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 have melting points lower than 100 °C and consist of ions. Their unique properties such as non-volatility, thermal stability, and solvation ability make them widely used in multiple applications. Ionic liquids are usually formed by bulky cations and large anions with low lattice energies.

The tetrahedral \(\mathrm{BF}_{4}^{-}\) anion consists of a central boron atom surrounded by four fluorine atoms. The ion has a negative charge, and since fluorine is highly electronegative, the electrons are pulled towards the fluorine atoms. The overall ionic radius of \(\mathrm{BF}_{4}^{-}\) is relatively small.

The \(\mathrm{SO}_{4}^{2-}\) anion is another tetrahedral anion made up of a central sulfur atom surrounded by four oxygen atoms. Since sulfur is larger than boron, the ionic radius of \(\mathrm{SO}_{4}^{2-}\) is larger than that of \(\mathrm{BF}_{4}^{-}\). Moreover, it has two negative charges, which makes it more negatively charged than the \(\mathrm{BF}_{4}^{-}\) anion.

Ionic liquids have low lattice energies, which result in their low melting points. Lattice energy depends on the charge and size of ions. In general, the lattice energy increases when the ion charges increase, and it decreases with increasing ion size. Therefore, for ionic liquids to form, ions with low lattice energies are preferentially formed.

The \(\mathrm{BF}_{4}^{-}\) anion's smaller size and lower charge compared to the \(\mathrm{SO}_{4}^{2-}\) anion make the lattice energy lower in salts containing \(\mathrm{BF}_{4}^{-}\). This lower lattice energy favors the formation of ionic liquids when salts containing \(\mathrm{BF}_{4}^{-}\) ions are formed. On the other hand, the greater size and higher charge of the \(\mathrm{SO}_{4}^{2-}\) anion lead to higher lattice energy in salts containing these ions. The higher lattice energy makes it more difficult for ionic liquids to form when salts containing the \(\mathrm{SO}_{4}^{2-}\) anion are produced. In conclusion, salts containing the tetrahedral polyatomic anion \(\mathrm{BF}_{4}^{-}\) form ionic liquids due to their lower lattice energy compared to salts containing the tetrahedral ion \(\mathrm{SO}_{4}^{2-}\).