Problem 90 - A Complete Resource Book in Chemistry for JEE Main

Question

Which of the following is arranged in the increasing order of enthalpy of vaporization? (a) \(\mathrm{PH}_{3}, \mathrm{AsH}_{3}, \mathrm{NH}_{3}\) (b) \(\mathrm{AsH}_{3}, \mathrm{PH}_{3}, \mathrm{NH}_{3}\) (c) \(\mathrm{NH}_{3}, \mathrm{AsH}_{3}, \mathrm{PH}_{3}\) (d) \(\mathrm{NH}_{3}, \mathrm{PH}_{3}, \mathrm{AsH}_{3}\)

Step-by-Step Solution

Answer

Option (a): \( \mathrm{PH}_{3}, \mathrm{AsH}_{3}, \mathrm{NH}_{3} \).

Step 1: Understand Enthalpy of Vaporization

Enthalpy of vaporization is the energy required to convert a substance from a liquid to its gaseous state. Substances with stronger intermolecular forces require more energy and thus have a higher enthalpy of vaporization.

Step 2: Analyze Given Compounds

Consider the three given compounds: - \(NH_3\) (ammonia), - \(PH_3\) (phosphine), - \(AsH_3\) (arsine).Evaluate their intermolecular forces, particularly looking at hydrogen bonding.

Step 3: Evaluate Intermolecular Forces

- \(NH_3\) can form strong hydrogen bonds because of its hydrogen atoms connected to nitrogen, which is highly electronegative.- \(PH_3\) and \(AsH_3\) exhibit weaker van der Waals forces due to the less electronegative phosphorus and arsenic.

Step 4: Arrange in Order of Increasing Enthalpy

Since \(NH_3\) has hydrogen bonds, it will have the highest enthalpy of vaporization. The order of enthalpy should be evaluated based on decreasing hydrogen bond presence and increasing molecular weight: \(PH_3 < AsH_3 < NH_3\).

Step 5: Match with Options

The analysis provides the order \(PH_3 < AsH_3 < NH_3\). Compare this order with the given options. Option (a): \(PH_3, AsH_3, NH_3\) is correct.

Key Concepts

Intermolecular forces

Intermolecular forces are the forces that act between molecules. These forces hold molecules together and determine many of their physical properties, such as boiling point and enthalpy of vaporization. Substances with strong intermolecular forces will typically have higher boiling points and require more energy to vaporize.
Ammonia ( NH_3"), phosphine ( PH_3"), and arsine ( AsH_3") are held together by such forces, but the strength of these forces varies.

• Hydrogen bonding: A strong type of intermolecular force, hydrogen bonding occurs in NH_3" because the nitrogen atom is highly electronegative and able to connect with hydrogen atoms.
• Van der Waals forces: PH_3" and AsH_3" mainly exhibit these weaker forces. They arise due to temporary dipoles and are generally less strong than hydrogen bonds.

Understanding these forces helps explain why NH_3" has a higher enthalpy of vaporization compared to PH_3" and AsH_3".

Hydrogen bonding

Hydrogen bonding is a particularly strong type of dipole-dipole interaction. It happens when hydrogen is bonded to a highly electronegative atom like nitrogen, oxygen, or fluorine. This type of bond is especially evident in NH_3".
In ammonia, nitrogen's high electronegativity pulls electron density away from hydrogen, creating a partial positive charge on hydrogen and a partial negative charge on nitrogen. This allows each hydrogen atom to form a bond with a nitrogen atom from another molecule of NH_3", resulting in a network of interactions.

• This bonding increases the amount of energy needed to move ammonia molecules from the liquid to gaseous phase.
• The result is a higher enthalpy of vaporization for NH_3" compared to other molecules like PH_3" and AsH_3" that lack this strong interaction.

This makes hydrogen bonding a critical factor when comparing the energy requirements for vaporization among these compounds.

Molecular weight analysis

Molecular weight refers to the combined atomic weights of all the atoms in a molecule. It can influence physical properties such as boiling point and enthalpy of vaporization. As molecules get heavier, typically, more energy is needed to vaporize them because heavier molecules tend to have stronger dispersion forces.
In comparing NH_3", PH_3", and AsH_3":

• NH_3" has the lowest molecular weight at 17 g/mol.
• PH_3" is heavier at 34 g/mol.
• AsH_3" is the heaviest at 78 g/mol.

Despite the increasing molecular weight from NH_3" to AsH_3", the order of enthalpy of vaporization is affected more by hydrogen bonding in NH_3".
Thus, although molecular weight can indicate trends in energy requirements, unique factors such as hydrogen bonding can significantly alter these predictions, as seen with NH_3" having the highest enthalpy of vaporization even though it is the lightest.