Draw the Lewis structures for each of the following molecules or ions. Which do not obey the octet rule? (a) \(\mathrm{NO},\) (b) \(\mathrm{BF}_{3}\), (c) \(\mathrm{ICl}_{2}^{-}\) (d) \(\mathrm{OPBr}_{3}\) (the \(\mathrm{P}\) is the central atom), (e) XeF 4 .

Understanding the octet rule is essential for drawing Lewis structures. The octet rule is based on the observation that atoms of main-group elements tend to bond in such a way that each atom has eight electrons in its valence shell, giving it the same electron configuration as a noble gas. This rule explains why elements form the number of bonds that they do. For example, in the exercise, \textbf{NO} and \textbf{BF\(_{3}\)} do not obey the octet rule since nitrogen in NO ends up with seven electrons, one shy of an octet, and boron in BF\(_{3}\) has only six. However, it is noteworthy that there are exceptions to the octet rule, which include molecules with an odd number of electrons, molecules in which one or more atoms possess more or fewer than eight electrons, and molecules with atoms that have expanded valence shells. Boron trifluoride is such an exception, where boron is stable with six valence electrons.

Valence electrons play the central role in chemical bonding and molecule formation. They are the electrons in the outermost shell of an atom and are involved in forming bonds to adjacent atoms. In the provided exercise, counting valence electrons is the first step and key to correctly drawing the Lewis structures. For instance, nitrogen has five valence electrons while oxygen has six, making a total of 11 for \textbf{NO}. Similarly, boron has three and fluorine has seven, totaling 24 for \textbf{BF\(_{3}\)}. The number of valence electrons determines how atoms bond and what molecular structure they form. In ions, it's important to account for gained or lost electrons as well, such as with the \textbf{ICl\(_{2}^{-}\)} ion, which includes an extra electron due to its negative charge.

Molecular geometry refers to the three-dimensional arrangement of atoms within a molecule. Understanding the geometry is crucial for predicting both the physical and chemical properties of the molecule. Lewis structures can be used to predict molecular geometry by applying VSEPR (Valence Shell Electron Pair Repulsion) theory, which says that electron pairs around a central atom will assume a geometry that minimizes the repulsion between them. In terms of the exercise, \textbf{BF\(_{3}\)} is a trigonal planar molecule since it has three bonding pairs and no lone pairs, whereas \textbf{XeF\(_{4}\)} forms a square planar structure due to the four bonding pairs and two lone pairs on xenon. When predicting molecular geometries, it's essential to consider both the number of bonding pairs and lone pairs on the central atom.