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) Do you think there are any unshared pairs of electrons in the \(\mathrm{P}_{4}\) molecule? (b) How many \(\mathrm{P}-\mathrm{P}\) bonds are there in the molecule? (c) Can you draw a Lewis structure for a linear \(\mathrm{P}_{4}\) molecule that satisfies the octet rule? (d) Using formal charges, what can you say about the stability of the linear molecule vs. that of the tetrahedral molecule?

Short answer

(a) There is one unshared pair of electrons on each P atom in the tetrahedral P4 molecule. (b) There are 6 P-P bonds in the P4 molecule. (c) A linear P4 molecule does not satisfy the octet rule. (d) The tetrahedral P4 molecule is more stable due to its formal charges being closer to zero compared to the linear P4 molecule.

Step-by-step solution

Understand the Tetrahedral P4 Molecule

A tetrahedral P4 molecule consists of four phosphorus (P) atoms connected in a tetrahedral shape, meaning that each P atom is bonded to three other P atoms. Let's first determine the number of valence electrons for one phosphorus atom. Phosphorus is in Group 15 of the periodic table, so it has five valence electrons.

Unshared Pairs of Electrons (a)

As each P atom is bonded to three other P atoms (forming three single bonds), each bond uses two electrons, for a total of six bonding electrons. However, phosphorus has five valence electrons. Therefore, there is one unshared pair of electrons (two unshared electrons) on each P atom in the P4 molecule.

Number of P-P Bonds (b)

There are four P atoms in the molecule, each of which forms single bonds with the three adjacent P atoms. Therefore, the total number of P-P bonds is: \(\frac{3 \times 4}{2} = 6\) There are 6 P-P bonds in the P4 molecule.

Lewis Structure for Linear P4 Molecule (c)

Now let's try to draw a Lewis structure for a linear P4 molecule following the octet rule. In a linear molecule, each P atom would bond with two other P atoms, forming two single bonds. This would account for 4 of the 5 valence electrons phosphorus has. Thus, each P atom would also have an unshared pair of electrons. However, the linear structure does not satisfy the octet rule. When the four P atoms are connected linearly, the terminal P atoms will have only six electrons (4 from the two single bonds and 2 unshared). The central P atoms will have only seven electrons (4 from single bonds and 3 unshared). Hence, the linear geometry does not satisfy the octet rule.

Stability of Linear vs. Tetrahedral Molecules (d)

To compare the stability of the linear and tetrahedral P4 molecules, we need to analyze their formal charges. Recall the formula to find formal charges: Formal Charge = (Valence Electrons) - (Bonding Electrons) - (Unshared Electrons)/2 The formal charge of the tetrahedral P4 molecule: (5) - (6) - (2)/2 = 0. In a linear P4 molecule, each P will have either 6 or 7 valence electrons, so when calculating the formal charge, the result is not zero. Since the formal charges of the atoms in the tetrahedral P4 molecule are closer to zero than the formal charges in the linear P4 molecule, the tetrahedral P4 molecule is more stable.

Key concepts

Tetrahedral Structure

The tetrahedral structure is a basic geometry in chemistry where four atoms surround a central atom, all equally spaced. In the case of \({\text{P}_4}\), each phosphorus atom forms a tetrahedral shape by connecting with three other phosphorus atoms. This arrangement is a crucial feature of \({\text{P}_4}\) because it balances the forces in the molecule, making it stable. Consider a pyramid-like shape, but with triangular sides and not one base but two opposite ones. The angles formed between the bonds are about 109.5 degrees, which allows the molecule to be stable.

When we consider the tetrahedral structure, it's easy to see why each atom reaches the most balanced stately configuration. Each phosphorus atom shares three bonding pairs of electrons, which allows them to achieve a stable configuration. This specific geometric form contributes significantly to the overall stability and symmetry of the \({\text{P}_4}\) molecule.

Valence Electrons

Valence electrons are the outermost electrons of an atom and are crucial in forming chemical bonds. For phosphorus, which resides in Group 15 of the periodic table, there are five valence electrons. These electrons are the determining factor in how atoms will bond with one another to create molecules.

In the context of a \({\text{P}_4}\) molecule, each phosphorus atom uses its valence electrons to form three bonds with three neighboring atoms. This accounts for six total bonding electrons, with one pair remaining as unshared. The presence of unshared electron pairs on each phosphorus atom is an integral aspect of its chemistry, affecting both the shape and reactivity of the molecule. By understanding valence electrons, we gain insights into how molecules like \({\text{P}_4}\) come together.

Lewis Structures

Lewis structures are a method for visualizing the bonds between atoms in a molecule and the lone pairs of electrons that may exist. They help in predicting how atoms are likely to combine to form molecules. For the tetrahedral \({\text{P}_4}\) molecule, the Lewis structure can be arranged in a way that each phosphorus atom shares electrons with three others.

Developing a Lewis structure involves distributing the valence electrons among the atoms in a way that satisfies the octet rule for each atom. A key point in \({\text{P}_4}\)'s configuration is that each phosphorus atom has one unshared pair of electrons, besides the electrons involved in bonding. Drawing these structures accurately can help elucidate the essence of molecular composition and predict the physical and chemical properties resulting from these bonds.

• Phosphorus atoms form three single bonds with other phosphorus atoms.
• Each P atom has one unshared pair of electrons.
• Illustrates molecular geometry and electron arrangement.

Formal Charges

Formal charges offer a way to assess the stability of molecules based on electron distribution. It's calculated by taking the number of valence electrons, subtracting the bonding electron pairs, and further subtracting half of the unshared electrons. For the tetrahedral \({\text{P}_4}\) molecule, each phosphorus has a formal charge of zero, which suggests stability.

Comparing the linear and tetrahedral versions of \({\text{P}_4}\), the latter comes off as more stable. This is due to the more optimal formal charge distribution among the phosphorous atoms in the tetrahedral structure. Conversely, in a linear structure, each phosphorus atom would not have a complete octet, leading to higher formal charges. Thus, the {\text{P}_4} tetrahedral formation is favored over the linear one due to balanced formal charges that closely approach zero for each atom, indicating greater intrinsic stability.