Worked example
A JEE Advanced-level example
Question. Arrange the following interactions in order of how quickly their energy decreases as intermolecular distance doubles: (i) ion-dipole, (ii) dipole-dipole (fixed orientation), (iii) London dispersion. Also calculate the factor by which each interaction energy decreases when r becomes 2r.
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- Step 1: Write the distance dependence for each. Ion-dipole: U ∝ 1/r². Dipole-dipole (fixed): U ∝ 1/r³. London: U ∝ 1/r⁶.
- Step 2: When r → 2r, the new energy U' = U × (1/2)ⁿ where n is the power of r in the denominator.
- Step 3: For ion-dipole (n=2): U' = U × (1/2)² = U/4. Energy becomes 1/4 of original.
- Step 4: For dipole-dipole (n=3): U' = U × (1/2)³ = U/8. Energy becomes 1/8 of original.
- Step 5: For London (n=6): U' = U × (1/2)⁶ = U/64. Energy becomes 1/64 of original.
- Step 6: Order of fastest decrease: London (64×) > dipole-dipole (8×) > ion-dipole (4×).
Answer: London dispersion decreases fastest (to 1/64), then dipole-dipole (to 1/8), then ion-dipole (to 1/4). Order: London > dipole-dipole > ion-dipole.
Solved twice independently; both solutions agree.