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 the speed from C to C + dC is given as:
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, the speeds of nitrogen gas molecules at C1 = 300 m/s and C2 = 600 m/s, are associated with equal value of Maxwell distribution function f(c)?
Options:
Answer:
C
Solution:
Equal f(c) needs c12 e-Mc12/2RT = c22 e-Mc22/2RT, i.e. ln(c22/c12) = M(c22 - c12)/2RT. Here ln(6002/3002) = ln 4 = 2ln 2 = 1.4 and c22 - c12 = 2.7 × 105 m2/s2. So T = M(c22-c12)/(2R × 1.4) = 0.028 × 2.7×105/(2 × 8 × 1.4) = 7560/22.4 = 337.5 K = 64.5°C. Hence Ans (c).
Stream:JEESubject:ChemistryTopic:Ideal GasSubtopic:Maxwell's Distribution Law
⏱ 2mℹ️ Source: QB
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