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How many of the following pairs of compounds have intermolecular interaction energy that is inversely proportional to the cube of the intermolecular distance (i.e., proportional to 1/r³)? (i) H2O + H2O (ii) CCl4 + C6H6 (iii) CHCl3 + CHCl3 (iv) Chlorobenzene + Fluorobenzene (v) K+ + I- (vi) He + Ne

1. 1
2. 2
3. 3
4. 4

Correct answer: 3

Solution

The interaction energy proportional to 1/r³ corresponds to: dipole-ion interaction (U ~ 1/r²) or dipole-dipole (Keesom, U ~ 1/r³ for the potential, but averaged orientation energy is 1/r⁶). Actually: dipole-dipole interaction energy (Keesom) for fixed orientation ~ 1/r³, but thermally averaged ~ 1/r⁶. Ion-dipole ~ 1/r². London (dispersion) ~ 1/r⁶. Ion-ion ~ 1/r. Dipole-induced dipole (Debye) ~ 1/r⁶. Strictly, interaction energy proportional to 1/r³ is the instantaneous dipole-dipole interaction (not thermally averaged). Pairs with permanent dipoles (dipole-dipole): (i) H2O+H2O (both polar), (iii) CHCl3+CHCl3 (both polar). K+ and I- is ion-ion (1/r). He+Ne are nonpolar noble gases (London, 1/r⁶). CCl4 is nonpolar; C6H6 is nonpolar — London (1/r⁶). Chlorobenzene (polar) + fluorobenzene (polar) — dipole-dipole (1/r³). So pairs with 1/r³ dependence: (i), (iii), (iv) = 3 pairs.

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