The correct order of increasing boiling points of hydrides (given below) of group 15 is:

(A) \(NH_3\)

(B) \(PH_3\)

(C) \(AsH_3\)

(D) \(SbH_3\)

(E) \(BiH_3\)

Choose the correct answer from the options given below:

B < C < A < D < E

The correct answer is option 3. B < C < A < D < E.

Here is a detailed explanation of the boiling points of Group 15 hydrides and why the correct order is \( \text{PH}_3 < \text{AsH}_3 < \text{NH}_3 < \text{SbH}_3 < \text{BiH}_3 \) (Option 3):

The hydrides of Group 15 elements (Nitrogen, Phosphorus, Arsenic, Antimony, and Bismuth) are as follows:

A. Ammonia (\(NH_3\))

B. Phosphine (\(PH_3\))

C. Arsine (\(AsH_3\))

D. Stibine (\(SbH_3\))

E.Bismuthine (\(BiH_3\))

Factors Influencing Boiling Points:

Hydrogen Bonding:

NH\(_3\): Ammonia can form hydrogen bonds due to the high electronegativity of nitrogen and the presence of lone pairs on the nitrogen atom. Hydrogen bonding significantly raises the boiling point compared to other hydrides in this group.

van der Waals Forces:

These are the forces between molecules that increase with molecular mass. As the size and mass of the molecules increase, the strength of van der Waals forces increases, leading to higher boiling points.

Detailed Analysis:

B.Phosphine (\(PH_3\)):

Boiling Point: \(-87.7^\circ \text{C}\)

Reason: Phosphine has the lowest boiling point among the Group 15 hydrides. It has weak van der Waals forces and does not form hydrogen bonds because phosphorus is less electronegative and the bonding is not strong enough for hydrogen bonding.

C. Arsine (\(AsH_3\)):

Boiling Point: \(-62.5^\circ \text{C}\)

Reason: Arsine has a higher boiling point than phosphine due to its greater molecular mass, which results in stronger van der Waals forces. However, it still does not have hydrogen bonding.

A. Ammonia (\(NH_3\)):

Boiling Point: \(-33.34^\circ \text{C}\)

Reason: Ammonia has the highest boiling point among the first three hydrides because it forms hydrogen bonds. This strong intermolecular interaction significantly raises its boiling point compared to phosphine and arsine.

D. Stibine (\(SbH_3\)):

Boiling Point: \(-17^\circ \text{C}\)

Reason: Stibine has a higher boiling point than ammonia due to its higher molecular mass and stronger van der Waals forces. Despite the absence of hydrogen bonding, the larger size and mass lead to stronger intermolecular forces.

E. Bismuthine (\(BiH_3\)):

Boiling Point: \(16.8^\circ \text{C}\)

Reason: Bismuthine, with the largest molecular mass among these hydrides, has the highest boiling point due to the strongest van der Waals forces. The boiling point is higher than stibine because of its larger molecular size and mass.

Given the above analysis, the correct order of increasing boiling points for the Group 15 hydrides is: \(PH_3 < AsH_3 < NH_3 < SbH_3 < BiH_3\)

This matches Option 3.