Question

(a) Write a Lewis structure for the phosphorus trifluoride molecule, \(\mathrm{PF}_{3}\). Is the octet rule satisfied for all the atoms in your structure? (b) Determine the oxidation numbers of the \(\mathrm{P}\) and \(\mathrm{F}\) atoms. (c) Determine the formal charges of the \(\mathrm{P}\) and \(\mathrm{F}\) atoms. (d) Is the oxidation number for the \(\mathrm{P}\) atom the same as its formal charge? Explain.

Short answer

The Lewis structure of PF3 is as follows: ``` F | P - F - F || ``` All atoms satisfy the octet rule. The oxidation numbers of P and F atoms are +3 and -1, respectively. The formal charges of P and F atoms are both 0. The oxidation number of P (+3) is not the same as its formal charge (0) due to different considerations regarding electron distribution and electronegativity.

Step-by-step solution

Draw the Lewis Structure of PF3

To draw the Lewis structure, first, note the number of valence electrons for each atom. Phosphorus (P) has 5 valence electrons, and Fluorine (F) has 7 valence electrons. The molecule has 3 fluorine atoms, so the total number of valence electrons is 5 + 3*(7) = 26. Now, place the P atom in the center and connect it to each of the F atoms with a single bond. By doing this, we have used 6 valence electrons. Next, distribute the remaining 20 valence electrons around the F atoms, so each F atom has 8 electrons (including the shared electrons in the bond). The final Lewis Structure is: ``` F | P - F - F || ```

Check Octet Rule

All the F atoms have 8 electrons (one bond and 6 lone pairs), satisfying the octet rule. The P atom has 8 electrons (three bonds and one lone pair), also satisfying the octet rule. Thus, the octet rule is satisfied for all the atoms in the PF3 molecule. #b) Finding Oxidation Numbers of P and F atoms#

Oxidation numbers

To determine the oxidation numbers of P and F atoms, assign electrons to the atoms according to a set of rules: 1. A fluorine atom has an oxidation number of -1. 2. Covalent bonds' shared electrons are assigned to the more electronegative atom. Phosphorus is less electronegative than fluorine, so all electrons in the P-F bonds are assigned to fluorine. Thus, each F atom has an oxidation number of -1, and the P atom has an oxidation number of +3 (as there are three F atoms). #c) Finding Formal Charges of P and F atoms#

Formal Charges

To determine the formal charges of P and F atoms, use the formula: Formal charge = (# of valence electrons) - (# of lone pairs) - 0.5*(# of bonding electrons) For P atom: Formal Charge(P) = 5 - 2 - 0.5*(6) = 0 For F atoms: Formal Charge(F) = 7 - 6 - 0.5*(2) = 0 Both P and F have a formal charge of 0. #d) Comparing Oxidation Number and Formal Charges of P Atom#

Oxidation Number vs Formal Charge

The oxidation number of P is +3, whereas its formal charge is 0. These two values are not the same. The oxidation number is related to the electronegativity differences between atoms in a compound and helps to identify electron transfer in redox reactions. On the other hand, the formal charge is related to the electron distribution within a molecule and helps to predict the most stable Lewis structure. In this case, the formal charge shows that the drawn Lewis structure follows the octet rule and is stable, but the oxidation number indicates that the phosphorus atom loses 3 electrons to the three fluorine atoms.

Key concepts

Octet Rule

The octet rule is a fundamental principle in chemistry which states that atoms are most stable when they have eight electrons in their valence shell, mimicking the electron configuration of noble gases. This rule is particularly applicable for atoms such as carbon, nitrogen, oxygen, and the halogens, including fluorine. However, it's useful to note that not all elements strictly follow the octet rule, especially those with available d orbitals, like phosphorus.

In the case of phosphorus trifluoride (\(\text{PF}_3\)), the octet rule is satisfied through the strategic sharing of electrons:

• Phosphorus, which has 5 valence electrons, forms three single bonds with each of the three fluorine atoms.
• Each fluorine atom has 7 valence electrons, and it achieves a full octet by sharing one electron with phosphorus.

This distribution ensures that every fluorine atom ends up with 8 electrons and the phosphorus atom also completes its octet through 8 electrons (three bonds and one lone pair), indicating a stable Lewis structure.

Oxidation Numbers

Oxidation numbers are theoretical charges assigned to atoms in molecules, representing a method to account for electron ownership in bonds. They are important in redox reactions to track electron transfers. The oxidation number is a formalism and does not necessarily represent actual charges on atoms but can provide insight into a compound's reactivity.

For \(\text{PF}_3\):

• Fluorine, being highly electronegative, has an oxidation number of -1 in virtually all compounds.
• Each P-F bond's shared electrons are considered to be "owned" by the fluorine, assigning phosphate an oxidation number of +3 since it forms three bonds with fluorine.

The oxidation number gives insight into electron distribution in the molecule, showing that phosphorus effectively "donates" electrons to fulfill the electron affinity of the fluorine atoms.

Formal Charge

Formal charge is a conceptual tool used to identify the most plausible Lewis structure among several possibilities. It is calculated using the formula: \[\text{Formal charge} = (\text{valence electrons}) - (\text{non-bonded electrons}) - 0.5 \times (\text{bonded electrons})\]

For \(\text{PF}_3\):

• The formal charge on phosphorus is calculated as: \(5 - 2 - 0.5 \times 6 = 0\)\
• Each fluorine atom has a formal charge calculated as: \(7 - 6 - 0.5 \times 2 = 0\)\

Both phosphorus and fluorine have a formal charge of 0, suggesting that this creation of the Lewis structure adheres to minimal charge separation, reinforcing stability. This is important because it supports using the octet rule while maintaining structural stability and minimizing potential energy.

Phosphorus Trifluoride

Phosphorus trifluoride is a chemical compound with the chemical formula \(\text{PF}_3\). This molecule is classified as a phosphorus halide and is notable for its use in chemical and industrial processes, often serving as a ligand in catalysts.

Its molecular geometry is trigonal pyramidal due to the sp³ hybridization of phosphorus. Here are some key aspects:

• Phosphorus is the central atom, surrounded by three fluorine atoms through single bonds.
• The molecule has 26 valence electrons, with each fluorine atom achieving an electron configuration similar to that of neon due to sharing electrons with phosphorus.
• The presence of a lone pair on the phosphorus atom is responsible for the deviation from a perfect tetrahedral shape.

Understanding the structure and bonding within \(\text{PF}_3\) helps in predicting its reactivity and role in chemical reactions, highlighting how formal charge and oxidation numbers provide insight into its molecular characteristics.