Question

Bond order in the MO theory depends on the number of bonding electrons and anti-bonding electrons. The bond order (1) always has an integer value (2) can have only fractional valuc (3) is always equal to onc (4) can be zero, integral or fractional

Short answer

Bond order can be zero, integral or fractional.

Step-by-step solution

Understand Bond Order Formula

Bond order in Molecular Orbital (MO) theory is determined using the formula: Bond order = 0.5 * (Number of bonding electrons - Number of antibonding electrons)

Identify Possible Values for Bond Order

Since the bond order formula involves the difference between bonding and antibonding electrons, and this difference can be any integer, the bond order can be an integer, a fraction, or zero.

Evaluate the Statements

(1) Bond order always has an integer value - This is incorrect because bond order can also be fractional.(2) Bond order can have only a fractional value - This is incorrect because it can also be integer and zero.(3) Bond order is always equal to one - This is incorrect; it varies.(4) Bond order can be zero, integral or fractional - This is correct based on bond order calculations.

Conclusion

Based on the evaluation of the possible values for bond order, the correct answer is that the bond order can be zero, integral or fractional.

Key concepts

Bond Order in Molecular Orbital Theory

The concept of bond order is crucial in understanding the strength and stability of a chemical bond within a molecule. In Molecular Orbital (MO) theory, the bond order is calculated using a specific formula. This formula takes into account the number of bonding and antibonding electrons in the molecule. Bond order essentially tells us how many chemical bonds exist between a pair of atoms.
Bond order is calculated as:
\[ \text{Bond order} = 0.5 * (\text{Number of bonding electrons} - \text{Number of antibonding electrons}) \] This means that the bond order can have several possible values:

• It can be zero, indicating that no bond exists between the atoms.
• It can be an integer (like 1, 2, or 3), which corresponds to single, double, or triple bonds.
• It can even be fractional, which might occur in compounds with resonance structures or delocalized electrons.

Understanding bond order helps in predicting the bond's length and energy. A higher bond order usually means a stronger and shorter bond.

Bonding Electrons

Bonding electrons are electrons that reside in molecular orbitals which help to bond atoms together. These electrons are found in what are called bonding orbitals. Bonding orbitals are lower in energy compared to the atomic orbitals from which they are formed. This energy difference is what makes these electrons contribute positively to the stability of the molecule.
Here are some important points about bonding electrons:

• They are found in orbitals that are formed by the constructive overlap of atomic orbitals.
• Bonding electrons help to reduce the energy of the molecule, leading to a more stable structure.
• They are directly involved in the formation of sigma (σ) and pi (π) bonds which keep the atoms together.

Understanding the role of bonding electrons is fundamental in predicting how molecules are formed and how they behave. These electrons are the key contributors to the formation of stronger and more stable chemical bonds.

Antibonding Electrons

Antibonding electrons reside in molecular orbitals that actually weaken the bond between atoms. These electrons are found in antibonding orbitals, which are higher in energy compared to the atomic orbitals that combine to form them. The presence of antibonding electrons acts counter to bonding electrons, and can reduce the overall stability of the molecule.
Key characteristics of antibonding electrons include:

• They are found in orbitals formed by the destructive overlap of atomic orbitals.
• Antibonding orbitals contain nodes, regions where the probability of finding an electron is zero, which correspond to areas of electron repulsion.
• They effectively increase the energy of the molecule, making the bond weaker.

When calculating bond order, the number of antibonding electrons is subtracted from the number of bonding electrons, affecting the final bond order value. If there are many antibonding electrons, the bond order can be low, leading to a less stable or even non-existent bond.