Question

Following is the structural representation of \(N_2O_3\) molecule in which \(x, y, z\) are bond angles and \(p, q, r\) are bond lengths. The correct orders of bond angles and bond lengths respectively are center

center

• A. \(x < z < y\) and \(p < q < r\)
• B. \(x < y < z\) and \(p < r < q\)
• C. \(y < z < x\) and \(p < r < q\)
• D. \(x < y < z\) and \(p < q < r\)

Hint:

Remember: \[ \text{Bond length} \propto \frac{1}{\text{Bond order}} \] Thus: \[ \text{Triple bond} < \text{Double bond} < \text{Single bond} \] in terms of bond length.

Answer 1

The Correct Option is C

Concept: This problem is based on:

• Molecular geometry

• Bond order and bond length relationship

• Hybridisation and electron pair repulsion
Important concepts used:

• Greater the bond order, smaller is the bond length

• Lone pair-bond pair repulsion compresses bond angles

• Double bonds occupy more space and increase adjacent bond angles

Step 1: Understand the structure of \(N_2O_3\). The given structure contains:

• One \(N-N\) single bond

• Two terminal oxygen atoms attached through double bonds

• One oxygen atom attached through single bond
The labelled quantities are: \[ x,y,z = \text{bond angles} \] \[ p,q,r = \text{bond lengths} \]

Step 2: Compare the bond angles. Angle \(x\):

• Present near nitrogen attached with double bonded oxygen

• Double bond exerts greater repulsion

• Therefore angle becomes larger
Hence \(x\) is the largest angle. Angle \(y\):

• Influenced strongly by lone pair repulsion

• Lone pair compresses the bond angle
Thus \(y\) becomes the smallest angle. Angle \(z\):

• Intermediate repulsion

• Therefore intermediate bond angle
Hence: \[ y < z < x \]

Step 3: Compare the bond lengths. Bond length depends inversely on bond order. Bond \(q\):

• Represents \(N-N\) single bond

• Single bonds are longest
Therefore \(q\) is maximum. Bond \(p\):

• Represents \(N=O\) double bond

• Double bond is shortest
Thus \(p\) is minimum. Bond \(r\):

• Intermediate character

• Hence intermediate bond length
Therefore: \[ p < r < q \]

Step 4: Write the final order. Thus: \[ \boxed{y < z < x} \] and \[ \boxed{p < r < q} \] Hence the correct option is: \[ \boxed{(C)} \]