Problem 192 - A Complete Resource Book in Chemistry for JEE Main

Question

The bond order in \(\mathrm{NO}\) is \(2.5\) while that in \(\mathrm{NO}^{+}\)is 3 . Which of the following statements is true for these two species? (a) bond length in \(\mathrm{NO}^{+}\)is greater than in \(\mathrm{NO}\) (b) bond length in \(\mathrm{NO}\) is greater than in \(\mathrm{NO}^{+}\) (c) bond length in NO' is equal than in NO (d) bond length is unpredictable

Step-by-Step Solution

Answer

(b) bond length in \( \text{NO} \) is greater than in \( \text{NO}^+ \).

Step 1: Understanding Bond Order

The bond order of a molecule is a measure of the number of chemical bonds between a pair of atoms. It is used as an indicator of bond strength and stability.

Step 2: Bond Order and Bond Length Relationship

There is an inverse relationship between bond order and bond length. As the bond order increases, the number of electrons in bonding orbitals increases, which strengthens and shortens the bond. Thus, a higher bond order generally corresponds to a shorter bond length.

Step 3: Comparing Bond Order in NO and NO+

The bond order in \( \text{NO} \) is 2.5, and in \( \text{NO}^+ \) it is 3. Since \( \text{NO}^+ \) has a higher bond order, it will have a shorter bond length compared to \( \text{NO} \).

Step 4: Evaluating the Given Statements

Given the relationship observed in the previous steps, we need to choose the statement showing \( \text{NO}^+ \) with a shorter bond length than \( \text{NO} \). This would make statement (b) correct: "bond length in \( \text{NO} \) is greater than in \( \text{NO}^+ \)."

Key Concepts

Bond Length

Bond length is a term that refers to the distance between the nuclei of two bonded atoms. It is an important concept in chemistry because it can give us insights into the strength and stability of a bond.

Generally, when atoms form a bond, they do so to achieve a more stable electron arrangement. The length of that bond can vary based on several factors including the bond order, the size of the atoms, and the type of bond.

• A higher bond order implies a stronger attraction between the atoms, leading to a shorter bond length.
• Conversely, a lower bond order suggests a longer bond length due to weaker attraction.

Thus, understanding bond length helps us in predicting molecular properties and reactivity. It allows chemists to visualize how tightly two atoms are connected within a molecule.

NO Molecule

The \( ext{NO}\) molecule is nitric oxide, a simple diatomic molecule that plays a variety of roles in both environmental chemistry and biochemistry.

In its ground state, \( ext{NO}\) has a bond order of 2.5. This bond order suggests that the molecule is relatively stable, with a bond length that is shorter than some other diatomic molecules with lower bond orders.

• The fractional bond order of 2.5 in \( ext{NO}\) indicates that there is some partial double bond character between the nitrogen and oxygen atoms.
• This fractional bond order arises because \( ext{NO}\) possesses both bonding and antibonding electrons, which affect the overall bond strength and length.

Despite having an unpaired electron, making it a free radical, \( ext{NO}\) is stable enough to exist under normal conditions.

NO+ Ion

The \( ext{NO}^+\) ion, often referred to as nitrosonium ion, differs from the neutral \( ext{NO}\) molecule primarily by the absence of an electron.

This lack of one electron in \( ext{NO}^+\) raises its bond order to 3, indicating a stronger and shorter bond compared to the \( ext{NO}\) molecule.

• With a bond order of 3, the bond is analogous to a triple bond, providing significant bond strength and stability.
• This change in electron configuration due to ionization results in a more stable molecular structure with reduced bond length.

The higher bond order and subsequent shorter bond length in \( ext{NO}^+\) highlight how ionization can influence molecular structure and bond dynamics.