Problem 10 - 43 Years JEE ADVANCED (1978-2020) + JEE MAIN Chapterwise & Topicwise Solved Papers Chemistry

Question

The intermolecular interaction that is dependent on the inverse cube of distance between the molecules is: (a) London force (b) hydrogen bond (c) ion - ion interaction (d) ion - dipole interaction

Step-by-Step Solution

Answer

The correct answer is (d) ion - dipole interaction.

Step 1: Understanding the Question

The problem is asking about a type of intermolecular force that varies with the inverse cube of the distance between molecules. We need to identify which of the given options fits this description.

Step 2: Option Analysis: London Forces

London forces, also known as dispersion forces, are a type of van der Waals force that occurs between non-polar molecules. They typically depend on the inverse sixth power of the distance between molecules.

Step 3: Option Analysis: Hydrogen Bonds

Hydrogen bonds occur between a hydrogen atom attached to an electronegative atom (like N, O, or F) and another electronegative atom. The strength of hydrogen bonds does not vary with the cube of the distance as they are more dominated by directional preferences.

Step 4: Option Analysis: Ion-Ion Interaction

Ion-ion interactions involve electrostatic forces between charged ions. These interactions typically depend on the inverse square of the distance between the ions, not the cube of the distance.

Step 5: Option Analysis: Ion-Dipole Interaction

Ion-dipole interactions occur between a charged ion and a polar molecule. These interactions depend on the inverse cube of the distance, as they involve interactions between the charge of an ion and the dipole moment of a molecule, which decrease rapidly with increased distance.

Step 6: Determining the Correct Answer

Since ion-dipole interactions vary with the inverse cube of the distance, the correct answer is (d) ion - dipole interaction.

Key Concepts

Inverse Cube Law

The inverse cube law describes a type of interaction where the strength of a force sharply decreases with increased distance. This is seen in certain types of intermolecular forces. If the force \( F \) is inversely proportional to the cube of the distance \( r \), it can be expressed as \( F \propto \frac{1}{r^3} \). This means as the distance triples, the force becomes \( \frac{1}{27} \) of its original strength.

Such a rapid decrease can significantly impact how molecules or ions interact with each other over varying distances. For example, in an ion-dipole interaction, as the charged ion moves further away from a polar molecule, the interaction force diminishes quickly, changing the dynamics of molecular interactions.

Ion-Dipole Interaction

Ion-dipole interactions are forces between a charged ion and a polar molecule. These are critical in many chemical reactions and biological processes. A prime example is when salt (NaCl) dissolves in water, where ions interact with water molecules.

The ion, having an electric charge, attracts the dipole of a polar molecule. The positive or negative end of the molecule aligns toward the ion, creating an attractive force. Ion-dipole forces are stronger than van der Waals forces but weaker than covalent bonds.

Importantly, ion-dipole interactions vary with the inverse cube of the distance. Therefore, as the distance between the ion and dipole increases, the force decreases quite rapidly. This rapid decrease is a defining characteristic of these interactions and influences their behavior significantly in various states of matter.

Molecular Distance Dependence

Molecular distance dependence refers to how the strength of an interaction changes based on the distance between molecules or ions. Different intermolecular forces have varying dependence on distance.

• **Ion-ion interactions:** Depend on the inverse square of the distance and diminish less rapidly compared to ion-dipole interactions.
• **Dispersion (London) forces:** Depend on the inverse sixth power, so they decrease extremely rapidly with distance.
• **Ion-dipole interactions:** Follow the inverse cube law, decreasing swiftly but not as quickly as dispersion forces.

Understanding how these forces change with distance is crucial in fields like chemistry and physics, where predicting the behavior of substances at the molecular level is essential. This concept helps explain differences in boiling and melting points, solubility, and the stability of compounds.