Chapter 8, Problem 8.120QP

(a)

Interpretation Introduction

Interpretation: The given compounds and ions in order of increasing carbon-oxygen bond lengths and increasing bond energies are to be ranked.

Concept introduction: The bond length is the distance between the nuclei of atoms and bond order is defined as the total number of bonds present in a molecule.

When the bond order is high, the bond length is shorter because of the stronger attraction between the atoms. Bond length shows inverse relation with the bond energy.

To determine: The order of increasing carbon-oxygen bond lengths for the given compounds and ion.

Answer to Problem 8.120QP

Solution

The order of increasing carbon-oxygen bond length is $\text{CO}<{\text{CO}}_2<{\text{CO}}_3^{2-}$.

Explanation of Solution

Explanation

The order of carbon-oxygen bond lengths is predicted by calculating the bond order of the given ions. The bond order is inversely proportional to the bond length in a given ion or a molecule. So, more is the bond order value less is the bond strength.

The given compounds and ions are $\text{CO}$, ${\text{CO}}_{\text{2}}$ and ${\text{CO}}_3^{2-}$. Carbon and oxygen belongs to $14$ and $16$ groups of the periodic table and has four and six valence electrons respectively. Therefore, $\text{CO}$ molecule has $4+6=10$ total valence electrons. It consists of three electron pair and one $\text{C}-\text{O}$ bond. The structure of $\text{CO}$ is,

Figure 1

The average bond order of $\text{C}-\text{O}$ bond in $\text{CO}$ is calculated by using the formula,

$\text{Average}\text{bond}\text{order}=\frac{\text{Total}\text{number}\text{of}\text{electron}\text{pair}\text{in}\text{C}-\text{O}\text{bonds}}{\text{Total}\text{number}\text{of}\text{C}-\text{O}\text{bonds}}$

Substitute the values of number of electron pair and $\text{C}-\text{O}$ bond in the above formula to calculate the bond order of $\text{CO}$ molecule.

$\begin{array}{c}\text{Average}\text{bond}\text{order}=\frac{3}{1}\\ =3\end{array}$

The bond order of $\text{C}-\text{O}$ bond in $\text{CO}$ is $3$.

The ${\text{CO}}_{\text{2}}$ molecule has one carbon and two oxygen atoms. Carbon and oxygen belongs to $14$ and $16$ groups of the periodic table and has four and six valence electrons respectively. The total valence electrons in ${\text{CO}}_{\text{2}}$ is calculated as,

$\begin{array}{c}1\text{C}+2\text{O}=1\left(4\right)+2\left(6\right)\\ =4+12\\ =16\end{array}$

The structure of ${\text{CO}}_{\text{2}}$ is,

Figure 2

The ${\text{CO}}_{\text{2}}$ molecule has four electron pair and two $\text{C}-\text{O}$ bonds. The average bond order of $\text{C}-\text{O}$ bond in ${\text{CO}}_{\text{2}}$ is calculated by using the formula,

$\text{Average}\text{bond}\text{order}=\frac{\text{Total}\text{number}\text{of}\text{electron}\text{pair}\text{in}\text{C}-\text{O}\text{bonds}}{\text{Total}\text{number}\text{of}\text{C}-\text{O}\text{bonds}}$

Substitute the values of number of electron pair and $\text{C}-\text{O}$ bonds in the above formula to calculate the bond order of ${\text{CO}}_{\text{2}}$.

$\begin{array}{c}\text{Average}\text{bond}\text{order}=\frac{4}{2}\\ =2\end{array}$

The bond order of $\text{C}-\text{O}$ bond in ${\text{CO}}_{\text{2}}$ is $2$.

The ${\text{CO}}_3^{2-}$ ion has one carbon and three oxygen atoms.

Carbon and oxygen belongs to $14$ and $16$ groups of the periodic table and has four and six valence electrons respectively. The total valence electrons in ${\text{CO}}_3^{2-}$ ion is calculated as,

$\begin{array}{c}1\text{C}+3\text{O}+\text{charge}\text{on}\text{ion}=1\left(4\right)+3\left(6\right)+2\\ =4+18+2\\ =24\end{array}$

The structure of ${\text{CO}}_3^{2-}$ ion is,

Figure 3

The ${\text{CO}}_3^{2-}$ ion has four electron pair and three $\text{C}-\text{O}$ bonds. The average bond order of $\text{C}-\text{O}$ bond in ${\text{CO}}_3^{2-}$ ion is calculated by using the formula,

$\text{Average}\text{bond}\text{order}=\frac{\text{Total}\text{number}\text{of}\text{electron}\text{pair}\text{in}\text{C}-\text{O}\text{bonds}}{\text{Total}\text{number}\text{of}\text{C}-\text{O}\text{bonds}}$

Substitute the values of number of electron pair and $\text{C}-\text{O}$ bonds in the above formula to calculate the bond order of ${\text{CO}}_3^{2-}$ ion.

$\begin{array}{c}\text{Average}\text{bond}\text{order}=\frac{4}{3}\\ =1.3\end{array}$

The bond order of $\text{C}-\text{O}$ bond in ${\text{CO}}_3^{2-}$ ion is $1.3$.

The increasing order of bond order for the given compounds and ion is ${\text{CO}}_3^{2-}<{\text{CO}}_{\text{2}}<\text{CO}$. As the bond order is inversely proportional to the bond length, the increasing order of bond lengths is $\text{CO}<{\text{CO}}_2<{\text{CO}}_3^{2-}$.

(b)

Interpretation Introduction

To determine: The order of increasing bond energies for the given compounds and ions.

Answer to Problem 8.120QP

Solution

The order of increasing bond energies for the given compounds and ions is ${\text{CO}}_3^{2-}<{\text{CO}}_{\text{2}}<\text{CO}$.

Explanation of Solution

Explanation

The bond energy shows inverse relation to the bond length that is more is the bond length lesser is the amount of energy required to break the bond.

Bond energy is directly proportional to the bond order in a given molecule or ion.

Hence, the increasing order of bond energies is ${\text{CO}}_3^{2-}<{\text{CO}}_{\text{2}}<\text{CO}$.

Conclusion

1. a. The increasing order of bond lengths is $\text{CO}<{\text{CO}}_2<{\text{CO}}_3^{2-}$.
2. b. The increasing order of bond energies is ${\text{CO}}_3^{2-}<{\text{CO}}_{\text{2}}<\text{CO}$.