Question

Which specics docs not exist? (1) \(\mathrm{BF}_{6}^{3-}\) (2) \(\mathrm{AIF}_{6}^{3-}\) (3) \(\mathrm{GaF}_{6}^{3-}\) (4) \(\mathrm{InF}_{6}^{3-}\)

Short answer

The species \(\text{BF}_{6}^{3-}\) does not exist.

Step-by-step solution

- Understanding the Species

We need to evaluate which of the given hexafluoride complexes do not exist: (1) \(\text{BF}_{6}^{3-}\) (2) \(\text{AIF}_{6}^{3-}\) (3) \(\text{GaF}_{6}^{3-}\) (4) \(\text{InF}_{6}^{3-}\).

- Evaluating the Central Atom

Evaluate if the central atom can have the required oxidation state and coordination number. For a stable \(\text{MF}_{6}^{3-}\) complex, the central atom (B, Al, Ga, In) must be capable of having 6 fluorides (coordination number 6) around it and maintain a -3 charge.

- Understanding the Periodic Table Trends

Consider the position of each element in the periodic table. Boron (B) belongs to Group 13 and period 2, whereas Aluminum (Al), Gallium (Ga), and Indium (In) are in periods 3, 4, and 5 respectively. Boron is much smaller and typically does not expand its valence shell to accommodate 6 ligands.

- Assessing Feasibility for Boron

Determine the ability of boron to expand its valence shell based on its size and electron structure. Boron is unable to accommodate 6 fluorine atoms due to its small size and lack of available d-orbitals for bonding expansion.

- Conclusion

Given above analysis, Boron (B) cannot form B\(\text{F}_6^{3-}\) because it cannot accommodate 6 fluoride ions around it due to its small size and unavailability of d-orbitals.

Key concepts

Hexafluoride Complexes

Hexafluoride complexes are chemical species where a central metal atom is bonded to six fluoride ions. These complexes are often denoted as \(\text{MF}_6\) with various oxidation states indicated by the superscript. Understanding the feasibility of these complexes involves evaluating the central atom's ability to bond with six fluorides. This ability depends on several factors like size, electronic configuration, and availability of orbitals for bonding.

Oxidation States

Oxidation states refer to the total number of electrons that an atom gains or loses to form a chemical bond. In the case of hexafluoride complexes, the central atom typically has a high oxidation state to bond with six fluoride ions. For instance, in \(\text{AIF}_{6}^{3-}\), aluminum has an oxidation state of +3. The oxidation state impacts the stability and structure of the complex. Elements in higher periods of the periodic table usually have higher possible oxidation states due to more available orbitals (including d-orbitals).

Periodic Table Trends

Periodic table trends help determine the feasibility of a compound. As we move down a group, the atoms get larger, and higher coordination numbers become possible. In group 13, Boron (B) is in period 2, making it too small with limited valence orbitals to form \(\text{BF}_6^{3-}\). However, Aluminum (Al), Gallium (Ga), and Indium (In) are in periods 3, 4, and 5 respectively, and are large enough to accommodate six fluoride ions due to their ability to utilize d-orbitals.

Valence Shell Expansion

Valence shell expansion refers to the ability of an atom to use its d-orbitals to accommodate more than the typical eight electrons in its valence shell. Boron, being in period 2, lacks d-orbitals and therefore cannot expand its valence shell. This restriction makes it impossible for boron to form a stable \(\text{BF}_6^{3-}\) complex. On the other hand, atoms like Aluminum (period 3), Gallium (period 4), and Indium (period 5) have available d-orbitals which allow for valence shell expansion, enabling the formation of hexafluoride complexes with these elements.