Question

Which has the greater bond lengths: ${\mathrm{NO}}_2^{-}$ or ${\mathrm{NO}}_3^{-}?$ Explain.

Short answer

${\mathrm{NO}}_2^{-}$ has greater bond lengths than ${\mathrm{NO}}_3^{-}$, because ${\mathrm{NO}}_3^{-}$ has more resonance structures (3) than ${\mathrm{NO}}_2^{-}$ (2), causing a more evenly distributed electron density and shorter bonds in ${\mathrm{NO}}_3^{-}$.

Step-by-step solution

Draw Lewis Structures of ${\mathrm{NO}}_2^{-}$ and ${\mathrm{NO}}_3^{-}$

We begin by drawing the Lewis structures of both ions. Count the total number of valence electrons available, place the less electronegative atoms in the center, and add bonds or lone pairs on the peripheral atoms accordingly. For ${\mathrm{NO}}_2^{-}$, there are 18 valence electrons (5 from N, 6 from each O, and 1 extra for the -1 charge). The O atoms are more electronegative, so N is placed in the center of the structure: O || N \ O For ${\mathrm{NO}}_3^{-}$, there are 24 valence electrons (5 from N, 6 from each O, and 1 extra for the -1 charge). Similar to the previous structure, O atoms are placed around the central N atom: O \ N // \ O O

Calculate Formal Charges

Now we calculate the formal charges for each atom in the structure to ensure that it is the most plausible structure, using the formula: $FormalCharge=GroupNumber-(NumberofBonds+NumberofLonePairElectrons)$ For ${\mathrm{NO}}_2^{-}$, the formal charge on nitrogen is +1 and on one oxygen atom is -1. For ${\mathrm{NO}}_3^{-}$, the formal charge on nitrogen is +1 and on one oxygen atom is -1, while the other two oxygen atoms have a formal charge of 0.

Compare Resonance Structures

Now we identify any resonance structures, which are alternative arrangements of electrons that result in an identical overall distribution of electron density. Increasing the number of equivalent resonance structures results in a smaller bond length. For ${\mathrm{NO}}_2^{-}$, there are two resonance structures with the double bond and the negative charge on different oxygen atoms. For ${\mathrm{NO}}_3^{-}$, there are three equivalent resonance structures, with the double bond and the negative charge rotating around the three oxygen atoms.

Determine Bond Length

Bond Length is inversely proportional to the bond order or number of resonance structures. Since ${\mathrm{NO}}_3^{-}$ has more resonance structures (3) than ${\mathrm{NO}}_2^{-}$ (2), the electrons are more evenly distributed, and the bonds in ${\mathrm{NO}}_3^{-}$ will be shorter. So, ${\mathrm{NO}}_2^{-}$ has greater bond lengths than ${\mathrm{NO}}_3^{-}$.

Key concepts

Lewis Structures

Lewis structures are an essential tool for representing the arrangement of atoms and electrons in a molecule. They help visualize both the bonding between atoms and the lone pairs of electrons that may exist. When creating a Lewis structure, it's important to follow specific steps to ensure accuracy.

Begin by counting the total number of valence electrons for the molecule or ion in question. This includes any extra electrons for negatively charged ions or missing electrons for positively charged ions. For instance, in ${\mathrm{NO}}_2^{-}$, there are 18 valence electrons including the extra electron due to the -1 charge. In ${\mathrm{NO}}_3^{-}$, there are 24 valence electrons.

Next, arrange the atoms with the less electronegative atom in the center. Typically, hydrogen and halogens will be peripheral unless combined with oxygen or nitrogen.

• Place the central atom first, and form single bonds to surrounding atoms.
• Distribute the remaining electrons to satisfy the octet rule, starting with the most electronegative atoms.

This process results in a clear schematic that aids in further analysis, such as determining formal charges and understanding resonance.

Resonance Structures

Resonance structures allow us to depict molecules with more than one valid Lewis structure, illustrating the delocalization of electrons within a molecule. Resonance is especially important when the molecule is stabilized by the distribution of electrons over multiple bonds rather than a single configuration.

In molecules like ${\mathrm{NO}}_2^{-}$ and ${\mathrm{NO}}_3^{-}$, resonance structures are essential for understanding electron distribution. For ${\mathrm{NO}}_2^{-}$, there are two resonance structures, each featuring a different oxygen atom holding a double bond.

• In one structure, the double bond is between nitrogen and one oxygen, with the other oxygen having a negative charge.
• In the alternate structure, the bond arrangement swaps, reflecting the equivalent resonance forms.

In comparison, ${\mathrm{NO}}_3^{-}$ exhibits three equivalent resonance structures, showing how the double bond and negative charge can rotate among the oxygen atoms. This larger number of resonance forms results in greater electron delocalization, leading to shorter and more stable bonds.

Formal Charge Calculation

Formal charge calculation is a method to predict the most likely structure for a molecule based on the distribution of electrons. It is calculated using the formula:$$FormalCharge=GroupNumber-(NumberofBonds+NumberofLonePairElectrons)$$
This calculation helps verify if the chosen Lewis structure is realistic or if there might be more plausible configurations.

For ${\mathrm{NO}}_2^{-}$:

• The formal charge of nitrogen is +1, while one of the oxygen atoms carries a formal charge of -1 to balance the ion's overall charge.

For ${\mathrm{NO}}_3^{-}$:

• The nitrogen atom has a formal charge of +1, while one oxygen atom has a formal charge of -1.
• The other two oxygen atoms are neutral.

Balancing formal charges across the molecule helps achieve the most stable configuration, minimizing formal charges wherever possible. This balance is key to validating the overall lewis and resonance structures and predicting bond lengths and strengths.