Question

what is the bond order of B² and B²⁺

and which has a longer bond

   I am assuming that the non-+ has a longerbond.

Answer 1

Concepts and reason

The bond order is the number of bonds present between two atoms. This is calculated using molecular orbital theory.

Higher the value of bond order lesser will be the bond length.

Fundamentals

Molecular orbital theory is used to explain bonding in molecules using linear combination of atomic orbitals. According to molecular orbital theory, the atomic orbitals combine linearly to form molecular orbitals. The number of atomic orbitals combining is equal to the number of molecular orbitals formed. These molecular orbitals are further divided into two parts bonding and anti-bonding molecular orbitals (represented using “*” at superscript).

The molecular orbital diagrams for ${{\rm{B}}_2}$ and ${\rm{B}}_2^ +$ are as follows:

The bond order can be calculated for these molecules using the following formula:

${\rm{Bond order}} = \frac{1}{2}\left( {{\rm{No}}{\rm{. of bonding electrons}} - {\rm{No}}{\rm{. of Antibonding electrons}}} \right)$

For ${\rm{B}}_2^{}$ ,

${\rm{B}}_2^{}$ have 6 bonding electrons and 4 anti-bonding electrons. Therefore, its bond order will be:

$\begin{array}{c}\\{\rm{Bond order}} = \frac{1}{2}\left( {6 - 4} \right)\\\\ = 1\\\end{array}$

For ${\rm{B}}_2^ +$ ,

${\rm{B}}_2^ +$ have 5 bonding electrons and 4 anti-bonding electrons. Therefore, its bond order will be:

$\begin{array}{c}\\{\rm{Bond order}} = \frac{1}{2}\left( {5 - 4} \right)\\\\ = 0.5\\\end{array}$

Ans:

${\rm{B}}_2^ +$ has longer bond length.