Question

White phosphorus, \(\mathrm{P}_{4}\), consists of four phosphorus atoms, with each atom bonded to the other three. Draw the three-dimensional shape of this molecule, showing all valence electrons and bond angles. (Hint: Begin by drawing one atom bonded to the three others using VSEPR theory, and then make the remaining connections.)

Short answer

White phosphorus (P4) has a tetrahedron-shaped structure with phosphorus atoms at each vertex. Each phosphorus atom has 5 valence electrons, resulting in 20 valence electrons to form bonds between the atoms. The bond angle between the atoms is approximately 109.5 degrees. The final structure resembles a 3D pyramid, with each phosphorus atom connected by a single bond to the other three phosphorus atoms, showing all valence electrons and bond angles within the P4 molecule.

Step-by-step solution

Determine the number of valence electrons

Phosphorus is in group 15 (also known as VA) in the periodic table. Thus, it has 5 valence electrons. Since there are 4 phosphorus atoms in a white phosphorus molecule (P4), we have a total of 20 valence electrons (5 * 4 = 20).

Use the VSEPR theory to predict the shape of the P4 molecule

According to the VSEPR theory, the electron pairs around the central atom will arrange themselves to minimize repulsion and maximize the bond angle between the atoms. In white phosphorus, there are no central atoms. Each phosphorus atom is surrounded by three other phosphorus atoms and no lone pairs since all valence electrons will be used to form bonds. This leads to a tetrahedron-shaped molecule with a bond angle of approximately 109.5 degrees between all phosphorus atoms.

Draw the three-dimensional shape of the P4 molecule

To visualise this tetrahedron-shaped molecule: 1. Start by drawing a phosphorus (P) atom at the center, connected to three other P atoms forming a triangle-like shape. 2. Add another P atom above the triangle such that it makes a bond with all three P atoms from the triangle and has a bond angle of approximately 109.5 degrees with each of the other atoms. 3. Finally, connect the three initial P atoms in the triangle, giving us a complete tetrahedron shape. The final structure of the P4 molecule should resemble a 3D pyramid, with each phosphorus atom located at the vertices and connected by single bonds to the three other phosphorus atoms, thus showing all valence electrons and bond angles within the P4 molecule.

Key concepts

VSEPR theory

Understanding the shape of molecules is crucial in the study of chemistry, and the Valence Shell Electron Pair Repulsion (VSEPR) theory provides a handy set of guidelines for this. Put simply, VSEPR theory is based on the idea that pairs of valence electrons around an atom repel each other and will, therefore, arrange themselves as far apart as possible in 3D space to minimize this repulsion.
This theory helps predict the geometry of molecules based on the number of valence electron pairs surrounding the central atoms. A crucial aspect to remember when using VSEPR theory is to count both bonding and lone pair electrons. In the case of white phosphorus, we look at each phosphorus atom as if it is a central atom bonded to three others, leading to a tetrahedral shape for the entire molecule.

Valence electrons

Valence electrons are the electrons that occupy the outermost shell of an atom. These are the electrons involved in forming bonds with other atoms. The number of valence electrons an atom has will determine how it can connect with other atoms, which ultimately dictates the molecule's shape.
In white phosphorus, each of the four phosphorus atoms has five valence electrons, adding up to a total of 20 valence electrons for the P4 molecule. These 20 electrons are completely used up in forming bonds, considering no lone pairs are present in the white phosphorus molecule. This total is key to defining the structure, as it leads to the use of all available valence electrons to create a network of bonds.

Tetrahedron molecular geometry

The geometry of white phosphorus is a classic example of a tetrahedron molecular shape, a concept often explored in chemistry. A tetrahedron comprises four triangular faces, six straight edges, and four vertex corners. Each phosphorus atom in the P4 molecule is a vertex of this tetrahedron.

Molicular Geometry of Tetrahedrons

In the context of molecules, this geometry occurs when an atom is bonded to four other atoms or groups, with angles optimized to minimize electron pair repulsion. It's a common geometry for molecules with four areas of electron density and no lone pairs around the central atom - which applies to each phosphorus atom in P4. Hence, the entire molecule forms a three-dimensional pyramid-like shape that is perfectly symmetrical.

Bond angles

Bond angles are a measure of the angle between two adjacent bonds. According to VSEPR theory, in a perfect tetrahedral molecule, these bond angles are about 109.5 degrees because it is the most effective way to distribute the electron pairs evenly to minimize repulsion.
In the structure of white phosphorus, every angle between bonded phosphorus atoms is identical and close to 109.5 degrees. This consistent bond angle reinforces the molecule's tetrahedral geometry and contributes to the molecule's stability. Understanding these angles is vital for predicting how molecules will behave in chemical reactions and how they will interact with each other.