Draw the Lewis structure for \(\mathrm{NO}^{+} .\) Is the nitrogen-oxygen bond in \(\mathrm{NO}^{+}\) longer, shorter, or the same length as the nitrogen- oxygen bond in NO? Explain.

Understanding the distribution of valence electrons is crucial when constructing Lewis structures for molecules and ions. Valence electrons are the outermost electrons of an atom and are important in the formation of chemical bonds.

To calculate the number of valence electrons, we must examine the periodic table and count the electrons in the outer shell or look at the group number for main-group elements. For example, nitrogen is in group 15 and has 5 valence electrons, while oxygen is in group 16 and has 6 valence electrons.

When considering ions like (NO+), we must adjust the valence electron count to reflect the ionic charge. A positive charge indicates the loss of electrons. Therefore, in the case of (NO+), we calculate the total valence electrons by adding the valence electrons of nitrogen and oxygen, and then subtracting one electron due to the positive charge: (5 from N) + (6 from O) - 1 = 10 valence electrons.

This step is vital because it dictates how electrons are distributed in the molecule, which in turn determines the molecular shape and bond characteristics.

The electron octet rule is a fundamental principle in chemistry that helps predict the arrangement of electrons in atoms during compound formation. It states that atoms tend to combine in such a way that they each have eight electrons in their valence shell, giving them the same electron configuration as a noble gas.

However, there are exceptions to this rule. In the Lewis structure of (NO+), we see that while oxygen can satisfy the octet rule by adding three lone pairs of electrons, the nitrogen atom cannot. Nitrogen in (NO+) is left with just six electrons: two shared with oxygen and four in the form of lone pairs. This is an exception to the octet rule since the nitrogen atom has less than eight electrons.

The incompleteness of nitrogen's octet in certain compounds like (NO+) can affect the overall stability and reactivity of the molecule. Notably, these exceptions to the octet rule often occur in molecules with an odd number of valence electrons, with electrons in d or f orbitals, or when bonding elements have a low electronegativity.

Chemical bond length is a key aspect of molecular structure. It refers to the distance between the nuclei of two bonded atoms. Bond lengths can vary depending on the type and strength of the bond. Generally, single bonds are longer than double bonds, and double bonds are longer than triple bonds due to the increased electron sharing and subsequently greater electrostatic attraction between atoms in multiple bonds.

In comparing the bond lengths of (NO+) and neutral NO, we observe that (NO+) has a single bond, while NO has a double bond between the nitrogen and oxygen atoms. This is reflective of the differing number of bonding electrons: a double bond in NO has two pairs of shared electrons, while the single bond in (NO+) only has one pair. Consequently, the nitrogen-oxygen bond in NO is indeed shorter than that in (NO+), which aligns with the Lewis structures and predicted bond strengths of these species.