Problem 56 - Chemistry: The Central Science in SI Units, Global Edition

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

The N-O bond lengths ordering based on their Lewis structures is NO^+ < NO3^- < NO2^-, as the bond orders from shortest to longest are 3 for NO^+, 2 for NO3^-, and 1.5 for NO2^-.

Step 1: Draw Lewis Structures for Each Ion

(1) NO^+ ion: The total number of valence electrons for this ion is 10 (five from nitrogen and six from oxygen, minus one from the positive charge). The Lewis structure for NO^+ is: ``` O = N →→ ``` (2) NO2^− ion: The total number of valence electrons for this ion is 18 (five from nitrogen, six from each oxygen, and one from the negative charge). The Lewis structure for NO2^- is: ``` O ¬ N ¬ O ↓ ``` (3) NO3^− ion: The total number of valence electrons for this ion is 24 (five from nitrogen, six from each oxygen, and one from the negative charge). The Lewis structure for NO3^- is a resonance structure that represents an average of the three possible structures: ``` O ¬ N ¬ O ↓ ↓ O ```

Step 2: Determine the Average N-O Bond Order for Each Ion

(1) NO^+ ion: The N-O bond in NO^+ is a triple bond, so its bond order is 3. (2) NO2^− ion: One N-O bond in NO2^- is a double bond, and the other is a single bond. The average bond order for the two N-O bonds in NO2^- is \((1 + 2)/2 = 1.5\). (3) NO3^− ion: Each N-O bond in NO3^- is a double bond, and there are three equivalent resonance structures. The bond order for N-O in NO3^- is 2 (since each double bond has an order of 2).

Step 3: Predict the Bond Length Order

Bond length is inversely proportional to bond order. A higher bond order corresponds to a shorter bond length. Considering the bond orders calculated in Step 2, we see that the order, from shortest to longest N-O bond length, is: Shortest: NO^+ (bond order = 3) < NO3^- (bond order = 2) < Longest: NO2^- (bond order = 1.5) Thus, the N-O bond lengths ordering is NO^+ < NO3^- < NO2^-.

Key Concepts

Understanding Bond Order

Bond order is an important concept when analyzing Lewis structures. It represents the number of chemical bonds between a pair of atoms.
For example, a bond order of 3 indicates a triple bond, a bond order of 2 indicates a double bond, and so on.
This value is crucial because it helps predict the strength and length of bonds.

• A higher bond order means a stronger bond, which is usually shorter.
• A lower bond order indicates a weaker and generally longer bond.

The exercise reveals that NO⁺ has a bond order of 3, implying very short bonds, while NO₃^- has a bond order of 2, with medium-length bonds. NO₂^-, with a bond order of 1.5, has the longest bonds among the examples given. Understanding bond order allows chemists to predict molecular behavior without measuring each bond directly.

Exploring Resonance Structures

Resonance structures are multiple ways of drawing the same molecule that differ only in the placement of electrons. These structures illustrate the concept that real molecules are a blend, or hybrid, of multiple structures.

• In resonance, atoms do not move; only the electrons do.
• Each resonance form contributes to the overall stability of the molecule.

For example, the NO₃^- ion has three equivalent resonance structures. This means the actual structure can be seen as an average of these forms. Thus, the bond order becomes more uniform across the different possible configurations. Resonance can affect properties like the bond order, making it crucial for understanding molecular structures.

Role of Valence Electrons in Lewis Structures

Valence electrons are the outermost electrons of an atom and are involved in forming bonds. In Lewis structures, they are represented as dots or lines that show how these electrons pair up between atoms.

• These electrons determine the type and number of bonds an atom can form.
• Analyzing valence electrons helps in predicting the shape and reactivity of molecules.

In the exercise, calculating valence electrons is the starting point for drawing each ion's Lewis structure. For instance, NO₂^- has 18 valence electrons in its structure accounted for by adding electrons from nitrogen, oxygen, and the extra from the negative charge. This approach is central in not only organizing electron pairs but also speculating on resonance forms and bond orders.