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 \(\mathrm{H}-\mathrm{O}-\mathrm{O}\) bond angle in \(\mathrm{H}_{2}\mathrm{O}_{2}\) is \(97^{\circ}\) (option a).

Step-by-step solution

Understanding Molecular Structure

The compound \(\mathrm{H}_{2}\mathrm{O}_{2}\) is known as hydrogen peroxide. In this molecule, two hydrogen atoms are bound to two oxygen atoms, which are themselves connected via an \(\mathrm{O}-\mathrm{O}\) single bond.

Valence Shell Electron Pair Repulsion (VSEPR) Theory

To determine the bond angle, we utilize the VSEPR theory which predicts the optimal geometry of molecules with regard to minimizing electron pair repulsion around the atom centers. For water \(\mathrm{H}_2\mathrm{O}\), the angle is about \(104.5^\circ\), but in \(\mathrm{H}_{2}\mathrm{O}_{2}\), extra repulsion occurs due to additional bonded pairs.

Calculating the \(\mathrm{H}-\mathrm{O}-\mathrm{O}\) Bond Angle

Unlike water, hydrogen peroxide has an additional oxygen, altering its structure slightly. Empirically, the bond angle for the \(\mathrm{H}-\mathrm{O}-\mathrm{O}\) is found to be approximately \(97^\circ\). This reduction from water's angle is due to the electron lone pairs on each oxygen exerting more repulsion.

Key concepts

Molecular Geometry

Molecular geometry refers to the three-dimensional arrangement of atoms within a molecule. In hydrogen peroxide (\(\mathrm{H}_2\mathrm{O}_2\)), this includes understanding how two hydrogen atoms connect to the two oxygen atoms. The overall geometry of \(\mathrm{H}_2\mathrm{O}_2\) is not linear or symmetrical. Instead, it adopts a skewed structure due to the connection between the two oxygen atoms through an \(\mathrm{O}-\mathrm{O}\) single bond.

Hydrogen peroxide is characterized by a specific molecular geometry that results from the various repulsive and attractive forces among its atoms and electron pairs. The repulsion between lone pairs and bonding pairs leads to a unique spatial orientation.

This geometry is not merely academic; it dictates many of the physical and chemical properties of \(\mathrm{H}_2\mathrm{O}_2\), such as its ability to act as both an oxidizing and reducing agent. By understanding molecular geometry, we can predict these properties and reactions better.

Bond Angles

Bond angles are a crucial aspect of molecular geometry. They determine how molecules interact with each other and their environment. In the case of \(\mathrm{H}_2\mathrm{O}_2\), the bond angle between the hydrogen, oxygen, and oxygen atoms (\(\mathrm{H}-\mathrm{O}-\mathrm{O}\)) is approximately \(97^\circ\). This angle affects the overall shape and reactivity of hydrogen peroxide.

Several factors influence bond angles, including the presence of lone pairs of electrons which tend to repel bonding pairs, thereby affecting the angle. In \(\mathrm{H}_2\mathrm{O}_2\), the relatively small bond angle compared to water (\(\mathrm{H}_2\mathrm{O}\)) with its \(104.5^\circ\) angle is due to additional lone pair interactions on the oxygens.

These interactions cause a closer approach of the hydrogen atoms toward each other within the molecule, compressing the \(\mathrm{H}-\mathrm{O}-\mathrm{O}\) bond angle. These subtle changes in bond angles can significantly influence their reactivity and physical properties, highlighting the importance of precise knowledge of molecular geometry.

Electron Pair Repulsion

Electron pair repulsion is a concept derived from VSEPR theory, stating that electron pairs around a central atom arrange themselves to minimize repulsive forces. This principle is crucial in predicting the molecular shape of many compounds, including \(\mathrm{H}_2\mathrm{O}_2\).

In hydrogen peroxide, the oxygen atoms have lone pairs that repel the bonding pairs, influencing the molecule's overall geometry and the \(\mathrm{H}-\mathrm{O}-\mathrm{O}\) bond angle. Since lone pairs repel more strongly than bonding pairs, they push the hydrogen atoms closer together, reducing the angle from what would be expected in a tetrahedral geometry.

The understanding of electron pair repulsion helps chemists anticipate how molecules will arrange spatially and predict their behavior in various environments. This determines not only the bond angles but also the resultant properties and interactions of the molecule. Thus, the application of VSEPR theory is vital for chemists seeking to understand molecular dynamics and properties effectively.