Question

The standard state of phosphorus at \(25^{\circ} \mathrm{C}\) is \(\mathrm{P}_{4}\). This molecule has four equivalent \(\mathrm{P}\) atoms, no double or triple bonds, and no expanded octets. Draw its Lewis structure.

Short answer

The Lewis structure for P4 consists of four P atoms connected in a tetrahedral structure with three lone pairs around each outer P atom and one additional lone pair on one of the P atoms, satisfying the octet rule.

Step-by-step solution

Determine the Total Number of Valence Electrons

Each phosphorus (P) atom has 5 valence electrons. For the P4 molecule, there are 4 P atoms, hence the total number of valence electrons is 4 x 5 = 20.

Sketch a Skeletal Structure

Connect the four P atoms in a tetrahedral arrangement such that each P atom is connected to three other P atoms. This ensures that all atoms follow the P4 molecule structure with no double or triple bonds and no expanded octets.

Distribute the Electrons Around Each Atom

Place 6 electrons (as three lone pairs) around each outer P atom to satisfy the octet rule. This uses up 18 of the 20 valence electrons.

Place the Remaining Electrons

Place the remaining 2 electrons as a lone pair on any one of the P atoms. Since all P atoms are equivalent, it does not matter which one is chosen.

Check the Octet Rule

Ensure that each P atom now has a complete octet, comprising of 6 electrons in lone pairs and 2 electrons from single bonds with adjacent P atoms. This completes the Lewis structure.

Key concepts

Valence Electrons

Understand the basics of valence electrons, which are the electrons in the outer shell of an atom that participate in chemical bonding. Phosphorus (P), with its position in the 15th group of the periodic table, has five valence electrons. These electrons are the ones responsible for forming chemical bonds with other atoms. When determining a molecule's Lewis structure, like P₄, our starting point is always to count the total number of valence electrons. For P₄, you would multiply the number of valence electrons of a single P atom by four, giving us a total of 20 valence electrons to work with.
In a Lewis structure, these valence electrons are represented as dots surrounding the chemical symbols. They can be in pairs or alone, where paired electrons are often found in the bond formation between atoms, while unpaired, or lone pairs, are electrons that do not participate in bonding but are still crucial for the structure of the molecule.

Octet Rule

The octet rule is like a golden rule for many elements in chemistry. It states that atoms tend to form bonds in such a way that each atom has eight electrons in its valence shell, giving it the same electronic configuration as a noble gas, which is known for its stability. However, it's important to note that the octet rule does not apply universally but is a good guideline for many elements, including phosphorus.
In the case of the P₄ molecule, the Lewis structure adheres strictly to this rule. Each of the four phosphorus atoms shares electrons through single bonds, forming a tetrahedral shape. As a result, each atom ends up with six electrons in the form of three lone pairs, and two more electrons from the single bonds with adjacent atoms. This ensures that all P atoms complete their octet accomplishing a stable structure, and tying right back to our basic concept of the desire of atoms to reach a noble gas configuration.

Chemical Bonding

Chemical bonding is the force of attraction that holds atoms together in molecules and compounds. Bonds are formed by the interaction between valence electrons of different atoms. In P₄, phosphorus atoms bond by sharing their valence electrons to achieve the stable octet configuration.
There are different types of bonding such as ionic, covalent, and metallic, with P₄ involving covalent bonds where electrons are shared evenly by the phosphorus atoms. This sharing of electrons in P₄ results in each phosphorus atom forming single bonds with three neighbouring atoms.

Importance of the Shape

The shape of the molecule—determined by these bonds—is crucial, as it affects the molecule's properties and reactivity. The tetrahedral arrangement of atoms in P₄ ensures that the molecule is symmetric, minimizing repulsion between the lone pairs of electrons and maintaining stability which plays a pivotal role in chemistry when predicting molecular behavior.