Problem 55 - A Complete Resource Book in Chemistry for JEE Main

Question

Which of the following has the lowest bond angle? (a) \(\mathrm{H}, \mathrm{O}\) (b) \(\mathrm{CH}_{4}\) (c) \(\mathrm{H}_{2} \mathrm{~S}\) (d) \(\mathrm{NH}_{3}\)

Step-by-Step Solution

Answer

H₂S has the lowest bond angle.

Step 1: Identify Molecular Geometry

To determine the molecule with the lowest bond angle, we first need to identify the molecular geometry of each molecule. This is based on the number of electron pairs around the central atom, including both bond pairs and lone pairs: - **(a) HO:** Diatomic, not applicable for bond angle. - **(b) CH₄:** Tetrahedral shape with no lone pairs. - **(c) H₂S:** Bent shape with two lone pairs due to its AX₂E₂ configuration. - **(d) NH₃:** Trigonal pyramidal shape with one lone pair.

Step 2: Predict Bond Angles from Geometry

Next, we use the identified geometries to predict the bond angles. Typically: - **Tetrahedral (like CH₄):** Bond angle is around 109.5°. - **Trigonal Pyramidal (like NH₃):** Bond angle is slightly less than 109.5° due to lone pair repulsion, around 107°. - **Bent (like H₂S):** Bond angle is further reduced due to lone pairs, generally around 92°.

Step 3: Compare Bond Angles

Compare the predicted bond angles: - **CH₄:** 109.5° - **NH₃:** 107° - **H₂S:** 92° The bond angle in H₂S is the smallest due to the significant lone pair repulsion in the bent configuration.

Key Concepts

Molecular Geometry

Molecular geometry is the three-dimensional arrangement of atoms within a molecule. It plays a critical role in determining the physical and chemical properties of substances. Several factors influence molecular geometry, including the number of bonding pairs and lone pairs of electrons around a central atom. Understanding molecular geometry allows us to predict the shape of a molecule, which in turn helps us understand its reactivity, polarity, phase of matter, color, magnetism, and biological activity.

• The Valence Shell Electron Pair Repulsion (VSEPR) theory is often used to predict molecular geometry by minimizing repulsion between electron pairs.
• The shape of a molecule and the angles between bonds can affect how a molecule will interact with others.

Grasping molecular geometry aids in comprehending the spatial relationships among atoms, which is a foundational concept in chemistry.

Tetrahedral Shape

A tetrahedral shape occurs when there are four bonds and no lone pairs around the central atom. This geometry results in bond angles of approximately 109.5°. The symmetry and equal distribution of electrons in tetrahedral molecules result in a stable structure.
Examples of molecules with a tetrahedral shape include methane (\(\mathrm{CH}_4\)). In methane, the carbon atom is central and is surrounded by four hydrogen atoms, forming a three-dimensional pyramid-like structure.

• Tetrahedral geometry ensures maximal separation between the bonded pairs of electrons.
• The angles between any two bonds in a perfect tetrahedron are all 109.5°, as they are trying to maintain the same distance for optimal stability.
• In practice, the perfect tetrahedral bond angle of 109.5° reflects the natural tendency of the atoms to arrange themselves as far apart as possible to minimize electron pair repulsion.

Trigonal Pyramidal Shape

The trigonal pyramidal shape is a molecular geometry that arises when there are three bonded atoms and one lone pair around a central atom. This geometry results in bond angles that are slightly less than the typical 109.5° seen in tetrahedral arrangements; for example, ammonia (\(\mathrm{NH}_3\)) has bond angles of approximately 107°.

• The presence of a lone pair introduces additional electron repulsion, pushing the bonded atoms closer together.
• This additional repulsion causes a slight reduction in the bond angle compared to a perfect tetrahedral shape.

An example is ammonia, where the nitrogen atom bears one lone pair, creating a distortion from a true tetrahedral angle. The lone pair occupies more space and consequently, squeezes the bond angle slightly, resulting in the observed geometry.

Bent Shape

The bent shape, commonly seen in molecules like water (\(\mathrm{H}_2\mathrm{O}\)) and hydrogen sulfide (\(\mathrm{H}_2\mathrm{S}\)), occurs when there are two bonded atoms and typically two lone pairs around the central atom. This results in a notable reduction in bond angles compared to other shapes like tetrahedral or trigonal pyramidal.

The Influence of Lone Pairs

Due to the presence of two lone pairs, the bond angles in bent-shaped molecules are significantly reduced, often falling between 104.5° to 92°. In \(\mathrm{H}_2\mathrm{S}\), the angle is around 92°, which is notably smaller.

• The lone pairs push the bonded atoms closer together as each lone pair occupies more space than bonding pairs which affects the bond angle drastically.
• Because of its small bond angle, the bent shape results in a more compact structure, which contributes to the molecule's polarity.

Understanding the bent shape is crucial for grasping concepts like molecular polarity and reactivity, as these are directly related to the spatial distribution of atoms within a molecule.