Problem 56 - Chemistry The Central Science In Si Units

Question

Based on Lewis structures, predict the ordering, from shortest to longest, of \(\mathrm{N}-\mathrm{O}\) bond lengths in \(\mathrm{NO}^{+}, \mathrm{NO}_{2}^{-},\) and \(\mathrm{NO}_{3}^{-}\).

Step-by-Step Solution

Answer

NO+ < NO2- < NO3- in bond length.

Step 1: Identify the Number of Bonding Electrons

First, determine the number of electrons involved in bonding for each molecule: \( \text{NO}^+, \text{NO}_2^- \text{, and } \text{NO}_3^- \). In Lewis structures, more bonding pairs (or higher bond order) translate to shorter bond lengths.

Step 2: Construct the Lewis Structures

Draw the Lewis structures for each ion: - \( \text{NO}^+\) has a triple bond between \(\text{N}\) and \(\text{O}\), giving it a bond order of 3.- \( \text{NO}_2^-\) has one \(\text{N=O}\) bond and one \(\text{N-O}\) single bond, effectively making the average bond order between \(\text{N}\) and \(\text{O}\) equal to 1.5.- \( \text{NO}_3^-\) has three \(\text{N-O}\) bonds that are delocalized across three \(\text{O}\) atoms, resulting in an average bond order of approximately 1.33.

Step 3: Compare Bond Order and Lengths

Recall that bond order is inversely related to bond length. Thus, the higher the bond order, the shorter the bond length. From the Lewis structures:- \( \text{NO}^+\) has the greatest bond order of 3 (shortest bond length).- \( \text{NO}_2^-\) has a lower bond order of 1.5.- \( \text{NO}_3^-\) has the lowest bond order of 1.33 (longest bond length).

Step 4: Rank the Bond Lengths

Based on bond orders, rank the \(\text{N-O}\) bond lengths from shortest to longest:1. \( \text{NO}^+\) (shortest)2. \( \text{NO}_2^-\)3. \( \text{NO}_3^-\) (longest)

Key Concepts

Understanding Bond Order

Bond order is an essential concept in chemistry that helps predict the stability and length of a chemical bond. It refers to the number of chemical bonds between a pair of atoms. A higher bond order means there are more shared electrons between atoms. This translates into a stronger and often shorter bond.

Let’s look deeper:

• A single bond consists of one pair of shared electrons, giving it a bond order of 1.
• A double bond shares two pairs of electrons, with a bond order of 2.
• A triple bond, the strongest, has three shared pairs, resulting in a bond order of 3.

In the context of \(\text{NO}^+\), the triple bond gives it a bond order of 3, the highest among the species compared, indicating a very strong and short bond. In \(\text{NO}_2^-\), bonds are averaged out due to resonance, leading to an intermediate bond order of 1.5. \(\text{NO}_3^-\) has an average bond order even lower, about 1.33, because of its delocalized bonding over three sites.

Comparing Bond Lengths

When discussing chemical bonds, it's crucial to understand how bond order impacts bond length. Generally, bond order and bond length are inversely related, meaning a higher bond order results in a shorter bond length. This inverse relationship is because more shared electrons pull the atoms closer together.

Let's illustrate further:

• For \(\text{NO}^+\), with a bond order of 3, the electron density between the nitrogen and oxygen is maximal, leading to the shortest bond.
• \(\text{NO}_2^-\), with a 1.5 bond order, sits somewhere in-between, not as compact as \(\text{NO}^+\), but tighter than \(\text{NO}_3^-\).
• Lastly, \(\text{NO}_3^-\), with the lowest bond order of approximately 1.33, has the most spread out electron density, resulting in the longest bond.

Understanding this principle helps us predict and compare molecular structures based on their Lewis structures.

Chemical Bonding Basics

Chemical bonding is the glue that holds atoms together in molecules. It's driven by the need for atoms to achieve a stable electronic configuration, often resembling the noble gases. Bonds can form in several types: ionic, covalent, and metallic, with covalent more relevant to this discussion.

Covalent bonding involves the sharing of electron pairs between atoms. Lewis structures, named after Gilbert N. Lewis, are simple diagrams that map out the valence electrons involved in bonds. They provide visual insight into the types of bonds (single, double, triple) and the potential bond order.

In the context of the molecules \(\text{NO}^+\), \(\text{NO}_2^-\), and \(\text{NO}_3^-\), the Lewis structures make it clear how the electrons are distributed and help in identifying bond orders and lengths by showing shared electron pairs.

Exploring Inversely Related Properties

In chemistry, the concept of inversely related properties is often used to predict how changes in one property affect another. The relationship between bond order and bond length is one classic example.

Here’s what that means:

• A high bond order indicates strong interatomic attractions due to more shared electron pairs. This results in shorter bond lengths.
• Conversely, a low bond order suggests fewer shared electrons and reduced atomic pull towards each other, leading to longer bond lengths.

Therefore, when analyzing chemical species like \(\text{NO}^+\), \(\text{NO}_2^-\), and \(\text{NO}_3^-\), understanding this inverse relationship allows one to predict which bonds are the longest and which are the shortest based on their calculated bond orders. This concept extends beyond just bond length; it’s applied broadly in chemistry for properties that affect molecular behavior and interactions.