Question

Predict the electron pair geometry, the molecular shape, and the bond angle for a phosphine molecule, \(\mathbf{P H}_{3},\) using VSEPR theory.

Short answer

The electron pair geometry is tetrahedral, the molecular shape is trigonal pyramidal, and the bond angle is approximately \(107^\circ\).

Step-by-step solution

Determine the Central Atom

In a phosphine (\(PH_3\)) molecule, phosphorus (P) is the central atom, surrounded by hydrogen atoms.

Count the Valence Electrons

Phosphorus has 5 valence electrons, and each hydrogen has 1 valence electron. Since there are 3 hydrogen atoms, the total valence electron count is \(5 + 3 \times 1 = 8\) electrons.

Determine Electron Pair Geometry

Using VSEPR theory, identify the number of 'electron clouds' around the central atom. Here, phosphorus has 3 bonds with hydrogen and one lone pair, totaling 4 regions of electron density. The electron pair geometry for 4 regions of electron density is tetrahedral.

Predict the Molecular Shape

In VSEPR theory, the presence of lone pairs can alter the molecular shape. With one lone pair and 3 bonds, the shape is trigonal pyramidal.

Calculate the Bond Angles

In a perfect tetrahedral arrangement, bond angles are \(109.5^\circ\). However, lone pairs repel more than bonding pairs, thus, in \(PH_3\), the bond angle reduces to about \(107^\circ\).

Key concepts

Phosphine Molecule

The phosphine molecule, represented as \(PH_3\), is a simple example of a compound with phosphorus as its central atom. Phosphine is made up of one phosphorus atom bonded to three hydrogen atoms. In this molecule, phosphorus has five valence electrons, three of which form bonds with each hydrogen atom, and the remaining two form a lone pair. This arrangement greatly influences the molecule's geometry and properties. Understanding the structure of phosphine is essential because it exemplifies how lone pairs can affect the molecular shape. The presence of this lone pair is a key factor in determining the molecule's overall geometry using VSEPR theory, a model used to predict the shape of molecules.

Electron Pair Geometry

The concept of electron pair geometry is crucial in predicting the spatial arrangement of electron pairs around a central atom. In the phosphine molecule, the electron pair geometry considers both the bonding pairs and lone pairs of electrons. Using the Valence Shell Electron Pair Repulsion (VSEPR) theory, the goal is to arrange these electron pairs as far apart as possible to minimize repulsion.

• Phosphorus in \(PH_3\) has 5 valence electrons.
• It forms three bonds with hydrogen atoms and retains a lone pair.
• This results in 4 regions of electron density around the phosphorus atom.

According to VSEPR theory, the presence of four regions of electron density leads to a tetrahedral electron pair geometry. However, it is important to note that the actual visible shape of the molecule, or its molecular shape, can be different.

Molecular Shape

While electron pair geometry sets the stage for understanding molecular structure, the actual molecular shape is how the molecule appears, devoid of lone pairs. In phosphine, the molecule is not simply tetrahedral due to the lone pair on phosphorus. Here is where we dive deeper into molecular shape:

• The three hydrogen atoms, bonded to phosphorus, form a basis for the shape.
• The lone pair, more repulsive than bonded pairs, pushes these hydrogen atoms downward.
• This results in a trigonal pyramidal shape rather than a flat trigonal planar shape.

This molecular shape is vital, as it directly affects the physical and chemical properties of phosphine, especially how it interacts with other molecules.

Bond Angle

Bond angles are instrumental in further defining the precise geometric structure of molecules. In a perfect tetrahedral arrangement, bond angles measure \(109.5^\circ\). However, lone pairs repulse the bonding pairs more strongly than bonding pairs repel each other.

• In the case of \(PH_3\), the lone pair on the phosphorus atom creates an asymmetrical distribution of electron density.
• This increased repulsion by the lone pair effectively reduces the bond angle slightly.
• As a result, the bond angle in phosphine is about \(107^\circ\).

The reduction in bond angle is a direct consequence of the electron repulsion explained by VSEPR theory. Understanding bond angles helps in predicting how such molecules might align or react with others, determining various aspects of their chemical behavior.