Question

The correct order of the O-O bond length in \(\mathrm{O}_{2}, \mathrm{H}_{2} \mathrm{O}_{2}\) and \(\mathrm{O}_{3}\) is (1) \(\mathrm{O}_{2}>\mathrm{O}_{3}>\mathrm{II}_{2} \mathrm{O}_{2}\) (2) \(\mathrm{O}_{3}>\mathrm{II}_{2} \mathrm{O}_{2}>\mathrm{O}_{2}\) (3) \(\mathrm{II}_{2} \mathrm{O}_{2}>\mathrm{O}_{3}>\mathrm{O}_{2}\) (4) \(\mathrm{O}_{2}>\mathrm{II}_{2} \mathrm{O}_{2}>\mathrm{O}_{3}\)

Short answer

The correct order is (3) H2O2 > O3 > O2.

Step-by-step solution

- Understand Bond Lengths

Bond length is the distance between the nuclei of two bonded atoms. For molecules with the same type of bond, bond length is usually influenced by the bond order.

- Determine Bond Orders

Bond order is the number of chemical bonds between a pair of atoms. Higher bond orders generally mean shorter bond lengths. Evaluate the bond orders of O2 (which is 2), H2O2 (single bonds between oxygens, bond order 1), and O3 (resonance gives bond order 1.5).

- Compare Bond Lengths

In terms of bond order: O2 (2) > O3 (1.5) > H2O2 (1). Higher bond order means shorter bond length.

- Conclude Correct Order

From bond orders, it follows that the shortest bond length is in O2, followed by O3, and the longest in H2O2.

- Select the Correct Option

The correct order of O-O bond lengths is H2O2 > O3 > O2.

Key concepts

bond length

Bond length is a crucial concept in chemistry. It refers to the distance between the nuclei of two bonded atoms. Imagine it as a 'bridge' connecting two points. The length of this bridge tells us a lot about the nature of the bond. For instance, shorter bond lengths typically indicate stronger bonds. The type of bond—whether single, double, or triple—also influences its length. Generally, bond length decreases as bond order increases. For example, in molecules with the same atoms, a triple bond will usually be shorter and stronger than a double bond and significantly shorter than a single bond.

bond order

Bond order essentially tells us how many bonds exist between two atoms. It's a straightforward way to understand the bonding structure within a molecule. Here's a neat way to visualize it:

• 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.

The higher the bond order, the stronger and shorter the bond. For instance, in our exercise, \(\text{O}_2\) has a bond order of 2 (since it's a double bond), while \(\text{H}_2\text{O}_2\) has a bond order of 1 (single bond between oxygens). With \(\text{O}_3\), resonance creates an average bond order of 1.5. So, when comparing bond lengths based on bond order, \(\text{O}_2\) would have the shortest bond, followed by \(\text{O}_3\), and then \(\text{H}_2\text{O}_2\) with the longest bond.

resonance in molecules

Resonance occurs when a molecule can be represented by two or more valid Lewis structures. These structures, called resonance structures, depict the same molecule but with different arrangements of electrons. In reality, the molecule doesn't switch between these forms. Instead, it exists as a hybrid, blending aspects of all the resonance structures. This fusion influences various properties, including bond length. For instance, \(\text{O}_3\) (ozone) showcases resonance. The \(\text{O}_3\) molecule can be represented by:

• One form where one oxygen-oxygen bond is a single bond and the other is a double bond.
• Another form where these bond types are reversed.

This resonance means the bond order isn't clearly 1 or 2 but averages out to 1.5. Therefore, the bond length in ozone is shorter than a single bond (order 1) but longer than a double bond (order 2), providing crucial insight into molecular structure and behavior.