Problem 191 - A Complete Resource Book in Chemistry for JEE Main

Question

The correct order of bond angles (smallest first) in \(\mathrm{H}_{2} \mathrm{~S}, \mathrm{NH}_{3}, \mathrm{BF}_{3}\) and \(\mathrm{SiH}_{4}\) is (a) \(\mathrm{H}_{2} \mathrm{~S}<\mathrm{SiH}_{4}<\mathrm{NH}_{3}<\mathrm{BF}_{3}\) (b) \(\mathrm{NH}_{3}<\mathrm{H}_{2} \mathrm{~S}<\mathrm{SiH}_{4}<\mathrm{BF}_{3}\) (c) \(\mathrm{H}_{2} \mathrm{~S}<\mathrm{NH}_{3}<\mathrm{SiH}_{4}<\mathrm{BF}_{3}\) (d) \(\mathrm{H}_{2} \mathrm{~S}<\mathrm{NH}_{3}<\mathrm{BF}_{3}<\mathrm{SiH}_{4}\)

Step-by-Step Solution

Answer

The correct order is (c) \(\mathrm{H}_{2}\mathrm{~S}<\mathrm{NH}_{3}<\mathrm{SiH}_{4}<\mathrm{BF}_{3}\).

Step 1: Determine the Bond Angles

First, establish the typical bond angles for each of the molecules based on their geometry. \(\text{H}_2\text{S}\) typically has a bond angle less than \(109.5^\circ\) due to lone pair repulsions on sulfur. \(\text{NH}_3\) has a bond angle of about \(107.3^\circ\) due to lone pair-bond pair repulsion. \(\text{BF}_3\) has a trigonal planar structure with bond angles of \(120^\circ\). \(\text{SiH}_4\) has a tetrahedral structure with bond angles of \(109.5^\circ\).

Step 2: Compare the Bond Angles

List the molecules in order of increasing bond angles interpreted from their molecular structure. \(\text{H}_2\text{S}\) will have the smallest bond angle due to lone pairs. Next comes \(\text{NH}_3\), also affected by lone pairs. \(\text{SiH}_4\) has bond angles of \(109.5^\circ\). Finally, \(\text{BF}_3\) has the largest bond angles at \(120^\circ\).

Step 3: Verify the Order with the Given Choices

Check the options provided against the established order of bond angles: \(\text{H}_2\text{S} < \text{NH}_3 < \text{SiH}_4 < \text{BF}_3\). Identify which choice matches this order.

Key Concepts

Molecular Geometry

Molecular geometry is the three-dimensional arrangement of atoms within a molecule. It significantly affects the physical and chemical properties of a molecule, including factors like reactivity, phase of matter, color, magnetism, and especially bond angles. Bond angles are determined by the molecular shape, which is influenced by the number of bonds and lone pairs around the central atom.

Understanding molecular geometry involves considering VSEPR (Valence Shell Electron Pair Repulsion) theory, which predicts the shape of the molecule based on the repulsion between electron pairs in the valence shell of the central atom. The arrangement aims to minimize this repulsion, leading to specific shapes, such as linear, trigonal planar, tetrahedral, and more.

For instance, \( ext{H}_2 ext{S}\) has a bent shape, \( ext{NH}_3\) adopts a trigonal pyramidal shape, \( ext{SiH}_4\) is tetrahedral, and \( ext{BF}_3\) is trigonal planar. Recognizing these shapes helps in predicting and comparing bond angles effectively.

Lone Pair Repulsion

Lone pair repulsion is a crucial factor in determining molecular geometry and bond angles. Lone pairs are pairs of valence electrons that are not involved in forming bonds. These pairs occupy more space than bonded pairs due to their higher electron density. As a result, they exert a stronger repulsive force on surrounding electron pairs, thus altering bond angles.

In \( ext{NH}_3\), for example, there is one lone pair on the nitrogen atom that pushes the hydrogen atoms closer together, reducing the bond angle from the ideal \109.5^\circ\ in a tetrahedral arrangement to approximately \107.3^\circ\.

Similarly, \( ext{H}_2 ext{S}\) has two lone pairs on the sulfur atom. This strong repulsive force reduces its bond angles even further, resulting in angles slightly less than \109.5^\circ\. Understanding lone pair repulsion helps explain why certain molecules deviate from their "ideal" geometrical angles.

Bond Angle Comparison

Bond angle comparison involves analyzing and ranking the bond angles across different molecules, usually starting from the smallest to the largest.

In the context of the given molecules, \( ext{H}_2 ext{S}\) has the smallest bond angle due to significant lone pair effects reducing the angle below \109.5^\circ\. \( ext{NH}_3\) follows next with a bond angle of approximately \107.3^\circ\, also diminished due to lone pair-bond pair repulsion.

While both \( ext{SiH}_4\) and \( ext{BF}_3\) do not have any lone pairs, their bond angles are significantly different. \( ext{SiH}_4\) maintains a perfect tetrahedral bond angle of \109.5^\circ\, unaffected by lone pairs. On the other hand, \( ext{BF}_3\) forms a trigonal planar, leading to larger angles of \120^\circ\. The comparison of these angles is essential for understanding molecular interactions and reactions.

Tetrahedral Structure

A tetrahedral structure is a common molecular geometry where four bonds are symmetrically arranged around a central atom at an angle of \109.5^\circ\. This shape is observed when there are no lone pairs on the central atom, allowing the four groups to repel each other equally.

In molecules like \( ext{SiH}_4\), the central silicon atom is bonded to four hydrogen atoms. The lack of lone pairs on silicon ensures that the repulsions between electron pairs maintain an ideal tetrahedral shape.

One significant aspect of a tetrahedral structure is its consistent bond angles, which are crucial in maintaining stability in three-dimensional space. This geometry is particularly important in complex organic and biochemical compounds, where tetrahedral carbon centers determine the shape of the molecule.

Trigonal Planar Structure

A trigonal planar structure occurs when three atoms are bonded to a central atom, forming a flat, triangular shape with bond angles of \120^\circ\. This geometry usually arises when there are no lone pairs on the central atom, allowing the bonded atoms to spread out evenly in a plane.

For \( ext{BF}_3\), the boron atom forms three single bonds with fluorine atoms. The absence of lone pairs on boron results in the \120^\circ\ bond angles corresponding to a perfect trigonal planar shape.

Trigonal planar structures are fundamental in the field of molecular chemistry, presenting a unique 2D arrangement distinct from the 3D tetrahedral configuration. This structure is critical in understanding the behavior of molecules in reactions, as the planar nature impacts how molecules interact with each other.