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On a Maxwell-Boltzmann speed distribution plot (distribution function f(v) vs speed v), three curves are labelled I, II, and III. The most probable speed (Vmp) is proportional to sqrt(2RT/M). Which of the following correctly identifies the three peaks I (leftmost), II (middle), and III (rightmost) corresponding to Vmp values of different gases at given temperatures?

1. Vmp of N2 (300K); Vmp of H2(300K); Vmp of O2(400K)
2. Vmp of H2 (300K); Vmp of N2(300K); Vmp of O2(400K)
3. Vmp of O2 (400K); Vmp of N2(300K); Vmp of H2(300K)
4. Vmp of N2 (300K); Vmp of O2(400K); Vmp of H2(300K)

Correct answer: Vmp of N2 (300K); Vmp of O2(400K); Vmp of H2(300K)

Solution

Vmp is proportional to sqrt(T/M). Computing the ratio: N2 at 300K gives sqrt(300/28)=3.27, O2 at 400K gives sqrt(400/32)=3.54, H2 at 300K gives sqrt(300/2)=12.25. Ranking I (lowest Vmp, leftmost peak) to III (highest Vmp, rightmost peak): I = N2(300K), II = O2(400K), III = H2(300K).

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