Problem 138 - A Complete Resource Book in Chemistry for JEE Main

Question

Match the following: List I List II (Species) (Bond order) 1\. \(\mathrm{O}_{2}^{2+}\) (i) \(1.0\) 2\. \(\mathrm{O}_{2}\) (ii) \(2.0\) 3\. \(\mathrm{F}_{2}\) (iii) \(2.5\) 4\. \(\mathrm{O}_{2}^{+}\) (iv) \(3.0\) The correct matching is: \(\begin{array}{llll}1 & 2 & 3 & 4\end{array}\) (a) (iv) (i) (ii) (ii) (b) (ii) (iii) (i) (iv) (c) (iv) (ii) (i) (iii) (d) (iii) (iv) (i) (ii)

Step-by-Step Solution

Answer

(b) (ii), (iii), (i), (iv)

Step 1: Understanding Bond Order

Bond order is an indicator of the stability of a bond. It is calculated using the formula: \[ ext{Bond Order} = rac{ ext{Number of Bonding Electrons} - ext{Number of Antibonding Electrons}}{2} \] A higher bond order indicates a stronger bond.

Step 2: Calculating Bond Order for \(\mathrm{O}_{2}^{2+}\)

For \(\mathrm{O}_{2}^{2+}\), remove two electrons from \(\mathrm{O}_{2}\). Molecular orbital configuration becomes \((\sigma_{1s})^2 (\sigma^*_{1s})^2 (\sigma_{2s})^2 (\sigma^*_{2s})^2 (\sigma_{2p_z})^2 (\pi_{2p_x})^2(\pi_{2p_y})^2\). Total bonding electrons = 8, total antibonding = 4. Bond order = \(\frac{8 - 4}{2} = 2.0\).

Step 3: Calculating Bond Order for \(\mathrm{O}_{2}\)

For \(\mathrm{O}_{2}\), the molecular orbital configuration is \((\sigma_{1s})^2 (\sigma^*_{1s})^2 (\sigma_{2s})^2 (\sigma^*_{2s})^2 (\sigma_{2p_z})^2 (\pi_{2p_x})^2(\pi_{2p_y})^2 (\pi^*_{2p_x})^1(\pi^*_{2p_y})^1\). Total bonding electrons = 10, antibonding = 6. Bond order = \(\frac{10 - 6}{2} = 2.0\).

Step 4: Calculating Bond Order for \(\mathrm{F}_{2}\)

For \(\mathrm{F}_{2}\), the molecular orbital configuration is \((\sigma_{1s})^2 (\sigma^*_{1s})^2 (\sigma_{2s})^2 (\sigma^*_{2s})^2 (\sigma_{2p_z})^2 (\pi_{2p_x})^2(\pi_{2p_y})^2 (\pi^*_{2p_x})^2(\pi^*_{2p_y})^2\). Total bonding electrons = 8, antibonding = 6. Bond order = \(\frac{8 - 6}{2} = 1.0\).

Step 5: Calculating Bond Order for \(\mathrm{O}_{2}^{+}\)

For \(\mathrm{O}_{2}^{+}\), remove one electron from \(\mathrm{O}_{2}\). Molecular orbital becomes \((\sigma_{1s})^2 (\sigma^*_{1s})^2 (\sigma_{2s})^2 (\sigma^*_{2s})^2 (\sigma_{2p_z})^2 (\pi_{2p_x})^2(\pi_{2p_y})^2 (\pi^*_{2p_x})^1\). Total bonding electrons = 10, antibonding = 5. Bond order = \(\frac{10 - 5}{2} = 2.5\).

Step 6: Matching the Bond Order to Species

Based on calculations: 1. \(\mathrm{O}_{2}^{2+} = 2.0\) (ii), 2. \(\mathrm{O}_{2} = 2.0\) (ii), 3. \(\mathrm{F}_{2} = 1.0\) (i), 4. \(\mathrm{O}_{2}^{+} = 2.5\) (iii). Thus, the correct sequence is (b) \((ii), (iii), (i), (iv)\).

Key Concepts

Molecular Orbital Theory

Molecular Orbital Theory (MOT) serves as a foundation in understanding how electrons are distributed in molecules, offering an advanced method for describing the electronic structure of molecules compared to simpler models like valence bond theory. In MOT, atomic orbitals of combining atoms merge to form molecular orbitals that belong to the molecule as a whole. These molecular orbitals can be categorized into bonding and antibonding types.

• Bonding orbitals enhance stability by creating an electron cloud between nuclei, favoring attraction.
• Antibonding orbitals reduce stability with nodes that push nuclei apart.

The energy difference between these orbitals explains phenomena such as bond strength and molecular polarity. For example, understanding bonding and antibonding orbitals helps demystify why some molecules form more easily and why some bonds are stronger than others.

Electron Configuration

Electron configuration within molecules refers to the arrangement of electrons across different molecular orbitals. Each electron prefers to occupy the lowest energy orbital available, following the Aufbau principle. When dealing with molecules like \( O_2\), the molecular orbitals derived from the combination of atomic orbitals will fill according to energy levels.

• The principle begins with occupying lower energy bonding orbitals.
• Progresses to higher energy antibonding orbitals if more electrons need placement.

For example, in dioxygen \(2\), the configuration ends with electrons in some antibonding orbitals, which explains its paramagnetic nature—meaning it's attracted to magnetic fields owing to unpaired electrons. This contrasts with diamagnetic molecules like nitrogen which have all their electrons paired.

Chemical Bonding

Chemical bonding occurs when atoms share or transfer valence electrons, leading to molecule formation. The type and strength of the bond directly influence molecular properties such as shape, reactivity, and stability. In the context of Molecular Orbital Theory, the strength of the bond is often expressed in terms of bond order, calculated as the difference between the number of electrons in bonding versus antibonding orbitals, divided by two.

• Higher bond order typically correlates with stronger, shorter bonds.
• Lower bond orders suggest weaker, longer bonds.

Thus, the bond order can serve as a quick indicator of molecular stability and potential reactivity. For instance, oxygen species like \(O_2\) and \(O_2^+\) have important roles in chemical and biological processes, partly due to their specific bond orders.

Oxygen Species

Oxygen species, such as \(O_2\), \(O_2^+\), and \(O_2^{2+}\), differ in electronic configuration, which influences their chemical behavior. These variations influence properties like stability, magnetism, and bond length. These species are critical in fields ranging from environmental science to biochemistry.

• \(O_2\) is a stable molecule with a fundamental role in respiration and combustion.
• \(O_2^+\) is less stable, existing typically in high-energy environments, such as mass spectrometry applications.
• \(O_2^{2+}\) has fewer electrons, meaning its bond order and magnetic properties differ significantly from neutral \(O_2\).

Understanding these variations is crucial, especially for processes sensitive to oxygen reactivity and molecular interactions.

Stability of Molecules

The stability of a molecule depends on several factors, often evaluated using Molecular Orbital Theory. Bond order, derived from the difference between bonding and antibonding electrons, is a primary determinant. A higher bond order means a more stable molecule due to stronger bonds.

• Species with higher bond orders are typically more energetically favorable and less reactive.
• Molecules with unpaired electrons or lower bond orders exhibit magnetic properties and higher reactivity.

Take oxygen species as an example: \(O_2\) and its ions \(O_2^+\) and \(O_2^{2+}\) demonstrate how bond order influences their respective stabilities and chemical behavior. Understanding how these variables interact aids in predicting how molecules will react in various chemical environments.