Problem 47 - 43 Years JEE ADVANCED (1978-2020) + JEE MAIN Chapterwise & Topicwise Solved Papers Chemistry

Question

Match the type of interaction in column A with the distance dependence of their interaction energy in column B : A \(\quad\) B (I) ion-ion (A) \(\frac{1}{\mathrm{r}}\) (II) dipole-dipole (B) \(\frac{1}{\mathrm{r}^{2}}\) (III) London dispersion (C) \(\frac{1}{\mathrm{r}^{3}}\) (D) \(\frac{1}{\mathrm{r}^{6}}\) (a) \((\mathrm{I})-(\mathrm{B}),(\mathrm{II})-(\mathrm{D}),(\mathrm{III})-(\mathrm{C})\) (b) \((\mathrm{I})-(\mathrm{A}),(\mathrm{II})-(\mathrm{B}),(\mathrm{III})-(\mathrm{D})\) (c) (I)-(A), (II)-(B), (III)-(C) (d) (I)-(A), (II)-(C), (III)-(D)

Step-by-Step Solution

Answer

The correct option is (d): (I)-(A), (II)-(C), (III)-(D).

Step 1: Review Ion-Ion Interaction

Ion-ion interactions arise between charged particles. The energy of interaction between two ions is typically described by Coulomb's law, which depends inversely on the distance between the ions. Therefore, the distance dependence for ion-ion interaction is \( \frac{1}{r} \). This matches to option (A).

Step 2: Review Dipole-Dipole Interaction

Dipole-dipole interactions occur between molecules that have permanent dipole moments. The energy of this interaction falls off with the cube of the distance as the orientation of the dipoles is significant. Hence, the distance dependence for dipole-dipole interaction is \( \frac{1}{r^3} \). This matches to option (C).

Step 3: Review London Dispersion Forces

London dispersion forces, or van der Waals forces, are weak forces resulting from temporary fluctuations in electron distribution. These forces are significant at very short distances and the interaction energy decreases rapidly with distance, typically with \( \frac{1}{r^6} \) dependence. This matches to option (D).

Step 4: Match Interactions to Answer Choices

Using the information from steps 1 through 3, match the interactions to the corresponding distance dependence options:- Ion-ion: \( \frac{1}{r} \) (A)- Dipole-dipole: \( \frac{1}{r^3} \) (C)- London dispersion: \( \frac{1}{r^6} \) (D)This corresponds to answer choice (d): (I)-(A), (II)-(C), (III)-(D).

Key Concepts

Ion-Ion Interaction

Ion-ion interactions are the forces at play between charged particles, or ions. These interactions are central to the structure of ionic compounds, such as sodium chloride (table salt), where positive and negative ions attract each other.
Coulomb's law mathematically describes ion-ion interactions. According to this principle, the force and, consequently, the energy of interaction between two point charges depends on the inverse of the distance between them.
Simply put, as the distance increases, the force decreases, following the formula:

• Ion-Ion Energy: \( V \propto \frac{1}{r} \)

This means the closer the ions are, the stronger the interaction. Therefore, shorter distances result in greater attractive or repulsive forces between ions. The strength and specific characteristics of ion-ion interactions are key to understanding many physical properties of materials, including boiling points and solubility.

Dipole-Dipole Interaction

Dipole-dipole interactions occur in molecules that have a permanent electric dipole moment.
This happens when there is an unequal distribution of electrons between atoms in a molecule, resulting in partial positive and negative charges within the molecule.
This asymmetric electron cloud creates a dipole, and these dipoles interact with each other.
When two such dipole-bearing molecules are close, the positive end of one can attract the negative end of another, and vice versa.
The effectiveness of these interactions is heavily dependent on molecular orientation and their spatial arrangement, causing the interaction strength to decrease more rapidly with distance than ion-ion interactions.
These interactions typically follow the energy formula:

• Dipole-Dipole Energy: \( V \propto \frac{1}{r^3} \)

The nature of dipole-dipole interactions influences things like the melting and boiling points of substances, as well as solubility and the structure of the molecules within a compound.

London Dispersion Forces

London dispersion forces, also known simply as dispersion forces or van der Waals forces, are a type of weak intermolecular force.
They are present in all atoms and molecules, regardless of whether a permanent dipole exists.
These forces are the result of temporary fluctuations in electron density in a molecule or atom that create an instantaneous dipole moment.
This temporary dipole can induce a dipole in a neighboring atom, resulting in a weak attraction force.
London dispersion forces are incredibly short-range; their strength diminishes rapidly with increasing distance, as reflected in the energy formula:

• London Dispersion Energy: \( V \propto \frac{1}{r^6} \)

These forces are particularly important in non-polar compounds where no other types of dipole interactions can occur. They play a crucial role in the condensation of gases into liquids and the overall physical properties of nonpolar substances. The size of atoms and molecules can affect the strength of these forces, with larger atoms or molecules generally having stronger London dispersion forces.