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Physics · KINETIC THEORY

हिन्दी

The density of liquid water is \( 1000\text{ kg m}^{-3} \) and the density of water vapour at \( 100^\circ\text{C} \) and \( 1\text{ atm} \) is \( 0.6\text{ kg m}^{-3} \). Assuming water molecules are packed closely in the liquid phase, if the average distance between molecules in liquid water is approximately \( 2\text{ Å} \), what is the average interatomic/intermolecular distance in the vapour phase under these conditions?

  1. A
    \( 20\text{ Å} \)
  2. B
    \( 24\text{ Å} \)
  3. C
    \( 120\text{ Å} \)
  4. D
    \( 40\text{ Å} \)
View Answer & Solution

Correct answer · Option B

\( 24\text{ Å} \)

Explanation

The ratio of volume in vapour to liquid is \( \frac{1000}{0.6} \approx 1667 \). Linear dimension scales as \( (1667)^{1/3} \approx 11.86 \), giving an interatomic distance of \( 2\text{ Å} \times 11.86 \approx 23.7\text{ Å} \approx 24\text{ Å} \).
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