(6)
1.85(7) 1.78(8) 1.78(6) 1.92(6) 1.58(8) 1.82(7) 1.81( 6 ) 2.42(6) 2.48(6) 1.74(8) 1.72(8) 1.80(7) 1.92(6) 2.31(6) 2.28( 7)
2.654( 6 ) 2.741(6) 2.646(6) 2.721(8) 2.668(7) 2.706(6) 2.686(6) 3.157(6) 3.081(6) 2.626(7) 2.674(7) 2.632(7) 2.776(6) 3.010(6) 3.034(7)
162(7) 161(7) 169(6 ) 150(6) 170(6) 173(7) 171(6) 154(6) 132(6) 176(7) 167(7) 166(6) 166(6) 138(6) 151(7)
0.88(6) 1.10(8) 0.89(7) 0.88(6) 0.81(8)
0.89(8) 0.97(8) 0.84(7) 0.88(6) 0.86(7) 0.83(8)
a Estimated standard deviations are given in parentheses. D is a donor atom, A an acceptor atom. distance and D-H...A angles indicate these are at most very weak hydrogen bonds.
TABLE V: Ranges of Interatomic Distances for Hydrated XO, ion
o.-o
o..*ow
PO,+
2.51-2.53
2.60-2.70
S0,Z-
2.39-2.42
2.70-2.95
~s0,3-
2.7 2-2.8 2
2.75-2.85
n-
' The D...A
Ionsa
ow***ow 3.80-4. 33' 2.81-3.18' 3.7 5-4.99d 2.85-4.80 3.52-4.80' 2.79-3.51 3.02-3.18'
x*.*ow
Ow...Ow(ideal)
3.44-3.90
4.33
3.5 0-4.00
4.55
3.91-4.03
3.14
Water molecules coordinated Ranges for the SO,z' ion calculated from data of ref 16, those for AsO,,- from ref 15. Water molecules coordinated t o differWater molecules tightly coordinated to the same Mg ion. t o the same oxygen, ent Mg ions.
oxygen atoms (Table IV) so that each O(P04) is the acceptor in three hydrogen bonds; all O(w).-O(PO4) distances are in the range of 2.600-2.706 A [mean = 2.665(34)] and are indicative of fairly strong 0-0 hydrogen bonds. Hydrogen H(16) of O(w8) is directed toward O(w5) and O(w6) in order to minimize H.-H repulsion. However, this may be considered as a very weak bifurcated hydrogen bond (Table IV). Hydrogen bonds involving H(21) and H(22) are also very weak. The two water molecules O(w8) and O(wl1) apparently play important roles in this structure even though they are not bonded to Mg ions. O(w8) is the acceptor in two hydrogen bonds which are the only links between the Mg(l)(H20)6octahedra in layer B. O(w8) is also the donor
in a hydrogen bond to an oxygen of PO4 in layer A, thus connecting layers A and B. The four possible hydrogen bonds involving O(wl1) link four different Mg(2)(HZO), octahedra in the A layers. It might be supposed that this water could be removed from the structure to form the hydrate Mg3(P04)2.20H20. However, the next known hydrate containing less water is Mg3(P04)Z.llH20.6 In the latter, at least part of the Mg(H20),octahedral water must be missing and some PO4 groups directly coordinated to Mg ions. Structural Models for X04"- Ion Hydration P043-Ion. Figure 3 shows the arrangement of the 12 water molecules around the PO4 group. If lines are drawn
The Journal of Physical Chemistry, Vol. 82,No. 21, 1978 2339
X04+ Ion Hydration
b
Flgure 4. The arrangement of 11 water molecules about the S042- ion as found in MgS04.6H20.
Figure 5. The configuration of water molecules about the A s 0 2 - as found in CaKAsO4.8H,O.
connecting the water molecules, a polyhedron is formed having 14 faces and 24 edges. Eight faces are triangles and six are quadrilaterals. The idealized form of this polyhedron is cuboctahedron which has symmetry Oh, and all edges (i.e., O(w)-.O(w) distances) equal in length. Table V gives the ranges of interatomic distances for various atom pairs found in the hydration of X04"-ions. The PO4 oxygen-water distances, O-O(w), (hydrogen bonds) found here fall in the range 2.60-2.70 A, and are significantly smaller than the O(w)-..O(w)distance, 2.85 A, found in pure waterlg and in this study (Table V). If one assumes the coordination geometry at a PO4 oxygen to be tetrahedral and that the PO4 oxygen to O(w) hydrogen bond length is 2.65 A (the avera e found here), the O(w)-.O(w) distance would be -4.33 for the ideal cuboctahedron. The P-O(w) distance would then be 3.48 A compared to the average value of 3.58 8, found here. The effect of the Mg ion has been to produce O(w)-.O(w) distances near 2.9 A, which skews the distribution of these bonds toward shorter distances and lengthens the P-O(w) distances. Ion. The environment of the S042-ion as found in MgS04-6H2016is shown in Figure 4. Eleven water molecules surround the SO-: ion, and their arrangement is very distorted from the ideal cuboctahedron. Pertinent pair distances are given in Table V. An implication for radial distribution studies of sulfate solutions is that peaks from O(w).-O(w) pairs at 2.85 A would not be resolved from those due to SO4 oxygen-water pairs. Peaks due to O(w)--O(w) in the primary solvation shell (cf. column 4, Table V) of SO4 might be resolved if excellent resolution is employed. The distortion of the hydration sphere has increased the range of O(w).-O(w) distances, hence the peaks in a radial distribution curve are expected to be quite broad. As04* Ion. Figure 5 shows the environment of the As04 ~ O . ' ~water molecules ion as found in C ~ K A S O ~ * ~ HSixteen completely surround the ion. The As043- ion is located a t a site with C2" (mm) symmetry so the polyhedron formed by the water molecules is more symmetric than in the case of Po43-.The idealized polyhedron has
1
ten quadrilateral, eight triangular faces, and 32 edges which are not all equal in length. The question of whether or not 16 waters is a typical coordination for the As02- ion remains open due to insufficient information. Its greater size as compared to PO:- and SO-: would favor a higher coordination number. However, tetrahedral coordination at an oxygen atom is favored, and the hydration of As02- in CaKAs04.8H20 seems to be somewhat unusual. The data in Table V should aid in interpretation of the features of a radial distribution curve which could be used to compare the geometry of the As02- hydration found in CaKAs04.8H20 with other hydration geometries.
Discussion The above X04n-ions are all considered to be "structure makers".1i20 Values for the solvation number of the SO-: ion lie in the range 7.9 to 12 depending strongly on concentration. This suggests that the configuration of the hydrated SO-: ion as described here is an appropriate one. We are unaware of experimental values for the hydration numbers of Po43-and As02- ions, but a value of 1 2 for the PO4%ion seems reasonable on the basis of the following considerations. The oxygens of the sulfate ion show a tendency toward tetrahedral coordination, which would lead to 12 waters in the primary coordination sphere, Although SO:- and Po43-are isoelectronic, theoretical calculations indicate that the gross charge on the oxygen is more negative for Po43-ions.21 One may expect water molecules to form stronger hydrogen bonds to PO>- ions than to S042-ions and hence shorter bonds. Thus, the PO?- ion will be more likely than the S042-ion to be surrounded by 12 water molecules given the same anion concentration and the same cation. The hydrated Pod3-ion found in Mg3(P04)2.22H20is at a site with no symmetry. Infrared studies of phosphate solutions reveal the theoretically inactive v1 vibration (Td symmetry) at 938 cm-'. This activity of vl is attributed to a lowering of the point group via hydration.22 Figure 3 shows that this can easily happen merely by small ro-
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The Journal of Physical Chemisfry, Vol. 82, No. 21, 1978
tations of water molecules about their hydrogen bonds. Figure 3 shows why nonlinear X 0 4 anion-.H-0 interactions are likely to occur. As the hydrogen bonds become shorter, the hydrogen atoms of the water molecules not involved in hydrogen bonding tend to stay as widely separated as possible. If this cannot be optimally accomplished by rotations of the water molecules about their hydrogen bonds, then bending the hydrogen bond will help. The configurations in Figures 3 and 4 suggest that the water molecules are slightly "bent away" from the PO4 oxygen-to-O(w) vector. Recent statistical and theoretical analysis of hydrogen bonds indicates that a nonlinear hydrogen bond, deviating by about loo from linearity, is energetically favorable in 30% of the observed cases.23The average O(w)-H.-O(PO,) angle for the PO4salt of the present study is 168". This value is subject to some error as shown by the fact that the locations of hydrogen atoms found by X-ray diffraction are usually too close to the donor atom. The models described above are also indicative of what effects are to be expected in radial distribution on studies of aqueous solutions of X04" ions. The radial distribution functions will be complicated in the 2.5-4.5-A region. For example, good resolution is required if the peaks due to PO4 oxygen-0(w) are to be separated from the O(w)...O(w) pairs. The O(w)-.O(w) interactions in the primary solvation shell of the present PO4 compound occur at distances up to 4.3 A, just slightly below the 4.5 A observed in pure water.19 Neutron diffraction of D 2 0 solutions is capable of yielding information about the orientational correlations of water molecules.2 The configurations given in Figures 3-5 suggest that orientational correlations in the primary hydration shell will be mainly accomplished by rotations of the water molecules about their hydrogen bonds. It is clear that Hq-H or De-D interactions will occur over a wide range due to variations in the rotation of water molecules. Interpretation of dynamical experiments, such as proton magnetic resonance, is likely to be complex since water molecules in the primarily hydration sphere are unlikely to reorient independently because of proton-proton interactions. One may be able to study aqueous solutions of X04nions at fairly low concentrations because the number of coordinated waters is high and provides many O(w).-O(w) interactions. Studies of lithium chloride solutions24were made with LiC1/H20 ratios as low as 1/136 or about 0.5 M. The configurations reported here should aid in in-
L. W. Schroeder, M. Mathew, and W. E. Brown
terpretation of similar investigations of the structure of solutions containing X04"- ions.
Acknowledgment. We thank P. Kingsbury for technical help. The figures were drawn with a local version of the ORTEP program of C. K. Johnson. This investigation was supported by Research Grant DE00572 to the American Dental Association Health Foundation from the National Institute of Dental Research and is part of the dental research program conducted by the National Bureau of Standards in cooperation with the American Dental Association Health Foundation. Supplementary Material Available: A listing of observed and calculated structure amplitudes for a single crystal of Mg3(P04)2.22H20(12 pages). Ordering information is given on any current masthead page.
References and Notes (1) J. F. Hinton and E. S.Amis, Chem. Rev., 71, 627 (1971). (2) R. Triolo and A. H. Narten, J . Chem. Phys., 63, 3624 (1975). (3) W. Bol, 4th National Congress of the Italian Association of Crystallography, Caglion, 1970 (4) A. Cristini, G. Licheri, G. Piccaluga, and G. Pinna, Chem. Phys. Left., 24, 289 (1974). (5) R. E. Burton and J. Daly, Trans. Faraday Soc., 66, 1219 (1971). (6) S.Ahmed, f a k . J . Sci., 25, 119 (1973). (7) J. R. Lehr, E. H. Brown, A. W. Frazier, J. P. Smith, and R. P. Thrasher, Tenn. Val. Auth., Chem. Eng. Bull., No. 6 (1967). (8) "International Tables for X-ray Crystallography", Vol. I, Kynoch Press, Birmingham, 1969, p 530. (9) P. G. Lenhert, J . Appl. Crystallogr., 8, 568 (1975). (10) L. Finger and E. Prince, Natl. Bur. Stand. ( U . S . )Tech. Note, No. 854 (1975). 11) "International Tables for X-ray Crystallography", Vol. IV, Kynoch Press, Birmingham, 1974, p 99, 149. 12) A. Whitaker and J. W. Jeffery, Acta Crysfallogr., Sect. 5,26, 1429 (1970). 13) G. Ferraris and M. Franchini-Angela, Acta Crystallogr., Sect. 5,28, 3572 (1972). 14) W. H. Baur, Acta Crystallogr., Sect. 5,30, 1195 (1974). 15) B. Dickens and W. E. Brown, Acta Crysfallogr., Sect. 5,28, 3056 (1972). (16) A. Zalkin, H. Ruben, and D. H. Templeton, Acta Crystallogr., 17, 235 (1964). (17) G.Feharis, D. W. Jones, and J. Yerkess, J . Chem. Soc., Dalton Trans., 816 (1973). (18) H. W. Ruben, D. H. Templeton, R. D. Rosenstein, and I.Olovsson, J . Am. Chem. Soc., 83, 620 (1961). (19) A. H. Narten and H. A. Levy, J . Chem. Phys., 55, 2263 (1971). (20) H. L. Friedman and C. V. Krishmon, Water, Compr. Treat., 3 (1973). (21) H. Johansen, Theor. Chim. Acta, 32, 273 (1974). (22) A. C. Chapman and L. E. Trilwell, Spctrochim. Acta, 20, 937 (1964). (23) J. Kroon, J. A. Kanters, J. G. C. M. Van Duijneveldt-van de Rijdt, F. B. Van Duijneveldt, and J. A. Vliegenthart, J . Mol. Struct., 24, 109 (1975). (24) A. H. Narten, F. Vaslow, and H. A. Levy, J. Chem. Phys., 58, 5017 (1973).
