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) Yes, there are unshared pairs of electrons in the P4 molecule. Each phosphorus atom has 1 unshared pair of electrons. (b) There are 6 P-P bonds in the tetrahedral P4 molecule. (c) The Lewis structure for a linear P4 molecule is: :P-P-P-P: (with unshared pair for each P atom) (d) The tetrahedral P4 molecule is more stable compared to the linear P4 molecule based on the formal charges.

Step-by-step solution

a) Unshared pairs of electrons in P4 molecule

First, we need to find the valence electrons of phosphorus. Phosphorus is in group 15 of the periodic table and has 5 valence electrons. In the tetrahedral P4 molecule, each phosphorus atom is bonded to three other phosphorus atoms, which means each phosphorus shares 3 electrons to form 3 single bonds with other phosphorus atoms. As a result, each phosphorus atom has 2 electrons left (5 initial valence electrons - 3 shared electrons). So, the answer is yes. Each phosphorus atom has 1 unshared pair of electrons in the P4 molecule.

b) Number of P-P bonds in P4 molecule

The tetrahedral P4 molecule has 4 phosphorus atoms, and each is bonded to 3 other phosphorus atoms. Thus, we have a total of 4 x 3 = 12 instances of bonding between phosphorus atoms. However, each bond connects two atoms, so we need to divide this number by 2 to count each bond only once. This results in 12/2 = 6 P-P bonds in the tetrahedral P4 molecule.

c) Lewis structure for a linear P4 molecule

To draw a Lewis structure for a linear P4 molecule that satisfies the octet rule, we need to have the phosphorus atoms in a line with each phosphorus forming 2 single bonds with neighboring phosphorus atoms so that its 4 electrons in the bonds and the 1 unshared pair give a total of 8 vertices around each phosphorus atom. The Lewis structure of the linear molecule would look like this: :P-P-P-P: :: (unshared electron pair for each phosphorus atom)

d) Stability of linear molecule vs. tetrahedral molecule

To compare the stability of the linear and tetrahedral molecules, we'll look at the formal charge for both. For the tetrahedral molecule: The number of valence electrons for phosphorus = 5 The number of unshared electrons = 2 The number of bonds = 3 Formal charge = valence electrons - unshared electrons - 1/2 (shared electrons) = 5 - 2 - 1/2(6) = 0 For the linear molecule: The formal charge for the terminal phosphorus atoms (first and last) in the linear molecule would be: Valence electrons = 5 Unshared electrons = 4 Bonds = 2 Formal charge = 5 - 4 - 1/2(4) = 0 The formal charge for the central phosphorus atoms (second and third) is: Valence electrons = 5; Unshared electrons = 2 Bonds = 4 Formal charge = 5 - 2 - 1/2(4) = 1 The linear molecule has a larger formal charge compared to the tetrahedral molecule, which suggests that the linear molecule is less stable than the tetrahedral one. Therefore, the tetrahedral P4 molecule is more stable compared to the linear P4 molecule on the basis of formal charge.

Key concepts

Valence Electrons

Valence electrons are the electrons available in the outermost shell of an atom. These electrons are crucial because they determine how an atom will interact with other atoms, including bond formation. For phosphorus, which resides in group 15 of the periodic table, there are 5 valence electrons. These electrons are key players in bonding and give phosphorus its characteristic chemistry. When considering molecules like \(\mathrm{P}_{4}\), each phosphorus atom starts with 5 valence electrons. Understanding the number of valence electrons can help anticipate how many other atoms phosphorus can connect to, by sharing or transferring electrons. In the case of \(\mathrm{P}_{4}\), these valence electrons allow phosphorus to form bonds, leading to a tetrahedral arrangement with unique electron pair arrangements. Additionally, knowing the valence electrons helps in determining if there will be any lone pairs or unshared electrons left after bonding.

Lewis Structures

Lewis structures are simplified diagrams that represent molecules, showing the bonds between atoms and any unshared electron pairs. They are incredibly useful for visualizing molecule shapes and ensuring that the octet rule is satisfied, meaning that each atom ideally has 8 electrons in its outer shell. For phosphorus, which forms part of the \(\mathrm{P}_{4}\) molecule, a Lewis structure will involve illustrating these phosphorus atoms with bonds and lone pairs. In a tetrahedral \(\mathrm{P}_{4}\), each phosphorus atom is connected to three others, forming single bonds, while any remaining valence electrons form one lone pair per phosphorus atom. In a different configuration, such as a linear molecule, the Lewis structure might reveal different bond arrangements and fulfillments of the octet rule, showing a sequence like :P-P-P-P: with unshared pairs depicted clearly. By drawing the Lewis structure, chemists ensure that their molecules are correctly represented and comply with electron distribution rules.

Formal Charge

Formal charge is a concept used to determine the charge of an atom within a molecule, based on its number of valence electrons, the shared electrons in bonds, and any lone pairs. The formula for formal charge is:Formal charge = valence electrons - unshared electrons - 1/2(shared electrons).By calculating the formal charge, chemists can predict the distribution of electron density across a molecule, adding insights into molecular stability. In a tetrahedral \(\mathrm{P}_{4}\) structure, each phosphorus atom's formal charge is zero, reflecting balanced electron distribution and stability. Conversely, in a linear \(\mathrm{P}_{4}\) molecule, while the terminal atoms have a zero formal charge, the central atoms show a positive formal charge of +1. This suggests uneven electron sharing and less stability. Understanding formal charge is essential for assessing how different molecular configurations influence overall molecular stability and reactivity.

Molecular Stability

Molecular stability is a vital concept as it determines how likely a molecule is to maintain its structure under various conditions. This stability often depends on the balance of forces within a molecule, including bonds formed between atoms and electron distribution.

• In tetrahedral \(\mathrm{P}_{4}\), the structure is symmetrical, allowing for a balanced distribution of electrons, contributing to stability.
• The zero formal charge across all atoms in the tetrahedral design suggests a highly stable molecule with minimal energy strain.
• On the other hand, the linear \(\mathrm{P}_{4}\) shows induced formal charges due to electron arrangements, negatively impacting stability.

The tetrahedral arrangement generally implies lower energy states compared to the linear form, which faces higher repulsion and unbalanced charges. Understanding molecular stability helps predict reaction pathways and the likelihood of transformation or decomposition under given environmental conditions.