One form of phosphorus exists as P4 molecules. Each P4 molecule has four equivalent P atoms, no double or triple bonds, and no expanded octets. Draw the Lewis structure for P4.

Valence electrons are the electrons found in the outermost shell of an atom and play a crucial role in chemical bonding and molecular structure. For phosphorus (P), a Group 15 element on the periodic table, the rule of thumb is that it has five valence electrons. Understanding this is essential for constructing Lewis structures, as these electrons take part in bond formation. For a P₄ molecule, we total the valence electrons from all four phosphorus atoms, resulting in 20 valence electrons (5 valence electrons per atom times 4 atoms).

When drawing a Lewis structure, these electrons are represented as dots around each atom, signifying their participation in bonds. Single bonds between phosphorus atoms each use up two electrons—one from each bonded atom—to form shared pairs. This accounting of electrons is fundamental for creating accurate molecular structures and predicting how atoms bond in molecules.

The octet rule is a crucial concept in chemistry, dictating that atoms tend to form bonds until they are surrounded by eight electrons, achieving an electron configuration similar to noble gases which are known for their stability. Phosphorus atoms follow this rule closely in the P₄ molecule, where each atom forms three single bonds with other phosphorus atoms, using six of its valence electrons. The remaining two valence electrons form a lone pair, bringing the total to eight for each phosphorus atom.

This complies with the octet rule, contributing to the molecule's stability. When drawing the Lewis structure, we must ensure that after all bonds are made, the octet rule is satisfied, showing that we have achieved a complete and stable arrangement of electrons around every phosphorus atom in the P₄ molecule.

The tetrahedral molecular geometry is a common shape for molecules where the center atom is bonded to four other atoms at the vertices of a tetrahedron. This shape is characterized by bond angles of approximately 109.5 degrees. In the case of the P₄ molecule, each phosphorus atom is at the center of its local tetrahedron, bonding to three other phosphorus atoms. As a result, the P₄ molecule as a whole does not form a single tetrahedron but resembles a 'four-membered ring'.

In each local tetrahedral arrangement, the lone pair of electrons also participates in determining the molecular shape, repelling the bonding pairs and contributing to the three-dimensional structure of the molecule. While the ideal angle in a perfect tetrahedral is 109.5 degrees, lone pairs can slightly compress these angles due to their larger electron cloud that exerts more repulsion than the shared electron pairs in the bonds. Thus, identifying tetrahedral geometry helps in predicting the spatial arrangement of atoms and understanding the molecular structure of a substance.