A number of salts containing the tetrahedral polyatomic anion, \(\mathrm{BF}_{4}^{-}\), are ionic liquids, whereas salts containing the somewhat larger tetrahedral ion \(\mathrm{SO}_{4}{ }^{2-}\) do not form ionic liquids. Explain this observation.

Ionic liquids are salts that exist in the liquid state at room temperature or below (typically below 100°C). They have unique properties like high thermal stability, low vapor pressure, and good solvating ability. To become an ionic liquid, a compound must have ionic species with a suitable balance between electrostatic forces and van der Waals forces. Generally, large and asymmetric ions with lower charge density form ionic liquids due to weaker lattice energies and reduced melting points.

Now let's look at the two ions mentioned, \(\mathrm{BF}_{4}^{-}\) and \(\mathrm{SO}_{4}{ }^{2-}\). Both ions have a tetrahedral structure. The \(\mathrm{BF}_{4}^{-}\) anion has one boron atom surrounded by four fluorine atoms, while the \(\mathrm{SO}_{4}{ }^{2-}\) anion has one sulfur atom surrounded by four oxygen atoms.

The \(\mathrm{BF}_{4}^{-}\) anion has a -1 charge whereas the \(\mathrm{SO}_{4}{ }^{2-}\) has a -2 charge. In the case of \(\mathrm{BF}_{4}^{-}\), the charge is distributed over the fluorine atoms due to the electronegativity of the fluorine atom, which results in more diffuse charges and lower overall charge density. In contrast, the oxygen atoms in the \(\mathrm{SO}_{4}{ }^{2-}\) anion have more localized charges due to their lesser electronegativity compared to fluorine, which leads to a higher overall charge density.

The larger, more diffuse charges present in \(\mathrm{BF}_{4}^{-}\) results in weaker electrostatic forces and reduced lattice energies. The lower lattice energies enable relatively easy separation of the ions at lower temperatures, leading to the formation of ionic liquids. On the other hand, in \(\mathrm{SO}_{4}{ }^{2-}\), due to the higher charge density, the electrostatic forces are stronger, leading to higher lattice energies. This results in higher melting points and prevents the formation of ionic liquids at lower temperatures. Thus, it can be concluded that salts containing the tetrahedral polyatomic anion \(\mathrm{BF}_{4}^{-}\) form ionic liquids due to the more diffuse charges and lower lattice energies, whereas salts with the somewhat larger tetrahedral ion \(\mathrm{SO}_{4}{ }^{2-}\) do not form ionic liquids due to their higher charge density and lattice energies.