A 25 × 10–3 m3 volume cylinder is filled with 1 mol of O2 gas at room… | JEE Main 2019 (10 Apr, Shift 1)

Q22JEE Main 2019 · 10 APR · SHIFT 1Medium

Mean Free Path & Real Gases

A 25 × 10–3 m3 volume cylinder is filled with 1 mol of O2 gas at room temperature (300K). The molecular diameter of O2, and its root mean square speed, are found to be 0.3 nm, and 200 m/s, respectively. What is the average collision rate (per second) for an O2 molecule?

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Answer: (b)

Number density $n = \dfrac{N_A}{V} = \dfrac{6.02\times10^{23}}{25\times10^{-3}} = 2.4\times10^{25}\text{ m}^{-3}$
Collision rate $f = \sqrt{2}\,n\pi d^2 v = 1.414\times2.4\times10^{25}\times3.14\times9\times10^{-20}\times200$
$f \approx 1.9\times10^{9}\text{ s}^{-1}$ , of order $10^{9}$ – $10^{10}$ per second.
Nearest option is (d) $\sim10^{10}$ ; key gives (b) $\sim10^{12}$ .

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