Problem 75 - Chemistry and Chemical Reactivity

Question

What are the orders of the \(\mathrm{N}-\) O bonds in \(\mathrm{NO}_{2}^{-}\) and \(\mathrm{NO}_{2}^{+} ?\) The nitrogen-oxygen bond length in one of these ions is \(110 \mathrm{pm}\) and \(124 \mathrm{pm}\) in the other. Which bond length corresponds to which ion? Explain briefly.

Step-by-Step Solution

Answer

\( \mathrm{NO}_{2}^{-} \) has a bond order of 1.5 and a bond length of 124 pm; \( \mathrm{NO}_{2}^{+} \) has a bond order of 2 and a bond length of 110 pm.

Step 1: Determine the Lewis structures

To start, let's draw the Lewis structures of the given ions, \( \mathrm{NO}_{2}^{-} \) and \( \mathrm{NO}_{2}^{+} \). \( \mathrm{NO}_{2}^{-} \) has a total of 18 valence electrons, distributed as \( \mathrm{N} = 5 \), \( \mathrm{O} = 6 \times 2 = 12 \), and an additional electron due to the negative charge. \( \mathrm{NO}_{2}^{+} \) has 16 valence electrons: \( \mathrm{N} = 5 \), \( \mathrm{O} = 6 \times 2 = 12 \), minus one electron due to the positive charge. For \( \mathrm{NO}_{2}^{-} \), the typical structure has one double bond and one single bond with a delocalized electron pair. \( \mathrm{NO}_{2}^{+} \) will have two double bonds.

Step 2: Calculate bond order for \( \mathrm{NO}_{2}^{-} \)

The bond order is calculated as the total number of chemical bonds ( - O bonds) divided by the number of oxygen atoms bonded to the nitrogen. For \( \mathrm{NO}_{2}^{-} \), there is one and a half bonds per \( \mathrm{N}- \mathrm{O} \) because of resonance (2 bonds shared over 2 oxygen atoms). This leads to a bond order of 1.5.

Step 3: Calculate bond order for \( \mathrm{NO}_{2}^{+} \)

For \( \mathrm{NO}_{2}^{+} \), each of the \( \mathrm{N}- \mathrm{O} \) bonds are double bonds, which gives a bond order of 2. This is because there are four bonding electron pairs shared over two oxygen atoms.

Step 4: Match bond lengths to ions

The bond order is inversely related to bond length, meaning bonds with higher order have shorter bond lengths. Therefore, since \( \mathrm{NO}_{2}^{+} \) has a bond order of 2, it should have the shorter bond length of 110 pm. Conversely, \( \mathrm{NO}_{2}^{-} \) bond, having a bond order of 1.5, corresponds to the longer bond length of 124 pm.

Key Concepts

Lewis Structures

Lewis structures are a way to represent molecules that shows the arrangement of atoms and the distribution of electrons among them. To draw a Lewis structure, you start by determining the total number of valence electrons for the molecule or ion. For instance, in the \(\mathrm{NO}_{2}^{-}\) ion, there are 18 valence electrons. Nitrogen contributes 5 electrons, each oxygen contributes 6 electrons (for a total of 12), and the negative charge of the ion adds one more electron.
In contrast, the \(\mathrm{NO}_{2}^{+}\) ion has 16 valence electrons (5 from nitrogen and 12 from oxygen), but since it has a positive charge, one electron is lost.

• For molecules like \(\mathrm{NO}_{2}^{-}\), electrons can form single, double, or even triple bonds, depending on the spatial configuration.
• It's important to ensure that all atoms (especially C, N, O, and F) get an octet of electrons, sometimes requiring resonance structures.

Understanding Lewis structures helps in visualizing how electrons are shared or transferred during chemical bonding.

Bond Order

Bond order is a concept that provides insight into the stability, length, and strength of a chemical bond. It quantifies the number of bonds between two atoms, which directly influences bond length and strength. To calculate bond order, consider the difference between bonding and antibonding electrons.
In cases like \(\mathrm{NO}_{2}^{-}\), resonance affects bond order. This molecule has a bond order of 1.5, which means the bond strength is between a single and a double bond.

• \(\mathrm{NO}_{2}^{+}\) showcases a bond order of 2 because each \(\mathrm{N}-\mathrm{O}\) bond is a double bond, indicating a stronger and shorter bond.
• Higher bond orders correlate with increased bond strength and decreased bond length, while lower bond orders mean weaker and longer bonds.

Knowing bond order assists in predicting how a molecule might interact in chemical reactions.

Resonance Structures

Resonance structures are alternate Lewis structures for molecules that cannot be accurately represented by a single structure due to delocalization of electrons. They are crucial for visualizing molecules that have equivalent ways of arranging their electrons.For \(\mathrm{NO}_{2}^{-}\), resonance is key because it has one double bond and one single bond that alternate between the oxygens, meaning the electrons are delocalized across both bonds evenly.

• This leads to two possible resonance structures, contributing to the true hybrid nature of the bonding.
• The real structure is a blend of these resonance forms, often resulting in intermediate bond lengths partly single, partly double.

In essence, resonance structures are used to represent a more accurate portrayal of electron distribution.

Bond Lengths

Bond length refers to the distance between the nuclei of two bonded atoms. It is a critical measure indicating the strength and character of a bond. Generally, bond length boils down to the type of bond and bond order present in molecules.
For example, in \(\mathrm{NO}_{2}^{+}\), with a bond order of 2, each \(\mathrm{N}-\mathrm{O}\) bond is shorter, measuring around 110 pm. Shorter bond lengths result from the stronger pull of double bonds, which hold atoms more tightly together.

• On the other hand, the \(\mathrm{NO}_{2}^{-}\) ion, with a bond order of 1.5, results in a longer bond length of 124 pm. This represents a mixture of single and double bonds, hence the longer distance.
• Bond length decreases with an increase in bond order, due to the increase in shared electron pairs causing a tighter bond.

Understanding bond lengths helps predict molecular behavior, including reactivity and interaction with other molecules.