States of Matter

States of Matter

Question

The intermolecular interaction that is dependent on the inverse cube of the distance between the molecule is:

  • ion-ion interaction

  • ion-dipole interaction

  • London force

  • hydrogen bond

Answer

B.

ion-dipole interaction

 ion-ion interaction is dependent on the square of the distance,
i.e, ion-ion interaction ∝ 1/r2
Similarly, 
ion-dipole interaction ∝ 1/r3
London forces ∝ 1/r6
and dipole-dipole interactions ∝ 1/r3
superficially it seems as both ions interaction and hydrogen bonding vary with the inverse cube of the distance between the molecules but when we look at the exact expressions of field (force) created in two situations it comes as,
In the case of ion-dipole interaction:
vertical line straight E vertical line space or space vertical line straight F vertical line space equals space fraction numerator 2 vertical line straight P vertical line over denominator 4 πε subscript straight o straight r cubed end fraction
and, In the case of dipole-dipole interaction
straight F space equals space fraction numerator 2 straight q squared straight r minus 4 straight q squared straight a over denominator 4 πε subscript straight o straight r cubed end fraction
From the above it is very clear, the ion-dipole interaction is the better answer as compared dipole-dipole interaction i.e. hydrogen bonding.

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