Chemistry - Ideal Gas Question with Solution | TestHub
A container contains 1 mole of an ideal gas at 27°C. It is heated to 927°C. Match Column I (parameters) with Column II (increases by a factor)
Column I | Column II |
|---|---|
A) Mean free path, λ | P) 1 (at constant volume) |
B) Collision number, Z₁ | Q) 2 (at constant volume) |
C) Collision frequency, Z₁₁ | R) 1/2 (at constant pressure) |
| S) 4 (at constant pressure) |
Options:
Answer:
Solution:
T rises from 300 K to 1200 K, a factor of 4, so √(T) rises by a factor of 2. λ = 1/(√(2)πd²(N/V)): at constant V it is unchanged, factor 1 (P); at constant P, V grows 4 times so N/V falls to 1/4 and λ grows 4 times, factor 4 (S), hence AP,S. Z₁ ∝ √(T)(N/V): at constant V the factor is 2 (Q); at constant P, N/V ∝ 1/T so Z₁ ∝ √(T)/T = 1/√(T), factor 1/2 (R), hence BQ,R. Z₁₁ ∝ √(T)(N/V)²: at constant V the factor is 2 (Q); at constant P it is √(T)/T² = 4-3/2 = 1/8, not listed, so CQ only. Hence AP,S; BQ,R; CQ.
