The answer is surprisingly simple, or perhaps elegant.
If we consider the radius ratios of nitrogen(V), phosphorous(V), arsenic(V), antimony(V), and bismuth(V) in VI-coordination with that of fluoride ion in I-coordination (for comparing gas phase acidic behaviour), we obtain the following:
| E |
Radius Ratio |
Value |
Octahedral (with ionic bonds) |
| $\ce{N}$ |
$\dfrac{r_\ce{N^{+5}}}{r_\ce{F-}}$ |
0.10 |
No |
| $\ce{P}$ |
$\dfrac{r_\ce{P^{+5}}}{r_\ce{F-}}$ |
0.29 |
No |
| $\ce{As}$ |
$\dfrac{r_\ce{As^{+5}}}{r_\ce{F-}}$ |
0.35 |
No |
| $\ce{Sb}$ |
$\dfrac{r_\ce{Sb^{+5}}}{r_\ce{F-}}$ |
0.46 |
Yes |
| $\ce{Bi}$ |
$\dfrac{r_\ce{Bi^{+5}}}{r_\ce{F-}}$ |
0.59 |
Yes |
These values are in close agreement with Pauling's values as well and, accordingly, $\ce{SbF6-}$ is the most natural octahedral hexafluoride complex.$^\text{1}$ Bismuth also shows a natural tendency to form octahedral hexafluoride complex, but with a slightly loosely packed structure. Nonetheless, antimony and bismuth are expected to form more stable octahedral hexafluoride complexes $\ce{EF6-}$ and stronger corresponding acids $\ce{HEF6}$ than other group-5 elements. This is supported by:
- Fluoride Ion Affinities
- Conductivity Measurements
Fluoride Ion Affinities$^\text{2}$
The fluoride ion affinity of $\ce{SbF5(g)}$, $\pu{-506 \pm 63 kJ mol^{-1}}$, is higher than that of $\ce{AsF5(g)}$, $\pu{-421 \pm 22 kJ mol^{-1}}$, suggesting $\ce{HSbF6(g)}$ is more strongly acidic than $\ce{HAsF6(g)}$.
Conductivity Measurements$^\text{3}$
The order of acidity of group-5 pentafluorides, based on conductivity measurements is:
$$
\ce{SbF5>BiF5>AsF5>PF5}
$$
Suggesting the following order of acidity.
$$
\ce{HSbF6>HBiF6>HAsF6>HPF6}
$$
References
- Clifford, A. F., Beachell, H.C., and Jack W.M. (1967). The hydrogen fluoride solvent system—I A qualitative survey of acids. J. Inorg. Nucl. Chem., 5, 57. 10.1016/0022-1902(57)80081-5.
- Jenkins, H. D. B., Roobottom, H. K., and Passmore, J. (2003). Estimation of Enthalpy Data for Reactions Involving Gas Phase Ions Utilizing Lattice Potential Energies: Fluoride Ion Affinities (FIA) and pF- Values of mSbF5(l) and mSbF5(g) (m = 1, 2, 3), AsF5(g), AsF5·SO2(c). Standard Enthalpies of Formation: ΔfH°(SbmF5m+1-,g) (m = 1, 2, 3), ΔfH°(AsF6-,g), and ΔfH°(NF4+,g). Inorg. Chem., 42(9), 2886–2893. 10.1021/ic0206544.
- Gillespie, R. J., Ouchi, K., and Pez, G. P. (1969). Fluorosulfuric acid solvent system. VI. Solutions of phosphorus, arsenic, bismuth, and niobium pentafluorides and titanium tetrafluoride. Inorg. Chem., 8(1), 63–65. 10.1021/ic50071a015.
