Question

\(\mathrm{P}_{2}\) is not a stable form of phosphorus, but if it were, what would be its likely Lewis electron dot diagram?

Short answer

The Lewis structure for \(\mathrm{P}_2\) likely has a triple bond between the phosphorus atoms.

Step-by-step solution

Understand the Question

The question asks for a hypothetical Lewis dot structure for a molecule with the formula \(\mathrm{P}_2\). This involves arranging valence electrons around the phosphorus atoms to satisfy their usual bonding capacity.

Determine Valence Electrons

Phosphorus is in Group 15 of the periodic table, so it has 5 valence electrons. Therefore, \(\mathrm{P}_2\) has a total of \(5 + 5 = 10\) valence electrons to arrange in a Lewis structure.

Consider Bonding Pairs

To fulfill the octet rule for each phosphorus atom, start by forming a bond (single, double, or triple) between the two phosphorus atoms. Calculate the electrons used and the remaining electrons.

Draw the Single Bond

Start with a single bond between the two phosphorus atoms, which uses 2 electrons. Arrange the remaining 8 electrons to give each phosphorus an octet.

Evaluate the Need for Multiple Bonds

A single bond plus 3 lone pairs around each phosphorus uses the 10 electrons and gives each phosphorus an octet, but both will only have 7 electrons (including the bond shared), necessitating more bonds.

Draw a Triple Bond

Creating a triple bond between the two phosphorus atoms ensures each atom has 8 electrons (3 bonding pairs and 2 lone electrons on each phosphorus). This uses exactly 10 electrons.

Key concepts

Valence Electrons

Valence electrons are the electrons located in the outermost shell of an atom. They play a crucial role in chemical bonding. When atoms come together to form molecules, it's their valence electrons that interact. For example, phosphorus is an element in Group 15 of the periodic table. This means it has 5 valence electrons. When you are creating a Lewis dot structure, knowing the number of valence electrons is vital. You need this number to determine how electrons will be shared or transferred between atoms.
For the

• P
• 2

molecule, you sum up the valence electrons of each phosphorus atom. Since each phosphorus has 5, the total number of valence electrons for the whole molecule is 10. Understanding this helps you lay the foundation for constructing the molecule's Lewis structure.

Octet Rule

The octet rule is a principle in chemistry that atoms tend to bond in such a way that they each achieve eight electrons in their valence shell. This is because a full valence shell is associated with the stable electronic configuration of noble gases. For most elements, having eight electrons achieves this stable arrangement.
When applying the octet rule to draw the Lewis structure for a

• molecule, you aim to distribute electrons so that each atom appears to have eight electrons surrounding it.

In the case of the hypothetical

• P
• 2

molecule, the phosphorus atoms need to share enough electrons to simulate having eight valence electrons.
Initially, a single bond and lone pairs don't satisfy the octet rule. Therefore, additional bonds like double or triple bonds are explored until the octet requirement is met.

Triple Bond

A triple bond between two atoms involves the sharing of three pairs of valence electrons. This type of covalent bond is stronger and has higher energy compared to single or double bonds. In the context of Lewis structures, a triple bond helps fulfill the octet rule for those atoms involved.
When forming a triple bond in a hypothetical

• P
• 2

molecule, each phosphorus atom shares three pairs of electrons. This satisfies the octet rule by providing each atom with the equivalent of eight electrons. Therefore, each phosphorus atom in the molecule will have three shared pairs of electrons in the triple bond plus two lone electrons, making it stable under the octet rule.
This use of a triple bond to complete the octet rule for each atom is an elegant solution to ensuring molecular stability and follows the natural tendency of atoms to reach a noble gas electron configuration.