Problem 98 - A Complete Resource Book in Chemistry for JEE Main

Question

The correct order in which the O-O bond length increases in the following is (a) \(\mathrm{O}_{2}<\mathrm{H}_{2} \mathrm{O}_{2}<\mathrm{O}_{3}\) (b) \(\mathrm{O}_{3}<\mathrm{H}_{2} \mathrm{O}_{2}<\mathrm{O}_{2}\) (c) \(\mathrm{H}_{2} \mathrm{O}_{2}<\mathrm{O}_{2}<\mathrm{O}_{3}\) (d) \(\mathrm{O}_{2}<\mathrm{O}_{3}<\mathrm{H}_{2} \mathrm{O}_{2}\)

Step-by-Step Solution

Answer

The correct order is (d) O_{2}< O_{3}< H_{2}O_{2}.

Step 1: Understanding Bond Length

Bond length is the average distance between the nuclei of two bonded atoms. In general, the greater the number of bonds between a pair of atoms, the shorter the bond length. This concept can help determine the order of increasing bond lengths for different molecules.

Step 2: Analyzing O-O Bond in Oxygen Molecules

The molecule O_{2} has a double bond between the oxygen atoms. Double bonds are shorter than single bonds, so O_{2} will have the shortest bond length among the options due to its double bond.

Step 3: Analyzing O-O Bond in Hydrogen Peroxide

The bond between oxygen atoms in H_{2}O_{2} is a single bond because each oxygen atom is also bonded to a hydrogen atom. This single bond makes the O-O bond longer compared to a double bond in O_{2}.

Step 4: Analyzing O-O Bond in Ozone

The ozone molecule O_{3} consists of a resonance structure where the bond order is about 1.5. Consequently, the O-O bond in O_{3} is longer than the double bond in O_{2}, but shorter than the single bond in H_{2}O_{2}.

Step 5: Arranging Bond Lengths in Order

Based on the above analysis, we can order the bond lengths as: 1. O_{2} (shortest, double bond) 2. O_{3} (intermediate, bond order of 1.5 due to resonance) 3. H_{2}O_{2} (longest, single bond) Hence, the correct order of increasing O-O bond length is O_{2}

Key Concepts

Bond Length Concepts

Bond length is an essential concept in chemistry that refers to the average distance between the nuclei of two bonded atoms. Understanding bond length helps in predicting the strength and stability of the bond. Generally, the more bonds shared between two atoms, the shorter the bond length. This is due to the greater pull between the atoms, which keeps them closer together.

Bond length is influenced by several factors:

• Number of bonds: More bonds (like double or triple bonds) result in shorter bond lengths.
• Atomic size: Larger atoms have longer bond lengths because the nuclei have more electron shells pushing them apart.
• Covalent radius: It represents the size of an atom that forms part of a single covalent bond, affecting how close the bonded atoms can get.

This understanding is crucial in determining the properties of molecules and their reactivity.

Double Bond vs Single Bond

When comparing double and single bonds, the double bonds are generally shorter and stronger. This is because double bonds involve sharing two pairs of electrons between atoms, resulting in a stronger attractive force that pulls the atoms closer together, influencing their bond length.

Here's a breakdown of the differences:

• Double bonds involve two shared pairs of electrons, leading to shorter bond lengths.
• Single bonds have only one pair of shared electrons, resulting in relatively longer bond lengths.
• The bond energy is higher in double bonds due to the increased number of shared electrons.

The differences between single and double bonds affect a molecule's physical and chemical properties, including reactivity, boiling and melting points, and structural stability.

Resonance Structures

Resonance structures are a way to represent molecules where the electrons can be distributed in different arrangements, but the actual structure is a hybrid of these possibilities. This concept helps in explaining molecules like ozone ( O_3 ) where traditional single or double bond representations fall short.

Here is how resonance structures affect bonds:

• Resonance results in a fractional bond order, for example, a bond order of 1.5 in ozone, indicating bonds are stronger than a single bond but weaker than a double bond.
• Electrons are delocalized over the atoms, which helps in stabilizing the structure.
• The bond lengths in resonance structures are intermediate compared to typical single or double bonds.

Understanding resonance provides insights into molecular stability and reactivity, as it affects how bonds distribute electrons throughout a molecule.

Bond Order Significance

Bond order is a concept that reflects the number of bonds between a pair of atoms. It indicates the strength and length of a bond in a molecule. A higher bond order means there are more shared electron pairs between atoms, leading to shorter and stronger bonds.

Let's see how bond order works:

• In diatomic oxygen ( O_2 ), a double bond indicates a bond order of 2, suggesting strong and short bonds.
• For peroxide ( H_2O_2 ), with a single bond between oxygens, the bond order is 1, indicating a longer and weaker bond.
• The unique bond order of 1.5 in ozone ( O_3 ) is due to resonance, meaning the bonds are intermediate in length.

Understanding bond order is essential for predicting the physical properties of molecules and assessing the stability of chemical reactions.

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Key Concepts

Bond Length Concepts

Bond length is an essential concept in chemistry that refers to the average distance between the nuclei of two bonded atoms. Understanding bond length helps in predicting the strength and stability of the bond. Generally, the more bonds shared between two atoms, the shorter the bond length. This is due to the greater pull between the atoms, which keeps them closer together.

Bond length is influenced by several factors:

• Number of bonds: More bonds (like double or triple bonds) result in shorter bond lengths.
• Atomic size: Larger atoms have longer bond lengths because the nuclei have more electron shells pushing them apart.
• Covalent radius: It represents the size of an atom that forms part of a single covalent bond, affecting how close the bonded atoms can get.

This understanding is crucial in determining the properties of molecules and their reactivity.

Double Bond vs Single Bond

When comparing double and single bonds, the double bonds are generally shorter and stronger. This is because double bonds involve sharing two pairs of electrons between atoms, resulting in a stronger attractive force that pulls the atoms closer together, influencing their bond length.

Here's a breakdown of the differences:

• Double bonds involve two shared pairs of electrons, leading to shorter bond lengths.
• Single bonds have only one pair of shared electrons, resulting in relatively longer bond lengths.
• The bond energy is higher in double bonds due to the increased number of shared electrons.

The differences between single and double bonds affect a molecule's physical and chemical properties, including reactivity, boiling and melting points, and structural stability.

Resonance Structures

Resonance structures are a way to represent molecules where the electrons can be distributed in different arrangements, but the actual structure is a hybrid of these possibilities. This concept helps in explaining molecules like ozone ( O_3 ) where traditional single or double bond representations fall short.

Here is how resonance structures affect bonds:

• Resonance results in a fractional bond order, for example, a bond order of 1.5 in ozone, indicating bonds are stronger than a single bond but weaker than a double bond.
• Electrons are delocalized over the atoms, which helps in stabilizing the structure.
• The bond lengths in resonance structures are intermediate compared to typical single or double bonds.

Understanding resonance provides insights into molecular stability and reactivity, as it affects how bonds distribute electrons throughout a molecule.

Bond Order Significance

Bond order is a concept that reflects the number of bonds between a pair of atoms. It indicates the strength and length of a bond in a molecule. A higher bond order means there are more shared electron pairs between atoms, leading to shorter and stronger bonds.

Let's see how bond order works:

• In diatomic oxygen ( O_2 ), a double bond indicates a bond order of 2, suggesting strong and short bonds.
• For peroxide ( H_2O_2 ), with a single bond between oxygens, the bond order is 1, indicating a longer and weaker bond.
• The unique bond order of 1.5 in ozone ( O_3 ) is due to resonance, meaning the bonds are intermediate in length.

Understanding bond order is essential for predicting the physical properties of molecules and assessing the stability of chemical reactions.