Animated Solution for Chemistry - States of Matter: The correct statements (s) about intermolecular forces is(are)

Welcome to the fascinating world of intermolecular forces! In this problem, we are tasked with evaluating four distinct statements regarding how different types of particles interact with each other over a distance.

The core concept to remember is that the interaction energy $E$ between particles is generally proportional to $\frac{1}{r^n}$, where $r$ is the distance separating them. The larger the exponent $n$, the more rapidly the energy drops to zero as the distance increases. Let's keep this mathematical reality in mind as we dissect each option.

Let's begin with statement A, which compares ion-ion and ion-dipole interactions. First, consider two point charges, representing an ion-ion interaction. According to Coulomb's law, their potential energy is proportional to $\frac{1}{r}$.

Now, contrast this with an ion-dipole interaction. Because a dipole consists of two equal and opposite charges separated by a very small distance, its electric field partially cancels out and falls off much faster. Consequently, the potential energy for an ion-dipole interaction is proportional to $\frac{1}{r^2}$.

So, which one approaches zero more rapidly as the distance $r$ approaches infinity? Mathematically, $\frac{1}{r^2}$ decays much faster than $\frac{1}{r}$. Therefore, the ion-dipole energy approaches zero more rapidly. Statement A claims the exact opposite, making it false.

Moving on to statement B, we encounter two rotating polar molecules. When polar molecules are in a fluid state, thermal energy causes them to constantly rotate and tumble, rapidly changing their dipole orientations.

The average interaction energy over all these random orientations is known as the Keesom interaction. Because the attractive and repulsive orientations partially average out, the effective energy drops off very steeply, exhibiting a $\frac{1}{r^6}$ dependence. Statement B incorrectly claims it has a $\frac{1}{r^3}$ dependence, which is only true for stationary, perfectly aligned dipoles in a solid lattice. Thus, statement B is false.

Let's examine statement C, which discusses the dipole-induced dipole interaction, also known as the Debye force. In this scenario, a permanent dipole approaches a polarizable molecule and distorts its electron cloud, inducing a temporary dipole.

The strength of this interaction depends solely on the polarizability of the second molecule and the dipole moment of the first. Crucially, the induced dipole is always perfectly aligned to be attractive with the permanent dipole, regardless of how the molecules are tumbling. Because thermal rotation doesn't disrupt this alignment, the interaction is completely independent of temperature. Therefore, statement C is true.

Finally, we arrive at statement D. Can nonpolar molecules, which lack a permanent dipole, actually attract each other? Yes, they absolutely can!

Even in perfectly nonpolar molecules, the electrons are in constant motion. At any given instant, the electron distribution might become slightly asymmetrical, creating a temporary, instantaneous dipole. This fleeting dipole then induces a corresponding dipole in a neighboring molecule, leading to a net attractive force known as the London dispersion force. This universal force is the very reason why nonpolar gases like helium or methane can be condensed into liquids. Hence, statement D is true.

To summarize our rigorous analysis, statements A and B are incorrect due to flawed distance dependencies. Conversely, statements C and D accurately describe the physics behind dipole-induced dipole and London dispersion forces. Therefore, the correct options are C and D.