Problem 108 - General Chemistry: Principles and Modern Applications

Question

Chemists have successfully synthesized the ionic compound \(\left[\mathrm{N}_{5}\right]\left[\mathrm{SbF}_{6}\right],\) which consists of \(\mathrm{N}_{5}^{+}\) and \(\mathrm{SbF}_{6}^{-}\) ions. Draw Lewis structures for these ions and assign formal charges to the atoms in your structures. Describe the structures of these ions. [Hint: The skeleton structure for \(\mathrm{N}_{5}^{+}\) is \(\mathrm{N}-\mathrm{N}-\mathrm{N}-\mathrm{N}-\mathrm{N}\) and several resonance structures can be drawn.].

Step-by-Step Solution

Answer

The \(\mathrm{N}_{5}^{+}\) ion is linear with four nitrogen atoms bonded in the middle of the structure and the fifth at the end carrying a positive charge. The \(\mathrm{SbF}_{6}^{-}\) ion consists of a central Antimony atom single-bonded to six Fluorine atoms, with the complete ion carrying a negative charge. All atoms in both ions follow the octet rule for electron configuration.

Step 1: Drawing the Skeleton Structures

First, start by drawing the skeleton structures for the given ions. For \(\mathrm{N}_{5}^{+}\), the skeleton is \(\mathrm{N}-\mathrm{N}-\mathrm{N}-\mathrm{N}-\mathrm{N}\) and for \(\mathrm{SbF}_{6}^{-}\), place the Antimony atom in the center surrounded by six Fluorine atoms attached by single bonds.

Step 2: Add Octet Electrons

Each atom (except Hydrogen) strives to have an octet; thus, dots are added to each atom until each atom has an octet. Strive to give all atoms, except hydrogen, an octet. If you do, it will conform to the octet rule, that is, except for hydrogen, all the other atoms have 8 valence electrons which is the reason they can form bonds.

Step 3: Assign Formal Charges

The next step is to calculate the formal charge of each atom in these structures. The formal charge can be calculated using the formula: Formal Charge = Valence Electrons - (non-bonding electrons + 1/2 bonding electrons). Using this formula, calculate the formal charge for each atom.

Step 4: Describe Structures

With all the above steps completed, you are now ready to describe the structures. For \(\mathrm{N}_{5}^{+}\), you are to indicate the resonance structures; which are the several ways that a Lewis Structure can be drawn for a compound. For \(\mathrm{SbF}_{6}^{-}\), describe how each Fluorine atom is single bonded with the Antimony atom.

Key Concepts

Formal Charge Calculation

Understanding the concept of formal charge is crucial when drawing Lewis structures, as it helps in determining the most stable configuration for molecules and ions. Formal charge calculation is a bookkeeping method to assess the distribution of electrons in a molecule.

The formula to calculate the formal charge is:
\[\begin{equation}\text{Formal Charge} = (\text{Valence Electrons}) - (\text{Non-bonding Electrons} + \frac{1}{2} \times \text{Bonding Electrons})\end{equation}\] In simple terms, you subtract the number of non-bonding (lone pair) electrons and half the number of bonding (shared) electrons from the total number of valence electrons that an atom possesses in its ground state. Let's take a nitrogen atom in a \[\begin{equation}\mathrm{N}_{5}^{+}\end{equation}\] ion as an example. Nitrogen normally has five valence electrons. If, in the structure, nitrogen has one lone pair (two electrons) and participates in three bonds (three pairs of bonding electrons), the formal charge calculation would be: \[\begin{equation}5 - (2 + \frac{1}{2} \times 6) = 5 - 5 = 0\end{equation}\] This nitrogen atom would have a formal charge of zero. A formal charge closer to zero often indicates a more stable structure. An accurate Lewis structure will have the entire molecule or ion bearing a net formal charge that matches its charge. It's one of the crucial criteria for verifying the validity of a Lewis structure.

Octet Rule

The octet rule is a fundamental principle that governs the structure of atoms within a molecule. It states that atoms are generally most stable when they have eight electrons in their valence shell, resembling the electron configuration of a noble gas.

This rule is particularly important when drawing Lewis structures. Atoms will share or transfer electrons through covalent or ionic bonds to achieve a complete octet. For instance, in compounds like \[\begin{equation}\mathrm{SbF}_{6}^{-}\end{equation}\], each Fluorine atom needs one additional electron to complete its octet—hence the single bonds with Antimony, which shares its electrons with Fluorines to help them achieve this state.

Antimony, on the other hand, being in the 15th group of the periodic table, is able to hold more than eight electrons due to available d-orbitals—thus the Octet Rule is not strictly adhered to for elements beyond the second period of the periodic table. Despite its exceptions, the octet rule is a helpful starting point in predicting and rationalizing bonding patterns in many molecules.

Resonance Structures

Resonance structures come into play when a single Lewis structure isn't sufficient to represent the distribution of electrons in a molecule or ion. They illustrate the delocalization of electrons, showing different possible structures with the same arrangement of atoms, but different placements of the electrons.

Hence, for complex ions like \[\begin{equation}\mathrm{N}_{5}^{+}\end{equation}\], several Lewis structures, called resonance structures, can be depicted. Each resonance structure displays a possible distribution of single and double bonds among the nitrogen atoms. These structures must all have the same number of electrons and conform to the octet rule for each nitrogen, but electron pairs are moved around between the nitrogen atoms.

It is important not to consider these structures as isomers or different compounds; rather, they are 'snapshots' of a dynamic electron distribution. The actual molecule is best represented by a resonance hybrid, which is a 'blend' of all possible resonance structures. The hybrid reflects a more accurate picture of where the electrons are likely to be found. This concept of resonance is essential for understanding the behavior and properties of certain molecules or ions, such as stabilization due to delocalized electrons.