A common form of elemental phosphorus is the tetrahedral \(\mathrm{P}_{4}\) molecule, where all four phosphorus atoms are equivalent: At room temperature phosphorus is a solid. (a) Are there any lone pairs of electrons in the \(\mathrm{P}_{4}\) molecule? (b) How many \(\mathrm{p}-\mathrm{p}\) bonds are there in the molecule? (c) Draw a Lewis structure for a linear \(P_{4}\) molecule that satisfies the octet rule. Does this molecule have resonance structures? (d) On the basis of formal charges, which is more stable, the linear molecule or the tetrahedral molecule?

Each phosphorus atom (P) in the P4 molecule has 5 valence electrons. Since there are 4 phosphorus atoms in the molecule, there would be a total of 4 * 5 = 20 valence electrons. To determine if there are any lone pairs in the P4 molecule, we need to analyze its structure and see how the valence electrons are distributed.

In the tetrahedral P4 molecule, all four phosphorus atoms are equivalent, and they are symmetrically linked to each other. Each phosphorus atom forms 3 single bonds with the other 3 phosphorus atoms. Therefore, there is no possibility for any lone pairs to exist in this molecule structure. So, (a) there are 0 lone pairs of electrons in the P4 molecule.

To count the number of pp bonds in the P4 molecule, examine all the phosphorus atoms and count the bonds formed between them. In the tetrahedral structure, each phosphorus atom forms bonds with the other three phosphorus atoms. So, there are 3 bonds associated with each phosphorus atom. Since there are 4 such atoms, we have 4 * 3 = 12 bonds in total. However, counting this way, we would count each bond twice, so we must divide the result by 2 to get the actual number of pp bonds. So, (b) there are 12 / 2 = 6 pp bonds in the P4 molecule.

For a linear P4 molecule, we need to arrange the four phosphorus atoms in a straight line. P–P–P–P Following the octet rule, each phosphorus atom needs to have 8 electrons in its valence shell. To achieve this, we can use the remaining 16 valence electrons to form double bonds between each pair of phosphorus atoms, giving every atom 6 electrons. We will add one lone electron pair per phosphorus atom to end up with every atom having 8 valence electrons. [ O=P=P=P=P=O ]^{-} So, (c) the linear P4 molecule has the following Lewis structure with no resonance structures as no alternative structures can be formed without breaking the octet rule.

To determine the stability of the linear and tetrahedral P4 molecule forms, we need to calculate their formal charges. For the tetrahedral P4 molecule, each phosphorus atom shares three electrons with its neighboring atoms. Therefore, the formal charge would be 0 for each phosphorus atom in the tetrahedral P4 molecule. For the linear P4 molecule, each phosphorus atom shares 6 electrons with its neighboring atoms. The formal charge would again be 0 for each phosphorus atom in the linear P4 molecule. So, (d) based on formal charges, both the linear and tetrahedral molecules have the same stability levels. However, experimentally it's observed that the tetrahedral structure is the most common and stable form for elemental phosphorus. This is likely due to other factors such as molecular geometry and electron repulsion within the molecule.