Problem 117 - Chemistry The Science in Context

Question

Explain why the nitrogen-oxygen bond lengths in \(\mathrm{N}_{2} \mathrm{O}_{4}\) (which has a nitrogen-nitrogen bond) and \(\mathrm{N}_{2} \mathrm{O}\) are nearly identical ( 118 and 119 pm, respectively).

Step-by-Step Solution

Answer

The nitrogen-oxygen bond lengths in dinitrogen tetroxide (N2O4) and dinitrogen monoxide (N2O) are nearly identical primarily because both molecules have double bonds between nitrogen and oxygen atoms. Although the nitrogen-oxygen double bonds in N2O4 are slightly weakened due to electron repulsion with the nitrogen-nitrogen bond, the effect is not significant enough to cause a noticeable difference in bond lengths. Consequently, the bond lengths in N2O4 (118 pm) and N2O (119 pm) are very similar.

Step 1: Understand the molecular structure of \(\mathrm{N}_{2}\mathrm{O}_{4}\)

Dinitrogen tetroxide (\(\mathrm{N}_{2}\mathrm{O}_{4}\)) can be viewed as two dinitrogen trioxide (\(\mathrm{N}_{2}\mathrm{O}_{3}\)) molecules bonded together. In the \(\mathrm{N}_{2}\mathrm{O}_{3}\) molecule, each nitrogen atom is bonded to one oxygen atom by a double bond (which is a relatively strong and short bond) and to another oxygen atom by a single bond (which is relatively weaker and longer). When two \(\mathrm{N}_{2}\mathrm{O}_{3}\) molecules bond together to form \(\mathrm{N}_{2}\mathrm{O}_{4}\), a nitrogen-nitrogen bond is created, and the double bonds between nitrogen and oxygen become weaker due to electron repulsion.

Step 2: Understand the molecular structure of \(\mathrm{N}_{2}\mathrm{O}\)

Dinitrogen monoxide (\(\mathrm{N}_{2}\mathrm{O}\)) consists of two nitrogen atoms bonded together with a triple bond and one oxygen atom bonded to one of the nitrogen atoms by a double bond. In this case, the nitrogen-nitrogen triple bond is quite strong and relatively short. The nitrogen-oxygen double bond is also a strong bond with a relatively short length.

Step 3: Compare the bond lengths in \(\mathrm{N}_{2}\mathrm{O}_{4}\) and \(\mathrm{N}_{2}\mathrm{O}\)

In both molecules, the nitrogen-oxygen bonds are double bonds, which tend to be shorter and stronger than single bonds. As mentioned in Step 1, the nitrogen-oxygen double bonds in \(\mathrm{N}_{2}\mathrm{O}_{4}\) become weaker due to the electron repulsion caused by the nitrogen-nitrogen bond formation. However, this weakening effect is not significant enough to considerably weaken the nitrogen-oxygen double bonds, resulting in only a small change in bond length.

Step 4: Conclude the reason for the similarity in bond lengths

In conclusion, the nitrogen-oxygen bond lengths in \(\mathrm{N}_{2}\mathrm{O}_{4}\) and \(\mathrm{N}_{2}\mathrm{O}\) are nearly identical due to the nature of double bonds between nitrogen and oxygen atoms in both molecules. Although the nitrogen-oxygen double bonds in \(\mathrm{N}_{2}\mathrm{O}_{4}\) become slightly weaker due to electron repulsion with the nitrogen-nitrogen bond, this effect is not significant enough to cause a noticeable difference in bond lengths. Hence, the bond lengths in \(\mathrm{N}_{2}\mathrm{O}_{4}\) (118 pm) and \(\mathrm{N}_{2}\mathrm{O}\) (119 pm) are very similar.

Key Concepts

Molecular Structure of N2O4

Dinitrogen tetroxide, \(\text{N}_2\text{O}_4\), is an interesting molecule where two nitrogen atoms are linked by a single bond. This molecule can be thought of as two nitrite molecules coming together. Each nitrogen in \(\text{N}_2\text{O}_4\) forms a double bond with one oxygen atom and a single bond with another.
However, when these clusters of atoms bond together, it results in the overall molecular structure having a central nitrogen-nitrogen bond.

• This nitrogen-nitrogen bond causes some electron repulsion.
• The presence of both single and double bonds within \(\text{N}_2\text{O}_4\) suggests a variety of bond strengths.

Consequently, even though double bonds are typically stronger, the nitrogen-oxygen bonds here experience a slight elongation due to the repulsion effects.This results in the nitrogen-oxygen bonds being nearly the same length as in other similar molecules, with a length close to 118 pm.

Molecular Structure of N2O

Dinitrogen monoxide, \(\text{N}_2\text{O}\), operates with a different structure. In this case, the two nitrogen atoms are closely held together by a robust triple bond.
This means that three electron pairs are shared between the nitrogen atoms, making for a very compact bond.The oxygen atom connects to one of the nitrogen atoms through a double bond.

• Triple bonds are even shorter and stronger than double bonds.
• The nitrogen-oxygen double bond remains strong and close in comparison.

These factors combined mean that even though \(\text{N}_2\text{O}\) has a triple bond between the nitrogen atoms, the nitrogen-oxygen bond doesn't stretch significantly more than its double-bond counterparts in other nitrogen-oxygen frameworks. Thus, the length remains around 119 pm.

Double and Triple Bonds

The distinct characteristics of double and triple bonds come into play significantly in the lengths we observe in \(\text{N}_2\text{O}_4\) and \(\text{N}_2\text{O}\). Double bonds are known for their strength and shorter length, which accounts for strong molecular stability. Triple bonds, sharing three electron pairs, are even stronger and shorter.

• Double bonds involve sharing two pairs of electrons between atoms.
• Triple bonds share three pairs of electrons, resulting in a more robust connection.

Even though \(\text{N}_2\text{O}_4\) has weakened double bonds due to additional electron repulsion, the nature of double bonds keeps the nitrogen-oxygen bond lengths consistent with each other.The slight difference in the bond lengths between \(\text{N}_2\text{O}_4\) at 118 pm and \(\text{N}_2\text{O}\) at 119 pm highlights how the intrinsic properties of double and triple bonds contribute to similar bond dimensions.