Question

Which one of the following molecule has the shortest bond length? (1) \(\mathrm{C}_{2}\) (2) \(\mathrm{O}_{2}\) (3) \(\mathrm{F}_{2}\) (4) \(\mathrm{N}_{2}\)

Short answer

The molecule \(\text{N}_{2}\) has the shortest bond length.

Step-by-step solution

- Understand Bond Length

Bond length is the distance between the nuclei of two bonded atoms. Generally, a triple bond is shorter than a double bond, which is shorter than a single bond.

- Determine Bond Orders

Determine the bond order (number of bonds) for each molecule. For diatomic molecules of the second period elements: - \(\text{C}_{2}\) has a double bond. - \(\text{O}_{2}\) has a double bond with one bond being a π bond. - \(\text{F}_{2}\) has a single bond. - \(\text{N}_{2}\) has a triple bond.

- Compare Bond Lengths

Since a triple bond is shorter than a double bond, and a double bond is shorter than a single bond, compare the bond orders determined. The molecule with the highest bond order (triple bond) will have the shortest bond length.

- Identify the Shortest Bond Length

Identify that \(\text{N}_{2}\) with a triple bond has the shortest bond length compared to \(\text{C}_{2}\), \(\text{O}_{2}\), and \(\text{F}_{2}\) which have double and single bonds.

Key concepts

bond order

Bond order is an important concept in chemistry that helps us understand the strength and length of bonds between atoms. It's defined as the number of chemical bonds between a pair of atoms. The higher the bond order, the stronger and shorter the bond.

For example:

• A single bond has a bond order of 1.
• A double bond has a bond order of 2.
• A triple bond has a bond order of 3.

Generally, molecules with higher bond orders have shorter bond lengths because more electrons are shared between the atoms, pulling them closer together. In the exercise, \(\text{N}_{2}\) has a triple bond, \(\text{C}_{2}\) and \(\text{O}_{2}\) have double bonds, and \(\text{F}_{2}\) has a single bond. Hence, \(\text{N}_{2}\) with the highest bond order, has the shortest bond length.

triple bond

A triple bond is a type of chemical bond where three pairs of electrons are shared between two atoms. Triple bonds are the strongest and shortest among single, double, and triple bonds.

Key characteristics of triple bonds include:

• High bond energy: Triple bonds require more energy to break because of the high number of shared electrons.
• Short bond length: As more electrons are shared, the atoms are pulled closer together, making the bond length shorter.
• Examples: Diatomic nitrogen \(\text{N}_{2}\), acetylene \(\text{C}_{2}\text{H}_{2}\)

In the given exercise, \(\text{N}_{2}\) has a triple bond, which means its bond length is shorter compared to \(\text{C}_{2}\), \(\text{O}_{2}\), and \(\text{F}_{2}\). This is why \(\text{N}_{2}\) is identified as having the shortest bond length.

diatomic molecules

Diatomic molecules consist of only two atoms, which can be either of the same or different elements. Common diatomic molecules include oxygen \(\text{O}_{2}\), nitrogen \(\text{N}_{2}\), and fluorine \(\text{F}_{2}\). These molecules are important because they form the basic units of many elements.

Key points about diatomic molecules:

• Homonuclear diatomic molecules: These consist of two atoms of the same element, like \(\text{N}_{2}\) and \(\text{O}_{2}\).
• Heteronuclear diatomic molecules: These are composed of two different elements, such as carbon monoxide \(\text{CO}\).
• Bond types: Diatomic molecules can have single, double, or triple bonds. For example, \(\text{N}_{2}\) has a triple bond, \(\text{O}_{2}\) has a double bond, and \(\text{F}_{2}\) has a single bond.

Understanding the bond types in diatomic molecules helps in predicting properties like bond length and strength. In the exercise, \(\text{N}_{2}\), \(\text{O}_{2}\), \(\text{C}_{2}\), and \(\text{F}_{2}\) were compared based on their bond types to determine the shortest bond length.