Question

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?

Short answer

(a) There are no lone pairs of electrons in the P4 molecule. (b) There are 6 pp bonds in the P4 molecule. (c) The linear P4 molecule has the following Lewis structure: \( \mathrm{O=P-P-P-P=O} \), with no resonance structures. (d) Based on formal charges, both the linear and tetrahedral molecules have the same stability levels, but the tetrahedral structure is the most stable form due to other factors such as molecular geometry and electron repulsion.

Step-by-step solution

Determine the number of valence electrons and lone pairs

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.

Identify the structure of the P4 molecule

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.

Calculate the number of pp bonds 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.

Draw the Lewis structure for a linear 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.

Compare the stabilities of the linear and tetrahedral P4 molecules

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.

Key concepts

Tetrahedral Structure

The tetrahedral structure is a fascinating geometric shape that helps explain the arrangement of atoms in certain molecules and compounds. In a tetrahedral molecule like \(\mathrm{P}_{4}\), all four phosphorus atoms are symmetrically bonded to each other. This results in a three-dimensional shape where each phosphorus atom forms three single bonds with its neighboring atoms.
The symmetry and distribution of these bonds are crucial because they ensure that there are no lone pairs on phosphorus in this particular arrangement.

• The bonds between phosphorus atoms are evenly distributed, preventing lone pairs.
• The molecule forms a symmetric geometric shape, resembling a pyramid with a triangular base.

Due to its symmetry, the tetrahedral structure is quite stable, as the electron cloud is evenly distributed around the molecule, minimizing repulsion.

Valence Electrons

Valence electrons play a vital role in chemical bonding and molecule formation. They are the outermost electrons of an atom and are involved in forming bonds.
For phosphorus, there are 5 valence electrons per atom. Therefore, in a \(\mathrm{P}_{4}\) molecule, with 4 phosphorus atoms, there would be a total of \(4 \times 5 = 20\) valence electrons.

• These valence electrons are shared among atoms to create bonds.
• In the \(\mathrm{P}_{4}\) tetrahedral structure, each phosphorus atom forms 3 single bonds with its neighbors, using up all its valence electrons in the process.

Understanding valence electrons helps us predict how atoms will interact to form molecules and is fundamental in drawing structures like Lewis structures and anticipating the molecule's behavior.

Lewis Structure

A Lewis structure is a simplified representation that illustrates the arrangement of electrons in a molecule. By showing how valence electrons are distributed around atoms, we can predict bonding in molecules like \(\mathrm{P}_{4}\).
In the case of the tetrahedral \(\mathrm{P}_{4}\) molecule, no lone pairs are present because all valence electrons are involved in bonding. For the linear \(\mathrm{P}_{4}\) molecule, the structure is\( \text{P}=\text{P}=\text{P}=\text{P} \), each atom tries to reach a stable octet configuration by sharing electrons.

• Each phosphorus atom in a linear form needs double bonds to maintain the octet rule, partly because each atom starts with 5 valence electrons.
• The total of 16 other valence electrons are used to form double bonds, leaving each atom with a full set of 8 electrons (octet).

Creating Lewis structures helps chemists visualize bonding and electron distribution, making it easier to predict molecular properties and behaviors.

Formal Charge

The concept of formal charge is essential for understanding molecular stability. Formal charge helps determine the most stable configuration that a molecule could achieve.
In both the tetrahedral and linear \(\mathrm{P}_{4}\) structures, the formal charge calculation reveals that each phosphorus atom has a neutral charge.

• For tetrahedral \(\mathrm{P}_{4}\), each phosphorus bonds with three neighbors, leading to a balanced electron distribution.
• In linear \(\mathrm{P}_{4}\), each phosphorus shares six electrons with adjacent atoms.

Even though formal charges are zero in both configurations, the tetrahedral structure is more commonly observed and stable in nature.
Factors like molecular geometry and internal electron repulsions contribute to the actual observed stability, favoring the tetrahedral molecule over the linear one for phosphorus.