The mean free path of molecules of a certain gas at STP is 1500 d, where d is the diameter of the gas molecules. While maintaining the standard pressure, the mean free path of the molecules at 373 K is approximately:

Solution

Physics sir · 4 steps

At fixed pressure, heating the gas spreads the molecules out, so the mean free path grows in step with T.

1. Mean free path formula. The mean free path depends on how many molecules are packed into each unit of volume. Using n = P/kT, it can be written in terms of T and P.

   λ = 1/(√2 π d² n) = kT/(√2 π d² P)

2. Fix the pressure. Here P and d do not change, so λ ∝ T. STP means T₁ = 273 K, and the new temperature is T₂ = 373 K.
3. Put in numbers. λ₂ = λ₁ × T₂/T₁ = 1500 d × 373/273 = 1500 d × 1.366 ≈ 2049 d.
4. So. The mean free path at 373 K is about 2049 d, option (c).

The idea to keep. Always ask what is held fixed. At constant pressure the number density falls as 1/T, so λ ∝ T. At constant volume the number density stays the same, so λ does not change.

Answer from the NTA final answer key. Solution by PrepWiser.