Chemistry - Ideal Gas Question with Solution | TestHub
ChemistryIdeal GasMaxwell's Distribution LawMedium2 minQB
ChemistryMediumsingle choice
Passage / Comprehension
According to Maxwell's distribution law, the fraction of molecules per unit change in speed [velocity distribution function, f(c)], traveling with speeds from C to C + dC, is:
f(c) = (1/dC)·(dN/N) = 4π·(M / 2πRT)3/2·C²·e(-MC²/2RT). (R = 8.0 J/K-mol, ln 2 = 0.7)
At what temperature are the speeds C₁ = 200 m/s and C₂ = 400 m/s of nitrogen molecules associated with equal values of the Maxwell distribution function f(c)?
Options:
Answer:
C
Solution:
Equal f(c) requires ln(c₂²/c₁²) = M(c₂² - c₁²)/2RT. Here ln 4 = 2ln 2 = 1.4 and c₂² - c₁² = 1.2×10⁵ m²/s², so T = 0.028 × 1.2×10⁵/(2 × 8 × 1.4) = 3360/22.4 = 150 K = -123°C. Hence Ans (c).
Stream:JEESubject:ChemistryTopic:Ideal GasSubtopic:Maxwell's Distribution Law
⏱ 2mℹ️ Source: QB
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