Kinetic Theory

JEE Main level, single correct, medium

59 of 168

Question 59 of 168

A 25×10−3m325\times {10}^{-3}{m}^{3} volume cylinder is filled with 11 mol of O2{O}_{2} gas at room temperature (300K)(300K) . The molecular diameter of O2{O}_{2} , and its root mean square speed, are found to be 0.3nm0.3nm and 200m/s200m/s , respectively. What is the average collision rate (per second) for an O2{O}_{2} molecule?

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Answer: (B)  1012~{10}^{12}

Average collision rate =nv−d2π=nv^{-} {d}^{2}\pi
=6.023×102325×10−3×83π×200×(0.3×10−9)2π≈4×10−12=\dfrac{6.023\times {10}^{23}}{25\times {10}^{-3}}\times \sqrt{\dfrac{8}{3\pi }}\times 200\times {\left(0.3\times {10}^{-9}\right)}^{2}\pi \approx 4\times {10}^{-12}

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