Question

The species \(\mathrm{PBr}_{4}^{-}\) has been synthesized and has been described as a tetrahedral anion. Comment on this description.

Short answer

The description of the \(\mathrm{PBr}_{4}^{-}\) ion as a tetrahedral anion is accurate, considering the VSEPR theory. This theory predicts that the compound has a tetrahedral geometry due to its distribution of electrons.

Step-by-step solution

Identify the number of valence electrons

Identify the total number of valence electrons. Phosphorus (P) is in Group 5A, so it has 5 valence electrons, bromine (Br) is in Group 7A, so it has 7 valence electrons. As there are 4 bromine atoms, so we have a total of \(5+4*7=33\) valence electrons. However, the ion \(\mathrm{PBr}_{4}^{-}\) carries an extra negative charge which indicates an additional electron. Therefore, the total number of valence electrons is 34.

Setup the Lewis Structure

First, we place the least electronegative atom (P) in the center. Each of the four Bromine (Br) atoms is connected to the central Phosphorus (P) atom. We then distribute the remaining electrons as lone pairs on the surrounding atoms.

Comment on the description

The compound has one central atom (Phosphorus, P), surrounded by four other atoms (Bromine, Br). According to the VSEPR theory, such a configuration corresponds to a tetrahedral geometry. Therefore, the description of the \(\mathrm{PBr}_{4}^{-}\) ion as a tetrahedral anion is accurate.

Key concepts

Valence Electrons

Valence electrons are the outermost electrons of an atom and are crucial in determining its chemical bonding behavior. These electrons can be shared, gained, or lost in the formation of chemical bonds. The number of valence electrons is the primary factor in determining how elements react with one another.

In our exercise, the focus is on the tetrahedral anion \(\mathrm{PBr}_{4}^{-}\), which is formed by phosphorus and bromine atoms. The phosphorus atom, located in Group 5A of the periodic table, has five valence electrons, while each bromine atom, found in Group 7A, has seven valence electrons. When combined, the \(\mathrm{PBr}_{4}^{-}\) anion overall has 34 valence electrons, taking into account the additional electron contributed by the negative charge of the anion.

Understanding valence electrons enables students to predict and draw the Lewis structure of molecules and polyatomic ions, a significant step in exploring chemical bonding and molecule geometry.

Lewis Structure

The Lewis structure, also known as a Lewis dot diagram, represents the valence electrons of an atom or a molecule using dots. It is a simplistic graphical representation that shows the arrangement of valence electrons around atoms.

In the exercise regarding the \(\mathrm{PBr}_{4}^{-}\) anion, the Lewis structure is constructed by first placing the central atom, which is usually the least electronegative, and connecting it with single lines to represent bonds with surrounding atoms. In this case, phosphorus is the least electronegative and forms single bonds with four bromine atoms. After forming the bonds, the remaining valence electrons are distributed as lone pairs to fulfill the octet rule, where each atom attempts to have eight electrons in its valence shell.

The accurate depiction of the Lewis structure is foundational for understanding molecule geometry, as it sets the stage for the application of VSEPR theory to determine the three-dimensional shape of the molecule or ion.

VSEPR Theory

VSEPR theory, which stands for Valence Shell Electron Pair Repulsion theory, is a model used to predict the shape of individual molecules based on the repulsion between the electron pairs in the valence shell of an atom. The theory posits that because electron pairs repel each other, molecules will adjust their shape so that these pairs are as far apart as possible, leading to a specific molecular geometry.

For the \(\mathrm{PBr}_{4}^{-}\) ion described in the exercise, VSEPR theory helps us understand why it is referred to as a tetrahedral anion. After arranging the valence electrons according to the Lewis structure, we apply VSEPR theory to predict the ion's shape. With one central atom bonded to four other atoms, no lone pairs on the central atom, and electron pairs spread out to minimize repulsion, the geometry that satisfies these conditions is tetrahedral. This spatial arrangement is consistent with the description provided, affirming that the \(\mathrm{PBr}_{4}^{-}\) ion indeed forms a tetrahedral geometry.