Using only Lewis structures that obey the octet rule, determine the formal charge on each atom in (a) \(\mathrm{CH}_{3}^{+} ;\)(b) \(\mathrm{ClO}^{-} ;\)(c) \(\mathrm{CN}^{-}\)

When it comes to understanding molecular geometry and reactivity, Lewis structures serve as a fundamental tool for students and chemists alike. These simple diagrams provide a visual representation of the valence electron arrangement in molecules.

To draw a Lewis structure, first, identify the total number of valence electrons available, considering any charges the molecule may have. The electrons are then distributed to give each atom, ideally, an octet — eight electrons to fulfill the 'octet rule'. Atoms form bonds by sharing pairs of electrons, and any remaining valence electrons are shown as 'lone pairs' on individual atoms.

For example, when constructing the Lewis structure for \(\mathrm{CH}_{3}^{+}\), we recognize that carbon is the central atom and is connected to three hydrogen atoms. Since the molecule carries a positive charge, carbon lacks one of its usual four electrons. This deficiency is visually represented in the Lewis structure through fewer electron pairs around the carbon atom.

Valence electrons play a critical role in chemical reactions, as they are the electrons located in the outermost electron shell of an atom and can be involved in forming chemical bonds. The number of valence electrons an atom has is determined by its position in the periodic table.

For instance, in group 1 elements, like hydrogen, there is a single valence electron. In group 14, elements like carbon have four valence electrons. These valence electrons are key to drawing Lewis structures, as they indicate how many bonds an atom can form to achieve a stable octet. It is important to count the valence electrons correctly to apply the formal charge formula effectively, as shown in the step-by-step solutions for the given exercises.

Bonding electrons are those that are shared between atoms in a molecule, forming what we call chemical bonds. A single bond consists of one pair of shared electrons, illustrated by a single line in Lewis structures. Double and triple bonds, represented by two or three lines respectively, involve two or three pairs of shared electrons.

For example, in \(\mathrm{CN}^{-}\), carbon and nitrogen form a triple bond, sharing three pairs of electrons, which strongly influences the formal charge calculation. The bonding electrons are counted as belonging equally to both bonded atoms. So in the formal charge formula \(\text{Formal Charge} = \text{Valence electrons} - \frac{1}{2} \times \text{Bonding electrons} - \text{Lone pair electrons}\), bonding electrons are divided by two to fairly attribute them to both atoms involved in the bond.

Understanding these concepts is vital for grasping the formation and properties of chemical compounds, as well as for predicting the behavior of atoms during chemical reactions.