Research: Science and Education
Thermochemical Radii of Complex Ions Helen K. Roobottom and H. Donald B. Jenkins* Department of Chemistry, University of Warwick, Coventry CV4 7AL, West Midlands, UK; *
[email protected] Jack Passmore Department of Chemistry, University of New Brunswick, Fredericton, NB, E3B 6E2, Canada Leslie Glasser Centre for Molecular Design, Department of Chemistry, University of Witwatersrand, Johannesburg, P.O. WITS 2050, South Africa
Thermochemical radii (1–3) can be used in the Kapustinskii equation (1) for binary salts or in the more recent Glasser generalization of this equation (4 ) for more complex salts, to predict lattice potential energies and stabilities of new inorganic materials (see, for example, refs 5, 6 ). They also provide parameters of molecular size to correlate with other ion properties (see, for example, ref 7). Our previous “reappraisal” (3) of these magnitudes is widely cited in the literature and is quoted in inorganic textbooks (8–11) and many others. Our present work offers the largest self-consistent set of thermochemical radii yet produced. These tables include (i) ions previously not considered, (ii) estimates for complex ions of recent and evolving topical interest, and (iii) estimates to update the values of the radii for the more conventional ions where necessary. Estimation of Thermochemical Radii Bartlett et al. (12) demonstrated a linear correlation of lattice enthalpy against the inverse cubic root of the volume per molecule, V, for simple MX salts. We have generalized this correlation and have studied crystals containing complex anions partnered with alkali-metal counter ions of known radius, and have extended the correlation (13) to include complex salts of the type Mp X q . Thus for a crystal Mp X q containing pM q+ ions and q complex anions X p { whose thermochemical radius is to be assigned, we use the unit cell parameters (a, b, c, α , β, and γ ) derived from the crystal-structure data for the salts to calculate the volume per molecule, V :
V=
abc
Table 1. Anionic Thermochemical Radii of Ions in Salt Type MX (1:1) Anion
No. of Salts
Radius/nm
Ref 3
Anion
Radius/nm
Ref 3
AgF4 {
1
0.231 ± 0.019
—
2
0.242 ± 0.019
—
AlBr4 {
3
0.321 ± 0.023
—
IrF6{
4
0.220 ± 0.019
0.229
AlCl4 {
1
0.317 ± 0.019
0.295
MnO4{
4
0.241 ± 0.019
—
AlF4 {
4
0.214 ± 0.023
—
MoF6{
2
0.241 ± 0.019
—
AlH4
1
0.226 ± 0.019
—
MoOF5-
3
0.180 ± 0.019
0.195
AlI4 {
1
0.374 ± 0.019
—
N3{
5
0.254 ± 0.019
—
AsF6{
4
0.243 ± 0.019
—
NbF6{
0.194 ± 0.019
0.170
1
0.266 ± 0.019
—
NbO3{
1
Au(CN)2{
NCO{
3
0.193 ± 0.019
0.203
AuCl4{
1
0.288 ± 0.019
—
4
0.168 ± 0.019
—
AuF4{
1
0.240 ± 0.019
—
NH2{
0.190
1
0.229 ± 0.019
—
NH2CH2COO{ 1
0.252 ± 0.019
B(OH)4{
3
0.187 ± 0.019
0.192
BF4{
4
0.205 ± 0.019
0.232
NO2{
5
0.200 ± 0.019
0.179
BH4{
4
0.205 ± 0.019
0.193
NO3{
4
0.165 ± 0.019
0.158
Br{
4
0.190 ± 0.019
0.188
O2{
2
0.199 ± 0.034
0.177
BrF4{
2
0.231 ± 0.019
—
O3{
OH{
3
0.152 ± 0.019
0.133
BrO3{
4
0.214 ± 0.019
0.154
3
0.252 ± 0.020
—
CH3CO2{
1
0.194 ± 0.019
0.162
OsF6{
0.249 ± 0.019
—
3
0.168 ± 0.019
0.172
PaF6{
4
Cl{
1
0.252 ± 0.019
—
ClO2{
1
0.195 ± 0.019
—
PdF6{
5
0.242 ± 0.019
—
ClO3{
5
0.208 ± 0.019
0.171
PF6{
4
0.204 ± 0.019
—
ClO4{
6
0.225 ± 0.019
0.240
PO3{
1
0.247 ± 0.019
—
CN{
4
0.187 ± 0.023
0.191
PtF6{
1
0.239 ± 0.019
—
Cr3O8{
2
0.276 ± 0.019
—
PuF5{
4
0.240 ± 0.019
0.277
CuBr4{
1
0.315 ± 0.019
—
ReF6{
5
0.227 ± 0.019
—
F{
4
0.126 ± 0.019
0.126
ReO4{
0.242 ± 0.019
—
1
0.317 ± 0.019
—
RuF6{
3
FeCl4{
1
0.305 ± 0.019
—
GaCl4{
1
0.328 ± 0.019
0.289
S6{
1
0.320 ± 0.019
—
H{
4
0.148 ± 0.019
0.173
SbCl6{
5
0.252 ± 0.019
—
H2AsO4{
2
0.227 ± 0.019
—
SbF6{
1
0.205 ± 0.019
—
H2PO4{
2
0.213 ± 0.019
—
SbO3{ SCN{
2
0.209 ± 0.019
0.213
HCO2{
1
0.200 ± 0.019
0.169
SeCN {
1
0.230 ± 0.019
—
HCO3{
2
0.207 ± 0.019
0.156
SeH {
2
0.195 ± 0.019
0.205
HF2{
5
0.172 ± 0.019
0.172
SH {
5
0.191 ± 0.019
0.207
HSO4{
2
0.221 ± 0.019
—
3
0.214 ± 0.019
—
I{
4
0.211 ± 0.019
0.210
SO3F {
0.352 ± 0.019
—
1
0.261 ± 0.019
—
TaCl6{
1
I2Br {
4
0.250 ± 0.019
—
I3{
1
0.272 ± 0.019
0.294
TaF6{
1
0.192 ± 0.019
0.168
IBr2{
1
0.251 ± 0.019
—
TaO3{
3
0.301 ± 0.019
—
ICl2{
1
0.235 ± 0.019
—
UF6{
0.235 ± 0.019
—
1
0.307 ± 0.019
—
VF6{
2
ICl4{
4
0.201 ± 0.019
—
IO2F2{
1
0.233 ± 0.019
0.177
VO3{
1
0.337 ± 0.019
—
IO3{
6
0.218 ± 0.019
0.122
WCl6{
3
0.246 ± 0.019
—
IO4{
5
0.231 ± 0.019
—
WF6{
WOF5{
1
0.241 ± 0.019
—
{
1 – cos2 α – cos2 β– cos2 γ + 2cos α cos β cos γ z
where z is the number of molecules per unit cell. 1570
No. of Salts
Using our correlation between the total lattice potential energy, UPOT (taken from the tabulation [14 ] and Kapustinskii estimated values), and the inverse cubic root of the volume per molecule, V {1/3, for salts of type Mp X q enables the esti-
Journal of Chemical Education • Vol. 76 No. 11 November 1999 • JChemEd.chem.wisc.edu
Research: Science and Education
mation of UPOT(Mp X q); and via the Kapustinskii equation (using eq 2 of ref 3) a thermochemical radius for Xp { can then be established. These results are tabulated (along with the number of salts considered in obtaining the particular radius cited and previously assigned radii where possible) in Table 1 for MX (1:1) salts, Table 2 for M2X-type (2:1) salts, and Table 3 for Mp X q-type salts. In a similar manner we can derive cationic thermochemical radii by selecting halide salts that have, therefore, known anionic thermochemical radii. The corresponding cationic radii are tabulated in Table 4 for MX- and MX2-type salts. We can now use our thermochemical radii generated in Table 1 to generate further cationic radii and vice versa. The results of these estimates are found in Table 5 for MXtype salts, Table 6 for MX2-type salts, and Table 7 for Mp X q-type salts. Errors are assigned taking into consideration the correlation coefficient of the relationship between U POT (14 ) and V { 1/3 (which are found to range from .99 for salts of type MX and .98 for M2X to .90 for MX2) and the uncertainty in the value generated for UPOT and hence for the radius. Discussion Radii for planar ions (CO32{), “V ”-shaped ions (NO2{), and linear ions (CNS{, HF2{, etc.) are less representative of size than in typically spherical moieties. The trends in ion size observed in our previous study (3) are maintained. The thermochemical radii calculated here correlate well with the theoretically computed effective radii of Mingos et al. (7) and also with other radii that have been quoted for some of these ions (11). Our extended calculations now offer a vast and consistent range of thermochemical radii for ions and include new and relatively uncharted ions such as the polyatomic halogen and chalcogen cations as well as more familiar ions. Such radii can also be used to obtain estimates of the lattice potential energy, U POT (M p X q ), for the complex salt Mp X q , which is a key thermochemical quantity. Thus us-
Table 2. Anionic Thermochemical Radii of Ions in Salt Type M2 X (2:1) Anion
No. of Salts
Radius/nm
Ref 3
Anion
No. of Salts
Radius/nm
Ref 3
AmF6 2{
1
0.255 ± 0.019
—
3
0.421 ± 0.026
—
CdCl4 2{
1
0.307 ± 0.019
—
ReI62{
3
0.240 ± 0.019
0.264
CeCl6 2{
1
0.352 ± 0.019
0.353
RhF62{
1
0.336 ± 0.019
0.332
CeF6 2{
1
0.249 ± 0.019
—
RuCl62{
4
0.248 ± 0.019
—
CO3 2{
3
0.189 ± 0.019
0.178
RuF62{ S2{
4
0.189 ± 0.019
0.191
CoCl4 2{-
1
0.306 ± 0.019
0.319
1
0.251 ± 0.019
—
CoF4 2{
2
0.209 ± 0.019
—
S2 O3 2{
1
0.262 ± 0.019
—
CoF6 2{
1
0.256 ± 0.019
0.244
S2 O4 2{
1
0.270 ± 0.019
—
Cr2O72{
2
0.292 ± 0.019
—
S2 O5 2{
4
0.283 ± 0.019
—
CrF6 2{
3
0.253 ± 0.019
0.252
S2 O6 2{
1
0.275 ± 0.019
—
CrO4 2{
5
0.229 ± 0.019
0.256
S2 O7 2{
2
0.291 ± 0.019
—
CuCl4 2{
1
0.304 ± 0.019
0.321
S2 O8 2{
1
0.302 ± 0.019
—
CuF4 2{
3
0.213 ± 0.019
—
S3 O6 2{
1
0.325 ± 0.019
—
GeCl6 2{
1
0.335 ± 0.019
0.328
S4 O6 2{
1
0.382 ± 0.019
—
GeF6 2{
3
0.244 ± 0.019
0.265
S6 O6 2{
2
0.374 ± 0.019
—
HfF6 2{
3
0.248 ± 0.019
0.271
SbBr6 2{
1
0.276 ± 0.019
—
HgI4 2{
1
0.377 ± 0.019
—
ScF6 2{ Se2{
1
0.181 ± 0.019
0.209
IrCl6 2{
1
0.332 ± 0.019
0.335
1
0.363 ± 0.019
0.358
MnCl6 2{
3
0.314 ± 0.031
0.322
SeBr6 2{
2
0.336 ± 0.019
0.326
MnF4 2{
2
0.219 ± 0.019
0.256
SeCl6 2{
4
0.229 ± 0.019
0.249
MnF6 2{
3
0.241 ± 0.019
0.256
SeO4 2{
4
0.248 ± 0.019
0.259
MoBr6 2{
2
0.364 ± 0.019
—
SiF6 2{
2
0.195 ± 0.019
—
MoCl6 2{
3
0.338 ± 0.019
0.340
SiO3 2{
1
0.218 ± 0.019
—
MoF6 2{
1
0.274 ± 0.019
—
SmF4 2{
2
0.279 ± 0.020
—
MoO4 2{
3
0.231 ± 0.019
—
Sn(OH)6 2{
3
0.374 ± 0.019
0.363
MoOCl5 2{
1
0.334 ± 0.019
—
SnBr6 2{
3
0.345 ± 0.019
0.349
NbCl6 2{
1
0.343 ± 0.019
0.343
SnCl6 2{
2
0.265 ± 0.019
—
NbOCl5 2{
2
0.335 ± 0.019
—
SnF6 2{
2
0.427 ± 0.019
0.396
NbOF5 2{
1
0.280 ± 0.019
—
SnI6 2{
1
0.204 ± 0.019
—
NH2{
1
0.128 ± 0.019
—
SO3 2{
6
0.218 ± 0.019
0.258
Ni(CN)4 2{
1
0.322 ± 0.019
—
SO4 2{
2
0.363 ± 0.019
—
NiF4 2{
3
0.211 ± 0.019
—
TcBr6 2{
2
0.337 ± 0.019
—
NiF6 2{
3
0.249 ± 0.019
0.249
TcCl6 2{
2
0.244 ± 0.019
—
O2{
5
0.141 ± 0.019
0.149
TcF6 2{
1
0.260 ± 0.019
—
O2 2{
5
0.167 ± 0.019
0.173
TcH9 2{
2
0.419 ± 0.019
—
OsBr6 2{
2
0.365 ± 0.019
—
TcI6 2{ Te2{
1
0.220 ± 0.019
0.220
OsCl6 2{
2
0.336 ± 0.019
0.324
3
0.383 ± 0.019
0.359
OsF6 2{
1
0.276 ± 0.019
—
TeBr6 2{
3
0.353 ± 0.019
0.366
PbCl4 2{
1
0.279 ± 0.019
—
TeCl6 2{
1
0.430 ± 0.019
0.383
PbCl6 2{
2
0.347 ± 0.019
0.348
TeI6 2{
2
0.238 ± 0.019
—
PbF6 2{
2
0.268 ± 0.019
—
TeO4 2{
1
0.424 ± 0.019
—
PdBr6 2{
3
0.354 ± 0.019
—
Th(NO3 )6 2{
1
0.360 ± 0.019
—
PdCl4 2{
1
0.313 ± 0.019
—
ThCl6 2{
3
0.263 ± 0.019
—
PdCl6 2{
3
0.333 ± 0.019
0.319
ThF6 2{
2
0.356 ± 0.019
0.352
PdF6 2{
4
0.252 ± 0.019
—
TiBr6 2{
3
0.335 ± 0.019
0.331
PoBr6 2{
1
0.380 ± 0.019
—
TiCl6 2{
4
0.252 ± 0.019
0.289
PoI6 2{
1
0.428 ± 0.019
—
TiF6 2{
1
0.354 ± 0.019
0.337
Pt(NO2 )3 Cl3 2{ 1
0.364 ± 0.019
—
UCl6 2{
3
0.256 ± 0.019
—
Pt(NO2 )4 Cl2 2{ 1
0.383 ± 0.019
—
UF6 2{
1
0.204 ± 0.019
—
Pt(OH)2 2{
1
0.333 ± 0.019
—
VO3 2{
3
0.363 ± 0.019
0.336
Pt(SCN)6 2{
2
0.451 ± 0.019
—
WBr6 2{
3
0.339 ± 0.019
0.336
PtBr4 2{
1
0.324 ± 0.019
—
WCl6 2{
2
0.237 ± 0.019
—
PtBr6 2{
3
0.363 ± 0.019
0.342
WO4 2{
1
0.334 ± 0.019
—
PtCl4 2{
3
0.307 ± 0.019
0.293
WOCl5 2{
1
0.335 ± 0.019
0.299
PtCl6 2{
2
0.333 ± 0.019
—
ZnBr4 2{
1
0.306 ± 0.019
0.286
PtF6 2{
2
0.245 ± 0.019
0.296
ZnCl4 2{
2
0.219 ± 0.019
—
PuCl6 2{
1
0.349 ± 0.019
0.354
ZnF4 2{
1
0.384 ± 0.019
0.323
ReBr6 2{
3
0.371 ± 0.019
0.360
ZnIs 2{
1
0.334 ± 0.019
0.299
ReCl6 2{
3
0.337 ± 0.019
0.324
ZrBr4 2{
1
0.306 ± 0.019
0.286
ReF6 2{
3
0.256 ± 0.019
0.277
ZrCl4 2{
2
0.348 ± 0.019
0.358
ReF8 2{
2
0.276 ± 0.019
—
ZrCl6 2{
2
0.258 ± 0.019
—
ReH9 2{
1
0.257 ± 0.019
—
ZrF6 2{
JChemEd.chem.wisc.edu • Vol. 76 No. 11 November 1999 • Journal of Chemical Education
1571
Research: Science and Education Table 3. Anionic Thermochemical Radii of Ions in Salt Type Mp Xq Anion No. of Salts Radius/nm AlH6 3{
1
0.256 ± 0.042
2
0.237 ± 0.042
CdBr6 4{
2
0.374 ± 0.038
CdCl6 4{
2
0.352 ± 0.038
CeF6 3{
1
0.278 ± 0.038
CeF7 3{
1
0.282 ± 0.038
2
Anion MnCl6 4{
1
0.349 ± 0.038
N
3
0.180 ± 0.042
Ni(NO2 )6 3{
1
0.342 ± 0.038
Ni(NO2 )6 4{
1
0.383 ± 0.038
NiF6 3{
1
0.250 ± 0.042
O3{
1
0.288 ± 0.038
0.349 ± 0.038
P3{
3
0.224 ± 0.042
Co(NO2 )6 3{ 3
0.343 ± 0.038
3
0.299 ± 0.042
1
0.320 ± 0.038
PaF8 3{
1
0.230 ± 0.042
CoF6 3{
4
0.258 ± 0.042
1
0.281 ± 0.038
1
0.351 ± 0.038
PrF6 3{
3
0.345 ± 0.038
CrF6 3{
1
0.254 ± 0.042
1
0.428 ± 0.042
Cu(CN)4 3{
1
0.312 ± 0.038
Rh(SCN)6 3{
1
0.284 ± 0.042
Fe(CN)6 3{
4
0.347 ± 0.038
TaF8 3{
0.290 ± 0.038
5
0.298 ± 0.042
TbF7 3{
4
FeF6 3{
1
0.410 ± 0.042
HfF7 3{
1
0.277 ± 0.042
Tc(CN)6 5{
1
0.282 ± 0.042
3
0.268 ± 0.038
ThF7 3{
0.315 ± 0.038
1
0.347 ± 0.038
TiBr6 3{
2
Ir(CN)6 3{
3
0.271 ± 0.038
3{
1
0.338 ± 0.038
TlF6 3{
4
0.285 ± 0.042
Mn(CN)6 3{
1
0.350 ± 0.038
UF7
3{
3
0.275 ± 0.038
1
0.401 ± 0.042
YF6 3{
3
0.273 ± 0.038
AsO 4
3{
Co(CN)6 3{ CoCl5 3{
Cr(CN)6 3{
InF6 3{
Ir(NO2)6
Mn(CN)6 5{
3{
PO4 3{
Rh(NO2 )6 3{
ZrF7 3{
Table 4. Cationic Thermochemical Radii of Ions in Salt of Type MX (1:1) and MX 2 (1:2)
Cation
No. of Salts Radius/nm
Ref 3
N(CH3)4+
3
0.234 ± 0.019
0.201
N2H5+
1
0.158 ± 0.019
—
N2H62+
2
0.158 ± 0.029
—
NH(C2H5)3+
2
0.274 ± 0.019
—
NH3C2H5+
1
0.193 ± 0.019
—
NH3C3H7+
3
0.225 ± 0.019
—
NH3CH3+
2
0.177 ± 0.019
—
NH3OH+
2
0.147 ± 0.019
—
NH4+
3
0.136 ± 0.019
0.137
NH3C2H4OH+
2
0.203 ± 0.019
—
ing the above radii for Xp{ coupled with, for example, the appropriate thermochemical (Goldschmidt [15, 16 ]) radius for simple counter ions in the Kapustinskii equation, UPOT(MpXq ) can be found. Such values can be further used via the Born–Fajans–Haber cycle (Fig. 1) to estimate other thermodynamic parameters. Acknowledgment Helen Roobottom thanks the EPSRC for the provision of a studentship. Literature Cited 1. Kapustinskii, A. F. Q. Rev. 1956, 10, 283–294. 2. Smith, D. W. J. Chem. Educ. 1977, 54, 540–541. 3. Jenkins, H. D. B.; Thakur, K. P. J. Chem. Educ. 1979, 56, 576– 577. 4. Glasser, L. Inorg. Chem. 1995, 34, 4935–4936. 5. Jenkins, H. D. B.; Sharman, L.; Finch, A.; Gates, P. N. Inorg. Chem. 1996, 35, 6316–6326.
1572
pM(standard state) + qX(standard state)
No. of Salts Radius/nm
B
A ∆f Hº(MpXq, c)
[p ∆f Hº(Mq , g) + +
q ∆f Hº(Xp , g)] –
MpXq(c) D
∆UPOT(MpXq) +
C
+
E [p ∆hydHº(M , g) +
q ∆hydHº(Xp , g)] –
q+
p–
pM (aq) + qX (aq) H ∆trHº(MpXq, c; aq s)
∆solnHº(MpXq, c)
–
q+
∆solnHº(MpXq, c)
G
pMq (g) + qXp (g)
[p(nM+/2 - 2) + q(nX–/2 - 2)]RT
[p ∆f Hº(Mq , aq) + +
F
q ∆f Hº(Xp , aq)] –
[p ∆solvHº(Mq , g) + +
q ∆solvHº(Xp , g)] –
q+
p–
pM (s) + qX (s)
I
J
[p ∆f Hº(Mq , s) + q ∆f Hº(Xp , s)] +
–
Figure 1. Thermochemical cycle for a salt, Mp X q , involving its dissolution in water and in a nonaqueous solvent. Limb A represents the standard enthalpy of formation of the crystalline salt, limb B represents the combined standard enthalpies of formation of the p gaseous cations Mq + and the q gaseous anions Xp{, and limb C is the total lattice enthalpy: that is, the sum of the lattice energy UPOT(Mp Xq ) and {p [n (M+)/2 – 2] + q [n(X {)/2 – 2]}RT, where n(M +) and n (X{) are equal to 3 for monoatomic ions, 5 for linear polyatomic ions, and 6 for nonlinear polyatomic ions. Limb D represents the standard enthalpy of solution of Mp Xq in water, and limb G that in the nonaqueous solvent, s. Limb E represents the combined standard hydration enthalpies of the gaseous cations Mq+ and the gaseous anions Xp { in water, and limb I the corresponding solvation enthalpy of these ions in s. Limbs F and J are, respectively, the standard enthalpies of formation of the aqueous and nonaqueous cations Mq + and anions X p{, and limb H represents the combined standard enthalpies of transfer of the p cations Mq+ and the q anions Xp{ from water to the solvent s.
6. Burford, N.; Passmore, J.; Sanders, J. C. P. In From Atoms to Polymers: Isoelectronic Analogies; Liebman, J. F.; Greenberg, A., Eds.; VCH: Boca Raton, FL, 1989; Chapter 2. 7. Mingos, D. M. P.; Rohl, A. L.; Burgess, J. J. Chem. Soc., Dalton Trans. 1993, 423–426. 8. Huheey, J. E.; Keiter, E. A.; Keiter, R. L. Inorganic Chemistry, 4th ed.; Harper Collins College Publishers: New York, 1993; p 118. 9. Porterfield, W. W. Inorganic Chemistry, A Unified Approach; Academic: New York, 1993; p 85. 10. Wulfsberg, G. Principles of Descriptive Inorganic Chemistry; University Science Books: Sausalito, CA, 1991; p 34. 11. Marcus, Y. Ion Properties; Dekker: New York, 1997; p 43. 12. Mallouk, T. E.; Rosenthal, G. L.; Muller, G.; Busasco, R.; Bartlett, N. Inorg. Chem. 1984, 23, 3167–3173. 13. Roobottom, H. K.; Jenkins, H. D. B.; Passmore, J.; Glasser, L. Inorg. Chem. 1999, 38, 3609–3620. 14. Jenkins, H. D. B. In Handbook of Chemistry and Physics, 79th ed.; Lide, D. R., Ed.; CRC: Boca Raton, FL, 1998–99; pp 1222–12-33 ff. 15. Goldschmidt, V. M. Skrifter Norske Videnskaps-Akad. Oslo. Mat. Nat. v Kl., 1926, 1, 2. 16. Dasent, W. E. Inorganic Energetics, 2nd ed.; Cambridge University Press: Cambridge, 1982.
Journal of Chemical Education • Vol. 76 No. 11 November 1999 • JChemEd.chem.wisc.edu
Research: Science and Education Table 5. "Novel" Cationic and Anionic Thermochemical Radii of Ions in Salt Type MX (1:1)
Ion
As3 S4
No. of Radius/nm Salts 2 0.244 ± 0.027
+
As3 Se4
+
AsCl4 +
1
0.253 ± 0.027
1
0.221 ± 0.027
1
0.235 ± 0.038
Br 2
+
1
0.155 ± 0.027
Br 3 +
1
0.204 ± 0.027
Br 3
{
1
0.238 ± 0.027
Br 5 +
2
0.229 ± 0.027
BrClCNH2 +
1
0.175 ± 0.027
+
1
0.183 ± 0.027
B rF 4 +
1
0.172 ± 0.027
C1 0 F8 +
1
0.265 ± 0.027
C6 F6 +
1
0.228 ± 0.027
Cl(SNSCN)2 +
1
0.347 ± 0.027
Cl2 C=NH2 +
1
0.173 ± 0.027
Cl2 F+
1
0.165 ± 0.027
Cl3 +
1
0.182 ± 0.027
ClF2 +
1
0.147 ± 0.027
1
0.118 ± 0.027
1
0.317 ± 0.038
1
0.185 ± 0.027
1
0.225 ± 0.027
1
0.263 ± 0.027
1
0.196 ± 0.027
4
0.175 ± 0.036
1
0.209 ± 0.027
1
0.258 ± 0.027
1
0.186 ± 0.027
1
0.246 ± 0.027
1
0.214 ± 0.027
1
0.156 ± 0.027
3
0.311 ± 0.038
5
0.145 ± 0.027
2
0.153 ± 0.027
4
0.140 ± 0.027
1
0.275 ± 0.027
1
0.200 ± 0.027
2
0.246 ± 0.038
AuF 6
B rF 2
{
ClO2 +
GaBr4 { I2 + I3 + I5 +
IBr2 +
ICl2 + IF 6 +
N(S3 N2 )2
+
N(SCl)2 +
N(SeCl)2 +
N(SF2 )2
+
N2 F+
Nb 2 F 1 1 { NO
+
NO 2 + O2
+
O2 (SCCF3 Cl)2 ONCH3 CF3 +
OsOF5
{
+
Ion
S3 N2
No. of Radius/nm Salts 1 0.201 ± 0.027
+
S3 N2 Cl
+
S3 N3 {
1
0.232 ± 0.027
1
0.231 ± 0.038
1
0.252 ± 0.038
+
2
0.231 ± 0.027
S4 N3 (Ph)2 +
1
0.316 ± 0.027
S4 N4 H
1
0.178 ± 0.027
S5 N5 +
2
0.257 ± 0.027
S7 I+
3
0.262 ± 0.027
S3 N3 O4 S4 N3
{
+
1
0.518 ± 0.027
Sb2 F1 1 {
4
0.312 ± 0.038
Sb3 F1 4 {
3
0.374 ± 0.038
SBr3 +
2
0.220 ± 0.027
SCH3 O2 +
1
0.183 ± 0.027
SCH3 P(CH3 )3 +
1
0.248 ± 0.027
SCH3 PCH3 Cl2 +
1
0.205 ± 0.027
SCl(C2 H5 )2 +
1
0.207 ± 0.027
SCl2 CF3 +
1
0.207 ± 0.027
1
0.204 ± 0.027
5
0.185 ± 0.027
1
0.253 ± 0.027
1
0.245 ± 0.027
1
0.163 ± 0.027
2
0.260 ± 0.027
1
0.182 ± 0.027
6
0.192 ± 0.027
2
0.258 ± 0.038
3
0.179 ± 0.027
Sb(NPPh3 )4
+
SCl2 CH3 + SCl3 +
Se3 Br3 +
Se3 Cl3 +
Se3 NCl2 + Se6 I+
SeBr3 +
SeCl3 + SeCl5
{
SeF3 +
2
0.238 ± 0.027
+
1
0.196 ± 0.027
SeNCl2 +
1
0.157 ± 0.027
1
0.406 ± 0.027
1
0.294 ± 0.027
2
0.198 ± 0.027
1
0.210 ± 0.027
4
0.172 ± 0.027
1
0.275 ± 0.027
1
0.210 ± 0.027
SN
1
0.158 ± 0.027
SNCl5 (CH3 CN){
1
0.290 ± 0.038
1
0.308 ± 0.027
SNSC(CH3 )N+
1
0.225 ± 0.027
1
0.209 ± 0.027
SeI3 +
SeN2 Cl
(SeNMe3 )3 + SF(C6 F5 )2
+
SF2 CF3 +
+
SF2 N(CH3 )2 SF3
+
SFS(C(CF3 )2 )2 + SH2 C3 H7
+
1
0.197 ± 0.027
P(CH3 )3 D+
1
0.196 ± 0.027
2
0.235 ± 0.027
ReOF5 {
1
0.245 ± 0.038
1
0.207 ± 0.027
1
0.439 ± 0.027
SNSC(Ph)N
1
0.251 ± 0.027
1
0.265 ± 0.027
0.327 ± 0.027
S2 (CH3 )2 CN+
1
0.223 ± 0.027
SNSC(Ph)NS3 N2 + 1
1
0.233 ± 0.027
S2 Br5 +
1
0.267 ± 0.027
(Te(N(SiMe3 )2 )2 +
3
0.159 ± 0.034
S2 N2 C2 H3 +
1
0.211 ± 0.027
S2 NC2 (PhCH3 )2 + 1
0.310 ± 0.027
S2 NC3 H4 +
1
0.218 ± 0.027
1
0.225 ± 0.027
1
0.239 ± 0.027
1
0.245 ± 0.027
1
0.199 ± 0.027
1
0.261 ± 0.027
1
0.263 ± 0.027
1
0.233 ± 0.027
P(CH3 )3 Cl
PCl4
+
+
S(CH3 )2 Cl+
S(N(C2 H5 )3 )3 S2 (CH3 )2 Cl+ S2 (CH3 )3
+
S2 N+
S2 NC4 H8 + S3 (CH3 )3 + S3 Br3 +
S3 C3 H7 + S3 C4 F6 +
S3 CF3 CN+ S3 Cl3 +
+
+
(SNPMe3 )3
+
SNSC(CN)CH+ +
Table 6. "Novel" Cationic and Anionic Thermochemical Radii of Ions in Salt Type MX2 (1:2) Ion
2
0.230 ± 0.049
2
0.260 ± 0.049
Co2 S2 (CO)6 2 +
1
0.263 ± 0.035
FeW(Se)2 (CO)2 +
1
0.260 ± 0.035
I4 2 +
2
0.207 ± 0.035
Mo(Te3 )(CO)4 2 +
1
0.234 ± 0.035
NbCl6 {
2
0.338 ± 0.049
S1 9 2 +
1
0.292 ± 0.035
S2 (S(CH3 )2 )2 2 +
1
0.230 ± 0.035
S2 I4 2 +
1
0.231 ± 0.035
S3 N2 2 +
3
0.184 ± 0.035
S3 NCCNS3 2 +
1
0.220 ± 0.035
S3 Se2 +
1
0.326 ± 0.035
S4 N4 2 +
5
0.186 ± 0.035
S6 N4 2 +
1
0.232 ± 0.035
S8 2 +
2
0.182 ± 0.035
Se1 0 2 +
2
0.253 ± 0.035
Se1 7 2 +
1
0.236 ± 0.035
Se1 9 2 +
1
0.296 ± 0.035
Se2 I4 2 +
1
0.218 ± 0.035
Se3 N2 2 +
3
0.182 ± 0.035
Se4 2 +
1
0.152 ± 0.035
Se4 S2 N4 2 +
1
0.224 ± 0.035
Se8 2 +
2
0.186 ± 0.035
SeN2 S2 2 +
1
0.182 ± 0.035
(SNP(C2 H5 )3 )2 2 +
1
0.312 ± 0.035
TaBr6 {
3
0.351 ± 0.049
Te(trtu)4 2 +
1
0.328 ± 0.035
Te(tu)4 2 +
3
0.296 ± 0.035
Te2 (esu)4 Br2 2 +
1
0.356 ± 0.035
Te2 (esu)4 Cl2 2 +
1
0.361 ± 0.035
Te2 (esu)4 I2 2 +
1
0.342 ± 0.035
Te2 Se2 2 +
1
0.192 ± 0.035
Te2 Se4 2 +
4
0.222 ± 0.035
Te2 Se8 2 +
2
0.252 ± 0.035
Te3 S3 2 +
3
0.217 ± 0.035
Te3 Se2 +
1
0.193 ± 0.035
Te4 2 +
4
0.169 ± 0.035
Te8 2 +
1
0.187 ± 0.035
W(CO)4 (η3-Te)2 + 1
0.234 ± 0.035
W2 (CO)1 0 Se4 2 +
3
1
0.264 ± 0.027
1
0.371 ± 0.027
Te(N3 )3 +
1
0.226 ± 0.027
Te4 Nb3 OTe2 I6 +
1
0.407 ± 0.027
TeBr3 +
2
0.235 ± 0.027
TeCl3 +
8
0.216 ± 0.027
Ion
TeCl3 (15-crown-5)+ 1
0.282 ± 0.027
Bi2 Br8 2{
3
0.243 ± 0.027
1
0.266 ± 0.027
1
0.221 ± 0.027
XeF+
1
0.174 ± 0.027
XeF3 +
2
0.183 ± 0.027
3
0.186 ± 0.027
1
0.186 ± 0.027
Xe2 F1 1 + Xe2 F3 +
XeF5 +
XeOF3 +
Note: Values were calculated using crystal structures at varying temperatures. Ph = phenyl; Me = methyl.
0.290 ± 0.035
Note: Values were calculated using crystal structures at varying temperatures. trtu = trimethylthiourea; tu = thiourea; esu = ethyleneselenourea.
SNSC(PhCH3 )N+
TeI3 +
No. of Salts Radius/nm
ClS2 O6 {
CF3 SO3 {
Table 7. "Novel" Cationic and Anionic Thermochemical Radii of Ions in Salt Type Mp Xq No. of Salts Radius/nm 1
0.392 ± 0.055
Bi6 Cl2 0 2{
1
0.501 ± 0.073
I1 5 3 +
1
0.442 ± 0.051
Nb2 OCl1 0 2{
2
0.383 ± 0.055
Se3 N2 +
2
0.288 ± 0.042
SeS2 N2 +
1
0.282 ± 0.042
Te2 (su) 6 4 +
1
0.453 ± 0.034
Note: Values were calculated using crystal structures at varying temperatures. su = selenourea.
JChemEd.chem.wisc.edu • Vol. 76 No. 11 November 1999 • Journal of Chemical Education
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