Question

Which among the following can describe the bonding in diborane $({B_2}{H_6})$?
A. 4 center-2 electron bonds and 2 three center-2electron bonds
B. 3 two centers -2 electron bonds and 3 center-2 electron bonds
C. 2 two center-2 electron bonds and 4 three center-2 electron bonds
D. 4 two center-2 electron bonds and 4 two centers -2 electron bonds

Answer 1

Hint :Boron combines with dihydrogen to form several hydrides. These hydrides of boron are boranes. The simplest of boranes is diborane.

Step-by-step explanation:
Step 1
Diborane is an electron-deficient compound as its molecule does not have sufficient electrons to form normal covalent bonds. To explain the nature of bonding based on electron diffraction studies, it has been suggested that diborane contains a special type of bonding.
Step 2
Boron in the excited state has an electronic configuration as follows: ${B^*}:1{s^2},2{s^1},2p_x^1,2p_y^1,2p_z^1$.
So, boron in the excited state undergoes $s{p^3}$hybridization and acquires four hybrid orbitals of equal energy.
Step 3
Among the four hybrid orbitals present on each boron atom, three contain one electron each while the fourth one is the vacant orbital.
As the two boron atom combines the two singly filled $s{p^3}$hybrid orbitals of each boron atom overlaps with the singly filled 1s orbital of the two hydrogen atoms and form two $B - H\sigma$bonds. At this stage, both the boron atoms are left with one single occupied $s{p^3}$hybrid orbital and one vacant $s{p^3}$hybrid orbital. These hybrid orbitals of each boron atom are used in the formation of three center-two electron bonds.
Step 4
The singly occupied $s{p^3}$hybrid orbital of one boron atom and the vacant $s{p^3}$hybrid orbital of the other boron atom simultaneously overlap with the singly filled 1s orbital of the bridging hydrogen atom to form a delocalized molecular orbital. This phenomenon takes place for both the boron atoms.

Hence, the bonding in diborane $({B_2}{H_6})$is 3 two centers -2 electron bonds and 3 center-2 electron bonds which is option (b).

Note : Diborane molecule consists of two irregular $B{H_4}$tetrahedra sharing an edge. Electron diffraction studies have shown that the boron atoms and the four terminal hydrogen atoms lie in one plane whereas the two bridging hydrogen atoms lie above and below the plane.