Chapter 8, Problem 7STP

Interpretation Introduction

Interpretation:

The diatomic gas which has shortest bond between its two atoms is to be predicted.

Concept introduction:

The energy required to break a bond is termed as bond dissociation energy. The bond length depends on the bond dissociation energies. The longest bond has lowest bond energy and the shortest bond has highest bond energy.

Answer to Problem 7STP

The ${\text{N}}_{\text{2}}$ diatomic gas has shortest bond length. Therefore, the option (D) is the correct option.

Explanation of Solution

Reason for correct option: It is known that the bond length of bond decreases as the number of bonds between atoms increases. For example, single bond has longest bond length and triple bond has shortest bond length. The bond length also depends on the bond dissociation energies. The longest bond has lowest bond energy and the shortest bond has highest bond energy.

The given table is shown below.

The given diatomic gas is $\text{HI}$, ${\text{Cl}}_{\text{2}}$, ${\text{O}}_{\text{2}}$, and ${\text{N}}_{\text{2}}$. In $\text{HI}$, $\text{H}$ and $\text{I}$ is bonded via single bond. In ${\text{Cl}}_2$, both $\text{Cl}$ atoms are bonded via single bond. In ${\text{O}}_2$, both $\text{O}$ atoms are bonded via double bond. In ${\text{N}}_2$, both $\text{N}$ atoms are bonded via triple bond.

Among the given diatomic gases, ${\text{N}}_{\text{2}}$ also has highest bond dissociation energy $\left(945\text{kJ/mol}\right)$. Therefore, ${\text{N}}_{\text{2}}$ has shortest bond length. Therefore, the correct option is option (D).

Conclusion

Reason for incorrect option: The bond dissociation energy of $\text{HI}$ is $\text{299}\text{kJ/mol}$. So, A is incorrect option.

The bond dissociation energy of ${\text{O}}_2$ is $\text{498}\text{kJ/mol}$. So, B is incorrect option.

The bond dissociation energy of ${\text{Cl}}_2$ is $\text{242}\text{kJ/mol}$. So, C is incorrect option.