Question

Incomplete Lewis structures for the nitrous acid molecule, ${\mathrm{HNO}}_2,$ and the nitrite ion, ${\mathrm{NO}}_2^{-},$ are shown below. (a) Complete each Lewis structure by adding electron pairs as needed. (b) Is the formal charge on $\mathrm{N}$ the same or different in these two species? (c) Would either ${\mathrm{HNO}}_2$ or ${\mathrm{NO}}_2^{-}$ be expected to exhibit resonance? (d) Would you expect the $\mathrm{N}=\mathrm{O}$ bond in ${\mathrm{HNO}}_2$ to be longer, shorter, or the same length as the $\mathrm{N}-\mathrm{O}$ bonds in ${\mathrm{NO}}_2^{-}$ ? Explain. [Sections 8.5 and $8.6]$

Short answer

The completed Lewis structures for HNO₂ and NO₂⁻ are: HNO₂: H-O-N=O with lone pairs on O atoms. NO₂⁻: (-)O-N=O(-) with resonance. The formal charge on N is +1 in HNO₂ and 0 in NO₂⁻. Resonance is only exhibited in the NO₂⁻ ion. The N=O bond in HNO₂ is expected to be shorter than the average N-O bond length in NO₂⁻ due to resonance.

Step-by-step solution

Complete Lewis structures

First, we will complete the Lewis structures for HNO₂ and NO₂⁻. Recall that N has 5 valence electrons, O has 6, and H has 1. Here are the completed Lewis structures: For HNO₂: H-O-N=O with the following electron pairs (lone pairs in parentheses): )O-N=O( $$ For NO₂⁻: O-N=O with the following electron pairs (lone pairs in parentheses): (-)O-N=O(-)

Compare formal charges

Next, we calculate the formal charge on the nitrogen atom for both HNO₂ and NO₂⁻. Formal charge = (valence electrons) - (nonbonding electrons) - (1/2 * bonding electrons) For HNO₂: Formal charge on N = 5 - 0 - (1/2 * 8) = 5 - 4 = +1 For NO₂⁻: Formal charge on N = 5 - 0 - (1/2 * 10) = 5 - 5 = 0 The formal charge on nitrogen is different in these two species.

Resonance structures

A molecule exhibits resonance when there are multiple valid Lewis structures with the same arrangement of atoms but different electronic configurations. In HNO₂, there is only one valid Lewis structure, so it does not exhibit resonance. However, for NO₂⁻, there is another valid Lewis structure: (-)O-N=O<->O=N-O(-) Therefore, NO₂⁻ exhibits resonance.

Compare bond lengths

HNO₂ has a double bond between N and O (N=O), while NO₂⁻ has a combination of single and double bonds (N-O and N=O) due to resonance. The actual bond length in NO₂⁻ will be an average of single and double bond lengths. A double bond is shorter than a single bond, so we expect the N=O bond in HNO₂ to be shorter than the average N-O bond length in NO₂⁻ due to resonance.

Key concepts

Formal Charge

Understanding formal charge is crucial for determining the most stable Lewis structure of a molecule. A formal charge on an atom is an artificial charge assigned to it as a way of bookkeeping. It's calculated using the formula:
$$\text{Formal Charge}=(\text{Valence Electrons})-(\text{Nonbonding Electrons})-\frac{1}{2}\times (\text{Bonding Electrons})$$For example, in the nitrous acid molecule, ${\text{HNO}}_2$, the nitrogen atom has 5 valence electrons. After accounting for the shared and non-shared electrons, the formal charge on nitrogen in ${\text{HNO}}_2$ is calculated to be +1.
In contrast, in the nitrite ion, ${\text{NO}}_2^{-}$, the nitrogen atom carries a formal charge of 0. This distinct difference in formal charge helps predict and explain the differing chemical behaviors of ${\text{HNO}}_2$ and ${\text{NO}}_2^{-}$. This calculation is essential for determining molecular geometry and reactivity as molecules tend to arrange themselves to minimize formal charges across their atoms.

Resonance Structures

Resonance structures are different ways of depicting a molecule where the array of atoms stays constant, but the distribution of electrons varies. Such structures are crucial for molecules like ${\text{NO}}_2^{-}$, which can exhibit resonance. This reflects the potential for electrons to be shared between different oxygen atoms in different configurations.
While ${\text{HNO}}_2$ has only one Lewis structure, indicating no resonance, the nitrite ion ${\text{NO}}_2^{-}$ can resonate between two forms.

• In one structure, the negative charge is on the "left" oxygen, while in the other, it is on the "right" oxygen.
• This ability for resonance implies more stability for ${\text{NO}}_2^{-}$ due to equal distribution of charge and electron density.

Understanding resonance is essential because it explains why certain molecule or ions are more stable, makes calculations for predicted bond lengths possible, and affects how a molecule might react with others.

Bond Length Comparison

Bond length can tell us a lot about the strength and nature of bonds within a molecule. In general, double bonds are shorter than single bonds due to additional electron sharing strengthening the bond. In our exercise, ${\text{HNO}}_2$ has a fixed double bond between nitrogen and oxygen, implying a shorter bond length.
Conversely, ${\text{NO}}_2^{-}$ features resonance between its two structures, which results in neither a pure single nor double bond, but rather an intermediate bond length.

• Resonance blurs the division between single and double bond lengths.
• This results in bonds being shorter than a typical single bond but not as short as a typical double bond.

Thus, the $\text{N=O}$ bond in ${\text{HNO}}_2$ should be shorter than the bond lengths in ${\text{NO}}_2^{-}$ due to its definitive double bond, as opposed to the averaged bond length in ${\text{NO}}_2^{-}$ resulting from resonance.