Question

The correct sequence of decrease in the bond angle of following hydrides is (a) \(\mathrm{NH}_{3}>\mathrm{PH}_{3}>\mathrm{AsH}_{3}>\mathrm{SbH}_{3}\) (b) \(\mathrm{NH}_{3}>\mathrm{AsH}_{3}>\mathrm{PH}_{3}>\mathrm{SbH}_{3}\) (c) \(\mathrm{SbH}_{3}>\mathrm{AsH}_{3}>\mathrm{PH}_{3}>\mathrm{NH}_{3}\) (d) \(\mathrm{PH}_{3}>\mathrm{NH}_{3}>\mathrm{AsH}_{3}>\mathrm{SbH}_{3}\)

Short answer

The correct sequence is (a) \( \mathrm{NH}_{3} > \mathrm{PH}_{3} > \mathrm{AsH}_{3} > \mathrm{SbH}_{3} \).

Step-by-step solution

Understand the Bonding in Hydrides

The hydrides mentioned are ammonia \( \mathrm{NH}_{3} \), phosphine \( \mathrm{PH}_{3} \), arsine \( \mathrm{AsH}_{3} \), and stibine \( \mathrm{SbH}_{3} \). These molecules are all hydrides of group 15 elements, and they have similar pyramidal structures affected by the central atom's size and electronegativity.

Analyze Atomic Size and Electronegativity

The elements N, P, As, and Sb increase in atomic size and decrease in electronegativity as you move down the group. Larger atoms tend to hold their bonding pairs further apart, leading to smaller bond angles.

Predict Bond Angles

In \( \mathrm{NH}_{3} \), the bond angle is significantly larger because of nitrogen's high electronegativity and small size, resulting in strong lone pair-bond pair repulsion. As the central atom increases in size and decreases in electronegativity (in \( \mathrm{PH}_{3}, \mathrm{AsH}_{3}, \mathrm{SbH}_{3} \)), the bond angles decrease due to less effective repulsion.

Identify Correct Sequence

The correct sequence involves the bond angle decreasing from \( \mathrm{NH}_{3} \) to \( \mathrm{SbH}_{3} \). Therefore, the correct option that reflects the decrease in bond angles is \( \mathrm{NH}_{3} > \mathrm{PH}_{3} > \mathrm{AsH}_{3} > \mathrm{SbH}_{3} \).

Conclusion

The sequence of bond angles decreasing is affected by increasing atomic size and decreasing electronegativity as you move down group 15. The correct answer is option \(a\).

Key concepts

Group 15 Hydrides

Group 15 elements consist of nitrogen (N), phosphorus (P), arsenic (As), antimony (Sb), and bismuth (Bi). These elements form hydrides by combining with hydrogen, resulting in the compounds NH₃ (ammonia), PH₃ (phosphine), AsH₃ (arsine), and SbH₃ (stibine).
All of these hydrides share a similar pyramidal molecular structure due to the presence of a lone pair of electrons on the central atom. This lone pair significantly influences the geometry of the molecule.
The central atom in each hydride has a total of four regions of electron density, comprising three bonding pairs of electrons and one lone pair. The spatial arrangement of these electron pairs follows the principles of VSEPR (Valence Shell Electron Pair Repulsion) theory, which helps predict the bond angles in these molecules.

Atomic Size

Atomic size or atomic radius increases as you move down the group in the periodic table. In Group 15, nitrogen is the smallest atom, while bismuth is the largest.
This increase in size as you go from NH₃ to SbH₃ is due to the addition of electron shells in the atoms. With larger atoms, the central atom holds its bonding pairs further apart, which decreases the bond angle between the hydrogen atoms.
Therefore, larger atomic size leads to a decrease in bond angles across the hydrides: from NH₃ to PH₃, AsH₃, and finally SbH₃. This change impacts the overall shape and properties of the molecule, reflecting how fundamental atomic properties translate to molecular behavior.

Electronegativity

Electronegativity describes an atom's ability to attract shared electrons in a chemical bond. In Group 15, this property decreases as you move down the group, with nitrogen being the most electronegative and antimony the least.
Higher electronegativity in nitrogen compared to phosphorus, arsenic, and antimony, means nitrogen strongly attracts the shared electrons, leading to a larger bond angle in NH₃. As a result, NH₃ has a higher bond angle compared to the other hydrides.
In contrast, as electronegativity decreases from NH₃ to SbH₃, the bond angles diminish because the central atom is less able to pull bonding pairs closer, reducing lone pair-bond pair repulsion.

Lone Pair-Bond Pair Repulsion

The concept of lone pair-bond pair repulsion is critical in determining the shape and bond angles of molecules like group 15 hydrides. Lone pairs of electrons are not shared between atoms and tend to occupy more space than bonding pairs, leading to stronger repulsive forces between lone pairs and bonding pairs.
In NH₃, the strong lone pair-bond pair repulsion due to nitrogen's high electronegativity and small atomic size increases the bond angle significantly. As we go to larger atoms like phosphorus, arsenic, and antimony, this repulsion decreases, resulting in smaller bond angles.
This principle helps explain why NH₃ has the largest bond angle of these hydrides. The decrease in lone pair-bond pair repulsion as the atomic size increases down the group is essential for predicting and understanding the molecular geometry of these compounds.