Chapter 13, Problem 21E

Interpretation Introduction

(a)

Interpretation:

The electron-pair geometry for the molecules ${\text{BrO}}^{-},{\text{ClO}}_{\text{3}}{}^{-}$, and ${\text{PO}}_{\text{4}}{}^{3-}$ is to be explained and the Lewis diagram and wedge-and-dash diagram for the molecules are to be drawn.

Concept introduction:

The electron pairs in Lewis diagrams repel each other in real molecule and thus they distribute themselves in positions around the central atoms that are as far away from one another. This arrangement of electron pairs is called electron-pair geometry. The electron pairs may be shared in covalent bond, or they may be lone pairs.

Answer to Problem 21E

The Lewis diagrams for ${\text{BrO}}^{-},{\text{ClO}}_{\text{3}}{}^{-}$, and ${\text{PO}}_{\text{4}}{}^{3-}$ are shown as below.

, and

The wedge-and-dash diagrams for ${\text{BrO}}^{-},{\text{ClO}}_{\text{3}}{}^{-}$, and ${\text{PO}}_{\text{4}}{}^{3-}$ are shown as below.

, and

The electron pair geometry for ${\text{BrO}}^{-}$ is linear and the electron-pair geometry for the molecules ${\text{ClO}}_{\text{3}}{}^{-}$, and ${\text{PO}}_{\text{4}}{}^{3-}$ is tetrahedral.

Explanation of Solution

To write the Lewis diagram for a compound first the number of valence electrons is to be calculated. In the molecule, ${\text{BrO}}^{-}$, bromine has seven valence electrons and oxygen has six valence electrons. Since, ${\text{BrO}}^{-}$ has a negative charge so one electron is to be added in the total number of electrons. The total number of valence electron for the molecule ${\text{BrO}}^{-}$ is calculated below.

$\begin{array}{rll}\text{Total}\text{number}\text{of}\text{valence}\text{electron}& =& \left(7+6+1\right)e^{-}\\ & =& 14e^{-}\end{array}$

In the molecule, ${\text{ClO}}_{\text{3}}{}^{-}$, chlorine has seven valence electrons and each oxygen has six valence electrons. Since, ${\text{ClO}}_{\text{3}}{}^{-}$ has a negative charge so one electron is to be added in the total number of electrons. The total number of valence electron for the molecule ${\text{ClO}}_{\text{3}}{}^{-}$ is calculated below.

$\begin{array}{rll}\text{Total}\text{number}\text{of}\text{valence}\text{electron}& =& \left(7+3\times 6+1\right)e^{-}\\ & =& 26e^{-}\end{array}$

Similarly, in the molecule ${\text{PO}}_{\text{4}}{}^{3-}$, phosphorous has five valence electrons and each oxygen has six valence electrons. Since, ${\text{PO}}_{\text{4}}{}^{3-}$ has a three negative charge so three electrons are to be added in the total number of electrons. The total number of valence electron for the molecule ${\text{PO}}_{\text{4}}{}^{3-}$ is calculated below.

$\begin{array}{rll}\text{Total}\text{number}\text{of}\text{valence}\text{electron}& =& \left(5+4\times 6+3\right)e^{-}\\ & =& 32e^{-}\end{array}$

The atom which is least electronegative is the central atom. In ${\text{BrO}}^{-}$ bromine is least electronegative element. Therefore, bromine is the central atom. Bromine is bonded with one oxygen atom through single bond. In Lewis diagram, each electron is placed around the atom such that the octet rule is obeyed. Therefore, the Lewis diagram of ${\text{BrO}}^{-}$ is shown below.

Figure 1

In ${\text{ClO}}_{\text{3}}{}^{-}$ chlorine is least electronegative element. Therefore, chlorine is the central atom. Chlorine is bonded with three oxygen atoms. In Lewis diagram, each electron is placed around the atom such that the octet rule is obeyed. Therefore, the Lewis diagram of ${\text{ClO}}_{\text{3}}{}^{-}$ is shown as below.

Figure 2

In ${\text{PO}}_{\text{4}}{}^{3-}$ phosphorous is least electronegative element. Therefore, phosphorous is the central atom. Phosphorous is bonded with four oxygen atoms. In Lewis diagram, each electron is placed around the atom such that the octet rule is obeyed. Therefore, the Lewis diagram of ${\text{PO}}_{\text{4}}{}^{3-}$ is shown as below.

Figure 3

The electron-pair geometry depends on the number of electron pairs around the central atom. In the molecule ${\text{BrO}}^{-}$, there are one electron-pairs around the bromine. Therefore, the electron pair geometry is linear. In the molecule, ${\text{ClO}}_{\text{3}}{}^{-}$, there are four elctron pairs around the chlorine atom. Therefore, the electron-pair geometry is tetrahedral. Similarly, in the molecule ${\text{PO}}_{\text{4}}{}^{3-}$ there are four electron pairs around phosphorous atom. Therefore, the electron-pair geometry is tetrahedral.

The wedge-and-dash diagram for the molecules ${\text{BrO}}^{-}$ is shown below.

Figure 4

The wedge-and-dash diagram for the molecules ${\text{ClO}}_{\text{3}}{}^{-}$ is shown below.

Figure 5

The wedge-and-dash diagram for the molecules ${\text{PO}}_{\text{4}}{}^{3-}$ is shown below.

Figure 6

Conclusion

The Lewis and wedge-and-dash diagrams for ${\text{BrO}}^{-},{\text{ClO}}_{\text{3}}{}^{-}$, and ${\text{PO}}_{\text{4}}{}^{3-}$ are shown in the Figure 1, Figure 2, Figure 3, Figure 4, Figure 5, and Figure 6. The electron pair geometry for ${\text{BrO}}^{-}$ is linear and the electron-pair geometry for the molecules ${\text{ClO}}_{\text{3}}{}^{-}$, and ${\text{PO}}_{\text{4}}{}^{3-}$ is tetrahedral.

Interpretation Introduction

(b)

Interpretation:

The molecular geometry prdicted by the valence shell electron-pair repulsion theory for the molecules ${\text{BrO}}^{-},{\text{ClO}}_{\text{3}}{}^{-}$, and ${\text{PO}}_{\text{4}}{}^{3-}$ is to be explained and the Lewis diagram and wedge-and-dash diagram for the molecules are to be drawn.

Concept introduction:

Molecular geometry is the precise term that is used to describe the shape of molecules and arrangement of atoms around the central atom. The molecular geometry of a molecule is predicted by valence shell electron-pair repulsion theory or in short VSEPR theory. VSEPR theory applies to substances in which a second period element is bonded to two, three, four, or other atoms.

Answer to Problem 21E

The Lewis diagrams for ${\text{BrO}}^{-},{\text{ClO}}_{\text{3}}{}^{-}$, and ${\text{PO}}_{\text{4}}{}^{3-}$ are shown as below.

, and

The wedge-and-dash diagrams for ${\text{BrO}}^{-},{\text{ClO}}_{\text{3}}{}^{-}$, and ${\text{PO}}_{\text{4}}{}^{3-}$ are shown as below.

, and

The molecular geometry for ${\text{BrO}}^{-}$ is linear, for ${\text{ClO}}_{\text{3}}{}^{-}$ the molecular geometry is trigonal pyramidal, and for ${\text{PO}}_{\text{4}}{}^{3-}$ the molecular geometry is tetrahedral.

Explanation of Solution

To write the Lewis diagram for a compound first the number of valence electrons is to be calculated. In the molecule, ${\text{BrO}}^{-}$, bromine has seven valence electrons and oxygen has six valence electrons. Since, ${\text{BrO}}^{-}$ has a negative charge so one electron is to be added in the total number of electrons. The total number of valence electron for the molecule ${\text{BrO}}^{-}$ is calculated below.

$\begin{array}{rll}\text{Total}\text{number}\text{of}\text{valence}\text{electron}& =& \left(7+6+1\right)e^{-}\\ & =& 14e^{-}\end{array}$

In the molecule, ${\text{ClO}}_{\text{3}}{}^{-}$, chlorine has seven valence electrons and each oxygen has six valence electrons. Since, ${\text{ClO}}_{\text{3}}{}^{-}$ has a negative charge so one electron is to be added in the total number of electrons. The total number of valence electron for the molecule ${\text{ClO}}_{\text{3}}{}^{-}$ is calculated below.

$\begin{array}{rll}\text{Total}\text{number}\text{of}\text{valence}\text{electron}& =& \left(7+3\times 6+1\right)e^{-}\\ & =& 26e^{-}\end{array}$

Similarly, in the molecule, ${\text{PO}}_{\text{4}}{}^{3-}$, phosphorous has five valence electrons and each oxygen has six valence electrons. Since, ${\text{PO}}_{\text{4}}{}^{3-}$ has a three negative charge so three electrons are to be added in the total number of electrons. The total number of valence electron for the molecule ${\text{PO}}_{\text{4}}{}^{3-}$ is calculated below.

$\begin{array}{rll}\text{Total}\text{number}\text{of}\text{valence}\text{electron}& =& \left(5+4\times 6+3\right)e^{-}\\ & =& 32e^{-}\end{array}$

The atom which is least electronegative is the central atom. In ${\text{BrO}}^{-}$ bromine is least electronegative element. Therefore, bromine is the central atom. Bromine is bonded with one oxygen atom through single bond. In Lewis diagram, each electron is placed around the atom such that the octet rule is obeyed. Therefore, the Lewis diagram of ${\text{BrO}}^{-}$ is shown below.

Figure 1

In ${\text{ClO}}_{\text{3}}{}^{-}$ chlorine is least electronegative element. Therefore, chlorine is the central atom. Chlorine is bonded with three oxygen atoms. In Lewis diagram, each electron is placed around the atom such that the octet rule is obeyed. Therefore, the Lewis diagram of ${\text{ClO}}_{\text{3}}{}^{-}$ is shown below.

Figure 2

In ${\text{PO}}_{\text{4}}{}^{3-}$ phosphorous is least electronegative element. Therefore, phosphorous is the central atom. Phosphorous is bonded with four oxygen atoms. In Lewis diagram, each electron is placed around the atom such that the octet rule is obeyed. Therefore, the Lewis diagram of ${\text{PO}}_{\text{4}}{}^{3-}$ is shown below.

Figure 3

The molecular geometry depends on the number of electron pairs around the central atom and the number of lone pair on the central atom. In the molecule ${\text{BrO}}^{-}$, there are one electron-pairs around the bromine. Therefore, the molecular geometry is linear. In the molecule ${\text{ClO}}_{\text{3}}{}^{-}$ there are four elctron pairs around the chlorine atom and onr one pair on the chlorine atom. This lone pair repel to other lone pairs. Therefore, the molecular geometry would be distorted and change in to trigonal pyramidal. In the molecule ${\text{PO}}_{\text{4}}{}^{3-}$ there are four electron pairs around phosphorous atom no lone pair. Therefore, the molecular geometry is tetrahedral.

The wedge-and-dash diagram for the molecules ${\text{BrO}}^{-}$ is shown below.

Figure 4

The wedge-and-dash diagram for the molecules ${\text{ClO}}_{\text{3}}{}^{-}$ is shown below.

Figure 5

The wedge-and-dash diagram for the molecules ${\text{PO}}_{\text{4}}{}^{3-}$ is shown below.

Figure 6

Conclusion

The Lewis and wedge-and-dash diagrams for ${\text{BrO}}^{-},{\text{ClO}}_{\text{3}}{}^{-}$, and ${\text{PO}}_{\text{4}}{}^{3-}$ are shown in the Figure 1, Figure 2, Figure 3, Figure 4, Figure 5, and Figure 6. The molecular geometry for ${\text{BrO}}^{-}$ is linear, for ${\text{ClO}}_{\text{3}}{}^{-}$ the molecular geometry is trigonal pyramidal, and for ${\text{PO}}_{\text{4}}{}^{3-}$ the molecular geometry is tetrahedral.