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 why or why not.

Short answer

In the PF3 molecule, the Lewis structure satisfies the octet rule for all atoms, with the P atom having a lone pair and connected to three F atoms by single bonds. The oxidation numbers of P and F atoms are +3 and -1, respectively, while their formal charges are 0 and -1, respectively. The oxidation number and formal charge of the P atom are different because these values represent different properties of atoms in a molecule: oxidation numbers are a tool for balancing chemical reactions while formal charges give insight into the electron distribution within the molecule.

Step-by-step solution

Draw the Lewis Structure for PF3

To draw the Lewis structure for PF3, first count the number of valence electrons available. Phosphorus (P) has 5 valence electrons, and Fluorine (F) has 7 valence electrons. With three fluorine atoms, the total number of valence electrons is \(5 + (3 \times 7) = 26\). In the PF3 molecule, place the central atom P in the middle and surround it with three F atoms, connected by single bonds. This accounts for \(1\times 3 = 3\) valence electrons (1 from the P atom for each bond, and 1 from each F atom). The remaining valence electrons are 26 - 3 = 23. Distribute the remaining valence electrons as lone pairs, trying to satisfy the octet rule. Fill the octet of the three fluorine atoms with lone pairs, each having three lone pairs (6 valence electrons) and the central P atom with a lone pair (2 valence electrons). This accounts for all 26 valence electrons and satisfies the octet rule for all the atoms in the PF3 structure.

Determine Oxidation Numbers

To calculate the oxidation number of P and F atoms, use the following rules: 1. The oxidation number of atoms in a molecule sum up to the molecule's overall charge (zero for neutral molecules like PF3). 2. The oxidation number of fluorine (F) is always -1 in its compounds. There are three F atoms, with each having an oxidation number of -1. Therefore, the sum of their oxidation numbers is \(3\times -1 = -3\). To balance the oxidation numbers in the PF3 molecule, the P atom must have an oxidation number of +3. Thus, the oxidation numbers of P and F atoms are +3 and -1, respectively.

Determine Formal Charges

To calculate the formal charge of an atom, use the formula: \(Formal\ charge = Valence\ electrons - Non-bonding\ electrons -\frac{1}{2}\cdot Bonding\ electrons\). - For P atom, the formal charge is: \(5 - 2 - \frac{1}{2}(6) = 0\) - For F atoms (for each atom), the formal charge is: \(7 - 6 - \frac{1}{2}(2) = -1\) Thus, the formal charges of the P and F atoms are 0 and -1, respectively.

Compare Oxidation Number and Formal Charge

The oxidation number for the P atom in PF3 is +3, while its formal charge is 0. They are not the same. The difference is due to the fact that oxidation numbers and formal charges describe different properties of atoms in a molecule. The oxidation number represents the "apparent" charge assigned to an atom in a molecule, while the formal charge is a measure of how the actual electron density is distributed within the molecule. The formal charge represents a more accurate depiction of the actual electron distribution within the molecule, whereas the oxidation number is a useful tool for balancing chemical reactions and understanding redox processes.