Problem 31 - Chemistry The Central Science In Si Units

Question

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

Step-by-Step Solution

Answer

The smaller size and lower charge of \(\mathrm{BF}_{4}^{-}\) lead to lower lattice energy, allowing it to form ionic liquids, unlike \(\mathrm{SO}_{4}^{2-}\).

Step 1: Understanding Ionic Liquids

Ionic liquids are salts that are liquid below 100 °C. They have low melting points compared to typical salts which form crystalline solids at room temperature.

Step 2: Comparing Anion Sizes and Charges

The \(\mathrm{BF}_{4}^{-}\) ion is smaller and carries a single negative charge, while the \(\mathrm{SO}_{4}^{2-}\) ion is larger and carries a 2- charge.

Step 3: Analyzing Lattice Energy

Lattice energy is related to the forces holding the ions together. It depends on the charge and size of the ions. A smaller or less highly charged ion typically leads to lower lattice energy.

Step 4: Conclusion on Liquidity

The smaller size and single charge of the \(\mathrm{BF}_{4}^{-}\) ion result in lower lattice energy, allowing salts to form ionic liquids more readily than the larger, doubly charged \(\mathrm{SO}_{4}^{2-}\) ion.

Key Concepts

Anion Size

Anions are negatively charged ions, and their size can greatly influence the properties of the compounds they form. The size of an anion is affected by various factors including its atomic structure and the number of electrons it carries. Generally, larger anions have more electrons crowding around a central nucleus. This can affect how these ions interact with surrounding ions in an ionic compound.

When comparing two tetrahedral anions, such as \( \mathrm{BF}_4^{-} \) and \( \mathrm{SO}_4^{2-} \), the size difference is notable. \( \mathrm{BF}_4^{-} \) is composed of a boron atom surrounded by four fluorine atoms. The compactness of this structure results in a relatively small ionic radius.

On the other hand, \( \mathrm{SO}_4^{2-} \) is a larger entity, as sulfur's atomic radius is naturally bigger than boron's, and the sulfate ion also carries an additional charge which affects its overall size due to the increased electron-electron repulsion. The larger size of \( \mathrm{SO}_4^{2-} \) leads to stronger interactions with its neighboring ions, affecting its ability to form ionic liquids under normal conditions.

Lattice Energy

Lattice energy is a measure of the strength of the forces holding ions together in a crystalline lattice. It is a crucial factor in determining the melting point of ionic compounds. Several factors affect lattice energy, primarily the size and charge of the involved ions.

In terms of ionic liquids, lattice energy plays a pivotal role in dictating whether a salt can remain in a liquid state at relatively low temperatures. A smaller anion like \( \mathrm{BF}_4^{-} \) with a single negative charge generally results in a lower lattice energy because the ionic interactions are not as strong. This weaker attraction allows the salt to melt and function as a liquid at lower temperatures than similar compounds with larger or more highly charged ions.

Conversely, the \( \mathrm{SO}_4^{2-} \) ion, with its larger size and double negative charge, creates stronger ionic bonds within its crystalline structure, leading to a higher lattice energy. This means that salts made with \( \mathrm{SO}_4^{2-} \) require more energy to melt, thus they are less likely to form ionic liquids.

Polyatomic Ions

Polyatomic ions, like \( \mathrm{BF}_4^{-} \) and \( \mathrm{SO}_4^{2-} \), are ions composed of more than one atom. These ions are pivotal in the formation of various chemical compounds. The number of atoms and the nature of the chemical bonding within the polyatomic ion influence its stability and interaction with other ions.

Tetrahedral polyatomic ions, like the ones mentioned, have atoms arranged in a three-dimensional shape that resembles a pyramid with a triangular base. The specific arrangement of these atoms affects how the ion interacts with others in a compound.

For \( \mathrm{BF}_4^{-} \), the smaller size and single negative charge make it versatile in forming compounds that are liquids at low temperatures. This contrasts with \( \mathrm{SO}_4^{2-} \), which due to its larger size and additional negative charge, forms stronger interactions, typically resulting in the formation of solids rather than liquids under similar conditions. Understanding these properties highlights why some tetrahedral polyatomic ions form ionic liquids and others do not.