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Chapter 5: Problem 101

Draw a dot diagram for the \(\mathrm{NO}_{2}^{+}\) cation.

Short Answer

Expert verified
The dot diagram for \(\mathrm{NO}_{2}^{+}\) is: O : O - N = O : : In this structure, the nitrogen atom has an incomplete octet, with only 4 electrons. Both oxygen atoms have a complete octet with 3 lone pairs each, and there is a double bond between nitrogen and one oxygen atom, and a single bond between nitrogen and the other oxygen atom. Resonance structures can also be possible for this cation.

Step by step solution

01

Calculate the Valence Electrons

To draw the dot diagram, we first need to calculate the total number of valence electrons available in the \(\mathrm{NO}_{2}^{+}\) cation. Nitrogen has 5 valence electrons, and oxygen has 6 valence electrons. In the cation \(\mathrm{NO}_{2}^{+}\), one electron is lost, so we will subtract one electron. Total valence electrons: \(1 \times 5 + 2 \times 6 - 1 = 5 + 12 - 1 = 16\)
02

Arrange the Atoms

In the molecule \(\mathrm{NO}_{2}^{+}\), nitrogen atom (N) is the central atom, and the two oxygen atoms (O) are bonded to it. This results in a structure similar to: O - N - O
03

Distribute the Valence Electrons

Start by placing bond pairs of electrons (2 electrons for each bond) between the central nitrogen atom and each of the two oxygen atoms. We have 16 valence electrons, and after forming 2 bonds between N and O, we have used 2 × 2 = 4 electrons. Therefore, 16 - 4 = 12 valence electrons remain to be distributed.
04

Complete the Octet Rule for Oxygen Atoms

We will now use the remaining valence electrons to complete the octet of the oxygen atoms. We start by placing the electrons around the oxygen atoms as lone pairs. Each oxygen atom requires 6 more electrons for a complete octet (already having 2 electrons from the bond). Both oxygen atoms now have a complete octet, and all 12 electrons are used up. However, the nitrogen atom has only 4 electrons (2 from each bond to oxygen), but to satisfy the octet rule, it needs 8 electrons. In the case of the \(\mathrm{NO}_{2}^{+}\) cation, this rule is not satisfied, and it has fewer electrons than the octet. This makes the nitrogen atom electron-deficient.
05

Draw the Dot Diagram

With the electron distribution defined, we can now draw a dot diagram for the \(\mathrm{NO}_{2}^{+}\) cation by placing the lone pairs and bond pairs around the atoms. The dot diagram for \(\mathrm{NO}_{2}^{+}\) is: O : O - N = O : : In this case, the bond between nitrogen and one oxygen atom has a double bond, and the bond between nitrogen and the second oxygen atom has a single bond. The oxygen atoms have 3 lone pairs each, giving them a total of 8 electrons and fulfilling the octet rule. The nitrogen has an incomplete octet, with only 4 electrons. Keep in mind that resonance structures can also be possible for this cation.

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