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Question: Among the following molecules, N-Si bond length is shortest in: (a) \( N{(Si{H_3})_3} \) (b) \(...

Among the following molecules, N-Si bond length is shortest in:
(a) N(SiH3)3N{(Si{H_3})_3}
(b) N(SiH3)2N{(Si{H_3})_2}
(c) NH2(SiH3)N{H_2}(Si{H_3})
(d) All have equal N-Si bond length

Explanation

Solution

In Chemistry, Bond length is defined as the average distance between the centers or the nuclei of two bonded atoms. In molecules having N-Si bonds, back bonding occurs. Back bonding is the type of bonding that occurs between two atoms which are adjacent to each other; one having a lone pair of electrons while the other has a vacant orbital. The stronger the back bond, the smaller the bond length.

Complete answer:
In back bonding, A weaker π−bond\pi - {\text{bond}} is formed, since the two atoms already have a sigma bond (σ−bond).\left( {\sigma - {\text{bond}}} \right). The π−bond\pi - {\text{bond}} is formed due to sideways overlap between the filled orbital of one atom and the vacant orbital of the other atom. π−character\pi - {\text{character}} is exhibited by the bond due to its formation after σ−bond.\sigma - {\text{bond}}.
In the case of molecules having N-Si bonds, N atom has an electron pair in 2pπ2p\pi orbital while the Si atom has a vacant orbital 2dπ.2d\pi . Hence, π−back bonding\pi - {\text{back bonding}} occurs in the N-Si bond. When the number of Si atoms bonded to a N atom increases, the distribution of the electron pair occurs, due to which back bonding occurs to a lesser effect. Hence, the π−bond\pi - {\text{bond}} formed is not strong, and correspondingly the π−characteristic\pi - {\text{characteristic}} decreases. A direct effect of decrease in π−characteristic\pi - {\text{characteristic}} is the increase in the bond-length.
Accordingly, the decreasing order of bond length will be N(SiH3)3>N(SiH3)2>NH2(SiH3).N{(Si{H_3})_3} > N{(Si{H_3})_2} > N{H_2}(Si{H_3}). Therefore, among the given molecules, N-Si bond length is shortest in (c) NH2(SiH3).N{H_2}(Si{H_3}).

Note:
Back bonding is considered as intermolecular Lewis acid-base interaction being a π−bond.\pi - {\text{bond}}{\text{.}} It is seen that back bonding is most effective between the following orbital pairs:   2p−2p, 2p−3p, 2p−3d  \;2p - 2p,{\text{ }}2p - 3p,{\text{ }}2p - 3d\; and the extent of overlapping is in the order: 2p−2p> 2p−3d >2p−3p.    2p - 2p > {\text{ }}2p - 3d{\text{ }} > 2p - 3p.\;\; It has also been observed that back bonding does not occur between a certain pair of orbitals, the pair being   dx2 and   dx2−y2.\;{d_{{x^2}}}{\text{ and }}\;{d_{{x^2} - {y^2}}}.