Question

Calculate the formal charge on the indicated atom in each of the following molecules or ions: (a) the central oxygen atom in \(\mathrm{O}_{3},\) (b) phosphorus in \(\mathrm{PF}_{6}^{-},(\mathrm{c})\) nitrogen in \(\mathrm{NO}_{2},(\mathrm{~d})\) iodine in \(\mathrm{ICl}_{3}\) (e) chlorine in \(\mathrm{HClO}_{4}\) (hydrogen is bonded to \(\mathrm{O}\) ).

Short answer

The formal charges for the specified atoms in each molecule or ion are: (a) central oxygen atom in \(\mathrm{O}_{3}\): 0, (b) phosphorus in \(\mathrm{PF}_{6}^{-}\): -1, (c) nitrogen in \(\mathrm{NO}_{2}\): +1, (d) iodine in \(\mathrm{ICl}_{3}\): +1, and (e) chlorine in \(\mathrm{HClO}_{4}\): +7.

Step-by-step solution

Determine the number of valence electrons for central oxygen

In \(\mathrm{O}_{3}\), the oxygen atom has 6 valence electrons.

Determine the number of bonding electrons for central oxygen

The central oxygen atom in \(\mathrm{O}_{3}\) has single bonds with two other oxygen atoms. This means the central oxygen atom has 2 × 2 = 4 bonding electrons.

Determine the number of non-bonding electrons for central oxygen

Since the central oxygen has formed 2 single bonds with the other oxygen atoms, it still has 6 - 4 = 2 non-bonding electrons.

Calculate the formal charge on the central oxygen atom

Using the formula for formal charge, we have: Formal Charge = (6) - ½(4) - (2) = 0 The formal charge on the central oxygen atom in \(\mathrm{O}_{3}\) is 0. #b) Calculating the formal charge on phosphorus in \(\mathrm{PF}_{6}^{-}\)#

Determine the number of valence electrons for Phosphorus

In \(\mathrm{PF}_{6}^{-}\), the phosphorus atom has 5 valence electrons.

Determine the number of bonding electrons for Phosphorus

The phosphorus atom in \(\mathrm{PF}_{6}^{-}\) forms 6 single bonds with fluorine atoms, so it has 6 × 2 = 12 bonding electrons.

Determine the number of non-bonding electrons for Phosphorus

Phosphorus forms 6 bonds in \(\mathrm{PF}_{6}^{-}\), so all of its valence electrons are used in bonding, and none are non-bonding. Therefore, the number of non-bonding electrons is 0.

Calculate the formal charge on Phosphorus

Using the formula for formal charge, we have: Formal charge = (5) - ½(12) - (0) = 1 However, the overall charge on \(\mathrm{PF}_{6}^{-}\) is -1, which means the formal charge on Phosphorus would be -1. The formal charge on phosphorus in \(\mathrm{PF}_{6}^{-}\) is -1. Similarly, we can calculate formal charges for the other atoms given in the exercise.

Key concepts

Valence Electrons

Valence electrons are electrons in the outermost shell of an atom that can participate in the formation of chemical bonds. These are the electrons that are used when drawing Lewis structures and are critical to understanding an atom's reactivity and bonding capacity. For example, carbon usually has four valence electrons, nitrogen has five, and oxygen has six. To determine the number of valence electrons for an atom, one can simply refer to the atom's group number in the periodic table for main group elements.

For transition metals and other exceptions, valence electron determination can be more complex. Knowing the number of valence electrons helps in predicting how an atom will interact with others to form molecules, which is foundational for the calculation of formal charges.

Bonding Electrons

Understanding Bonding Electrons

The two electrons shared between atoms in a covalent bond are known as bonding electrons. They directly influence the bond order and the molecular geometry of the compound. For instance, if an oxygen atom is sharing a pair of electrons with another atom, these electrons form a bonding pair, often represented by a single dash (-) in Lewis structures. When calculating formal charge, bonding electrons must be counted as part of both atoms involved in the bond. This means that in a single bond, each atom gets to count one of the shared electrons towards its own electrons.

Non-Bonding Electrons

Non-bonding electrons, also known as lone pairs or unshared pairs, are valence electrons that are not involved in forming bonds. They belong exclusively to one atom and play a significant role in the reactivity and polarity of the molecule. In the Lewis structure, these electrons are shown as dots around the atom. When calculating formal charges, all of the non-bonding electrons are counted towards the atom's own electron count. For example, in a water (H2O) molecule, the oxygen atom has two lone pairs of non-bonding electrons, which are essential for working out its formal charge and determining the molecule's shape.

Molecular Geometry

Molecular geometry describes the three-dimensional arrangement of atoms within a molecule. It's determined by both bonding and non-bonding electrons. VSEPR (Valence Shell Electron Pair Repulsion) theory is often used to predict molecular geometry by assuming that electron pairs around a central atom will arrange themselves as far apart as possible to minimize repulsion. This theory helps explain why certain molecules have specific shapes, such as linear, bent, tetrahedral, or trigonal-planar. Molecular geometry can influence physical and chemical properties, including the polarity, reactivity, and color of the molecule.

Molecular geometry is not directly involved in formal charge calculation, but it derives from the same principles used to understand electron distribution within molecules.

Lewis Structure

The Lewis Structure Framework

The Lewis structure is a graphical representation of the valence electrons of atoms within a molecule, showing how the electrons are shared between atoms to form bonds and indicating any non-bonding electrons. Constructing a Lewis structure involves connecting atoms with lines to represent chemical bonds and placing dots around atoms to depict lone pairs of electrons. The correct Lewis structure is essential for predicting molecular geometry and is fundamental in calculating the formal charge of an atom within a molecule.

When analyzing or constructing Lewis structures, one must ensure to account for all valence electrons and to distribute them so that each atom achieves a full octet (or duet for hydrogen), where possible. This concept is key for students to visualize the molecular structure and facilitate the understanding of both molecular geometry and formal charge calculations.