Question

The \(\mathrm{H}-\mathrm{O}-\mathrm{O}\) bond angle in \(\mathrm{H}_{2} \mathrm{O}_{2}\) is: (a) \(97^{\circ}\) (b) \(106^{\circ}\) (c) \(104.5^{\circ}\) (d) \(109.28^{\circ}\)

Short answer

The bond angle in H₂O₂ is 97°.

Step-by-step solution

Understanding the molecule

Hydrogen peroxide (H₂O₂) is a simple peroxide, which consists of two OH groups connected by the oxygen-oxygen bond. The molecule has a non-linear structure due to the presence of lone pairs of electrons on the oxygen atoms which affect its geometry.

Analyzing Lewis structure

In H₂O₂, each oxygen atom is bonded to one hydrogen and another oxygen atom. The single bonds and lone pairs create a bent structure. We need to recall bond angle estimates for two-terminal central atom systems like this one, which are affected by lone electron pairs.

Predicting bond angle

The presence of the lone pairs on the oxygen atoms results in a repulsion that is greater than the bond pair-bond pair repulsion, leading to a smaller angle. For similar structures with two lone pairs on the central oxygen atom, the geometry tends to slant closer to tetrahedral angles.

Selecting the correct answer

Taking into account these interactions, bond angles are typically close to the tetrahedral angle (109.28°) but slightly less due to lone pairs. The correct bond angle for H₂O₂ is 97°. Therefore, the answer is (a) 97°.

Key concepts

Molecular Geometry

Molecular geometry is the three-dimensional arrangement of atoms in a molecule, which determines the molecule's shape. This shape is influenced by the number of electron groups around a central atom. In a simple understanding, an electron group can be a lone pair of electrons, a single bond, a double bond, or a triple bond.
When you visualize how these groups spread out in space, remember they repel each other. This repulsion occurs because all these groups carry negative charges, and like charges repel. In molecules such as hydrogen peroxide (H₂O₂), the geometry is particularly interesting. H₂O₂ consists of two hydrogen atoms bonded to two oxygen atoms, with the oxygen atoms connected by an O-O single bond.
The molecule's non-linear shape results because of the lone pairs on the oxygen atoms. They exert additional repulsion, pushing the bonded atoms closer together. This results in bond angles that are different from what you'd expect in a molecule with no lone pairs.

Lone Pair Repulsion

Lone pair repulsion is a critical factor in determining a molecule's shape. A lone pair refers to electron pairs that are not shared with another atom and belong exclusively to one atom. These lone pairs are highly important because they occupy more space around the central atom compared to a bonding pair of electrons.
This space-occupying nature leads to different repulsion strengths. In molecules like H₂O₂, the lone pairs on each oxygen atom play a dominant role. They need to sit in a way that minimizes repulsive force, thereby altering the ideal angles between the atoms.
Therefore, in H₂O₂, lone pair repulsion causes bond angles to shrink. They force the bonded hydrogen atoms to push further away than they would be in a molecule devoid of lone pairs. By observing lone pair interactions, we can predict that these lone pairs will reduce the angle from the standard tetrahedral angle of 109.28° to something closer to 97°.

Lewis Structure Analysis

Lewis structures are diagrams that illustrate the arrangement of electrons in a molecule. These structures help us understand the distribution of electrons that form bonds and those that exist as lone pairs.
While analyzing H₂O₂ using Lewis structures, we place single bonds between the hydrogen and oxygen atoms, and the two oxygen atoms themselves. Oxygen, being more electronegative, typically holds onto two lone pairs of electrons.
Drawing a Lewis structure involves:

• Identifying how many valence electrons each atom contributes.
• Placing single bonds where necessary.
• Ensuring all atoms satisfy the octet rule by adjusting lone pairs.

As we ascertain the Lewis structure of H₂O₂, it's evident that each oxygen has two lone pairs. This allows us to visualize their impact on the molecular geometry, leading us to expect deviations from the typical bond angles in a simpler structure without lone pairs.