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Chapter 22: Problem 80

On the basis of molecular orbital theory, would you expect \(\mathrm{NH}_{2}^{+}\) to be linear or bent?

Short Answer

Expert verified
According to the molecular orbital theory, \(\mathrm{NH}_{2}^{+}\) would be expected to have a linear shape.

Step by step solution

01

Determine the total number of valence electrons

Firstly, count the total number of valence electrons in the molecule. Nitrogen has 5 valence electrons and hydrogen has 1 valence electron. Since there is a positive charge on the molecule, it means one electron has been removed. Summing it up, \(\mathrm{NH}_{2}^{+}\) has \(5 + 2*1 - 1 = 6\) valence electrons.
02

Ascertain the type of molecular orbitals

Molecular orbitals combine from atomic orbitals. Two atomic orbitals combine to form two molecular orbitals, one bonding and the other antibonding. The types of molecular orbitals important to forming \(\mathrm{NH}_{2}^{+}\) include sigma \(\mathrm{s}\), sigma \(\mathrm{s}*\), sigma \(\mathrm{p}\), pi \(\mathrm{p}\) and pi \(\mathrm{p}*\). In this case, nitrogen contributes 2s and 2p atomic orbitals and hydrogen contributes 1s atomic orbitals.
03

Fill electrons in molecular orbitals according to the order

Electrons are filled in ascending order of energy levels in molecular orbitals. The first two electrons will occupy the sigma \(\mathrm{s}\) orbital, the next two will occupy the sigma \(\mathrm{s}*\) orbital, and the last two electrons will occupy the sigma \(\mathrm{p}\) orbital.
04

Decide the shape of molecule

From the molecular orbital theory, it is known the sigma \(\mathrm{p}\) orbital leads to linear geometry. After filling the electrons, we found that the six electrons of \(NH_{2}^{+}\) occupy sigma \(\mathrm{s}\), sigma \(\mathrm{s}*\) and sigma \(\mathrm{p}\) orbitals. There are no leftover lone pair electrons to cause a bend in the molecule, so it would be expected that \(\mathrm{NH}_{2}^{+}\) is linear.

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