A `25xx10^(-3)m^(3)` volume cylinder is filled with 1 mol of `O_2` gas at room temperature (300 K).The molecular diameter of `O_2`, 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 `O_2` molecule ?

Options

A. `-10^11`
B. `-10^(12)`
C. `-10^(10)`
D. `-10^(12)`

Answer

C

Explanation

collision frequency `=pid^2 sqrt(2) V_(" avg ")(nN_(A))/(V)`
`V_(" avg ")` : Avg. speed
V. Volume of container
Putting values
Collision frequency `=3.14xx(0.3xx10^(-9))^2xx sqrt(2)xx sqrt((9)/(3pi))xx V_(rms) xx (1xx6.023xx10^(23))/(25xx10^(-3)) { V(" avg. ")= sqrt((8)/(3pi))V_(rms)}`
`=3.14xx(0.3xx10^(-9))^2xx sqrt(2)xx sqrt((8)/(3pi))xx 200xx (1xx6.023xx10^(23))/(25xx10^(-3)) approx 1.8xx10^(9) approx 10^(10)` order.