Draw four reasonable resonance structures for the \(\mathrm{PO}_{3} \mathrm{~F}^{2-}\) ion. The central \(\mathrm{P}\) atom is bonded to the three O atoms and to the \(\mathrm{F}\) atom. Show formal charges.

Understanding how to calculate the formal charge in a molecule is key for predicting the stability and reactivity of molecules. The formal charge is a hypothetical charge you would assign to an atom in a molecule, assuming that electrons in all chemical bonds are shared equally between atoms, despite differences in electronegativity.

The formula for formal charge (FC) is given by: \( FC = V - (NB + \frac{1}{2} BE) \), where:

• \( V \) is the number of valence electrons in the free (unbonded) atom,
• \( NB \) is the number of non-bonding electrons (electrons not involved in forming bonds),
• \( BE \) is the number of bonding electrons, divided equally between the bonded atoms.

It's crucial to remember that for a molecule to be stable, the sum of formal charges should equal the overall charge of the molecule. Hence, when you work out formal charge for each atom in a structure, it can help identify the most favorable resonance structure, because generally, the structure with the smallest magnitude of formal charges is preferred.

When multiple valid resonance structures exist, as in the case of the \( PO_3F^{2-} \) ion, it is often helpful to draw these different structures to visualise how the formal charge can be distributed differently across the molecule.

The octet rule is a simple chemical rule of thumb that states that atoms tend to bond in such a way that each atom has eight electrons in its valence shell. This leads to an electron configuration similar to that of a noble gas, signifying a stable arrangement.

In the context of drawing resonance structures, as seen with the \( PO_3F^{2-} \) ion, it's important to remember that the octet rule helps us to place our remaining electrons. Atoms are more stable when they have a full octet, and they will usually form bonds to accomplish this. However, there are exceptions to the octet rule. Elements in the third period and beyond can hold more than eight electrons, and some elements, like hydrogen and helium, are stable with fewer than eight.

The octet rule is used as a guideline when determining the placement of the remaining electrons after forming the bonds. Highly electronegative elements, which tend to attract electrons more strongly, should be filled first. The rule is instrumental in predicting the molecular structure and in understanding the distribution of valence electrons among the atoms within the molecule.

Valence electrons are the outermost electrons of an atom and are involved in forming chemical bonds. The number of valence electrons an element has directly influences its chemical behavior and properties. For example, in the exercise featuring the \( PO_3F^{2-} \) ion, Phosphorus has 5 valence electrons, Oxygen has 6, and Fluorine has 7. Additionally, the ion has 2 extra electrons due to its \(2-\) charge.

When drawing resonance structures, valence electrons are the ones that you rearrange to form different bonding patterns. High electronegativity atoms like Oxygen and Fluorine want to complete their octet, hence, they will pull bonding electrons closer to them and are also more likely to carry a negative formal charge due to their tendency of holding more nonbonding electrons.

The concept of valence electrons is essential not only for determining how an atom will bond but also for calculating formal charges and applying the octet rule. It's these electrons that play the most significant role in the chemistry of elements and construct the basis for understanding chemical bonding and molecular structure.