Question

The correct order of the arrangement of bond length is (1) \(\mathrm{F}_{2}>\mathrm{N}_{2}>\mathrm{Cl}_{2}>\mathrm{O}_{2}\) (2) \(\mathrm{Cl}_{2}>\mathrm{F}_{2}>\mathrm{O}_{2}>\mathrm{N}_{2}\) (3) \(\mathrm{O}_{2}>\mathrm{Cl}_{2}>\mathrm{N}_{2}>\mathrm{F}_{2}\) (3) \(\mathrm{F}_{2}>\mathrm{Cl}_{2}>\mathrm{N}_{2}>\mathrm{O}_{2}\)

Short answer

Option 2 is correct. \(\mathrm{Cl_{2} > F_{2} > O_{2} > N_{2}}\).

Step-by-step solution

- Understand Bond Length

Bond length is the distance between the nuclei of two bonded atoms. Typically, the bond length is influenced by the size of the atoms and the bond order (single, double, triple bonds).

- Recognize the Elements and Bonds

Identify the molecules given in the options: \(\mathrm{F_{2}}, \mathrm{N_{2}}, \mathrm{Cl_{2}}, \mathrm{O_{2}}\). Fluorine (F) forms a diatomic molecule with a single bond, Nitrogen (N) forms a diatomic molecule with a triple bond, Chlorine (Cl) forms a diatomic molecule with a single bond, and Oxygen (O) forms a diatomic molecule with a double bond.

- Compare Atomic Sizes

Generally, larger atoms will have longer bond lengths. Cl (Chlorine, with atomic number 17) is larger than F (Fluorine, atomic number 9), but smaller than N and O.

- Bond Order Implications

Bond length also depends on the bond order. The greater the bond order, the shorter the bond length. Hence, the bond lengths should be ranked as follows based on bond order: \(\mathrm{N_{2}} (triple bond) < \mathrm{O_{2}} (double bond) < \mathrm{F_{2}} (single bond) = \mathrm{Cl_{2}} (single bond)\)

- Match with the Given Options

Review the provided options and match the correct ranking: For a correct arrangement, it should be that Chlorine has the highest bond length followed by Fluorine, Oxygen, and Nitrogen. Option 2 matches this: \(\mathrm{Cl_{2} > F_{2} > O_{2} > N_{2}}\).

Key concepts

Bond Length

Bond length is the distance between the nuclei of two bonded atoms. Imagine holding hands with someone. The distance from your hand to the other person’s hand is like a bond length. This distance can vary depending on several factors:
First, the size of the atoms matters. Bigger atoms tend to have longer bond lengths because their nuclei are further apart.
Second, the type of bond (or bond order) between the atoms affects the bond length. Bond order refers to whether the bond is single, double, or triple. A single bond is like holding hands with one hand, a double bond like holding with both hands, and a triple bond like holding with more force. The stronger or higher the bond order, the shorter the bond length.
Therefore, to determine the bond length, you should consider both the size of the atoms and the bond order.

Diatomic Molecules

Diatomic molecules are molecules composed of only two atoms. The term 'diatomic' comes from 'di-', meaning two, and 'atomic', referring to atoms.
Some common diatomic molecules you might encounter are:

• \(\text{H}_{2}\) - Hydrogen
• \(\text{O}_{2}\) - Oxygen
• \(\text{N}_{2}\) - Nitrogen
• \(\text{F}_{2}\) - Fluorine
• \(\text{Cl}_{2}\) - Chlorine

These gases naturally form pairs of atoms. This pairing offers stability to the molecules. In the given exercise, we specifically look at the bond lengths in \(\text{F}_{2}\), \(\text{N}_{2}\), \(\text{Cl}_{2}\), and \(\text{O}_{2}\). Each of these belongs to a group of diatomic molecules. By understanding their nature, we can more accurately predict how they bond and their bond lengths.

Bond Order

Bond order refers to the number of chemical bonds between a pair of atoms. It can be thought of as how tightly the atoms are held together. Bond order plays a significant role in determining bond length:

• Single Bond (Bond Order 1): This is the longest type of bond, as it involves only one pair of electrons holding the two atoms together.
• Double Bond (Bond Order 2): A bit shorter than a single bond, as two pairs of electrons pull the atoms closer together.
• Triple Bond (Bond Order 3): The shortest of all, with three pairs of electrons creating very strong attraction and minimal distance between the nuclei.

For the given diatomic molecules: \(\text{F}_{2}\) and \(\text{Cl}_{2}\) have single bonds, \(\text{O}_{2}\) has a double bond, and \(\text{N}_{2}\) has a triple bond. As bond order increases from a single bond to a triple bond, the bond length decreases. Remember this hierarchy while comparing bond lengths in different molecules.