Identify Correct Statements Regarding Intermolecular Forces and Dipole Interactions

To determine the correct statements regarding intermolecular forces, let us evaluate each option individually based on the principles of chemical bonding and molecular interactions.

Evaluation of Option A:

• The potential energy between two point charges $q_1$ and $q_2$ separated by distance $r$ is given by Coulomb's law: $U_{\text{charge-charge}} = \frac{q_1 q_2}{4\pi \varepsilon_0 r} \propto \frac{1}{r}$

• The potential energy between a point charge $q$ and a point dipole $\mu$ separated by distance $r$ is: $U_{\text{dipole-charge}} \propto \frac{1}{r^2}$

As the distance $r \to \infty$, the factor $\frac{1}{r^2}$ decays to zero at a faster rate than $\frac{1}{r}$. Therefore, the dipole-charge potential energy approaches zero more rapidly than the charge-charge potential energy. Hence, Option A is incorrect.

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Evaluation of Option B:

• For two stationary (fixed orientation) polar molecules, the dipole-dipole interaction energy depends on distance as: $U_{\text{fixed dipole-dipole}} \propto \frac{1}{r^3}$

• However, for freely rotating polar molecules, thermal motion causes averaging over all rotational orientations. The resulting orientation-averaged potential energy (Keesom interaction) is given by: $U_{\text{Keesom}} = -\frac{2\mu_1^2 \mu_2^2}{3(4\pi \varepsilon_0)^2 k_B T r^6} \propto \frac{1}{r^6}$

Thus, the average potential energy for rotating polar molecules depends on $\frac{1}{r^6}$, not $\frac{1}{r^3}$. Hence, Option B is incorrect.

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Evaluation of Option C:

• The dipole-induced dipole interaction (Debye force) occurs between a polar molecule with a permanent dipole moment $\mu$ and a nonpolar molecule with polarizability $\alpha$. The thermally averaged interaction energy is given by: $U_{\text{Debye}} = -\frac{\mu^2 \alpha}{(4\pi \varepsilon_0)^2 r^6}$

Since this expression does not contain the thermal energy factor $k_B T$, the average interaction energy is independent of temperature. Hence, Option C is correct.

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Evaluation of Option D:

• Nonpolar molecules experience London dispersion forces (instantaneous dipole–induced dipole forces).
• Momentary fluctuations in the electron distribution of a nonpolar molecule create an instantaneous dipole, which induces a dipole in a neighboring nonpolar molecule, leading to a net attractive interaction: $U_{\text{dispersion}} \propto -\frac{1}{r^6}$

Therefore, nonpolar molecules attract one another even in the absence of a permanent dipole moment. Hence, Option D is correct.

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Conclusion:

The correct statements are C and D.