Heat and Thermodynamics 4 Question 4

4. A 25×103m3 volume cylinder is filled with 1 mole of O2 gas at room temperature (300K). The molecular diameter of O2 and its root mean square speed are found to be 0.3nm and 200m/s, respectively. What is the average collision rate (per second) for an O2 molecule?

(2019 Main, 10 April I)

(a) 1010

(b) 1012

(c) 1011

(d) 1013

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Solution:

  1. Given,

Volume, V=25×103m3

N=1 mole of O2=6.023×1023 atoms of O2,

T=300K

Root mean square velocity of a gas molecule of O2,vrms=200m/s

Radius, r=0.32nm=0.32×109m

Now, average time, 1τ=νavλ where,

λ=RT2Nπr2pp=RTVλ=V2Nπr2

Average collision per second,

1τ=vavλ=83π×vrmsλ1τ=83π×200×2×6.023×023×π×0.094×101825×1031τ=4.4×108 per second 108

No option given is correct.



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