One gram mole `NO_2 "at" 47^@ C` and 2 atm pressure in kept in a vessel. Assuming the molecules to be moving with (rms) velocity. Find the number of collisions per which the molecules make with one square metre area of the vessel wall.

Answer

A, B, C

Explanation

`v _(r m s) = sqrt((3 R T)/(M)) = sqrt((3xx8.31 xx (273 + 57))/(46 xx 10^-3))`
= `423 m//s`
(##DCP_V03_C20_E01_090_S01##).
`Delta p =2 m v_( r m s)`
Mass of one gas molecule,
`m = (46)/(6.02 xx 10^23) g`
=`7.64 xx 10^-26 kg`
Let (n) molecules strike per second per unit area. Then,
Pressure `= F/A = (Delta P// Delta t)/A = (2 m n) v _(rms)`
`:. n = ("Pressure")/((2m)v_(r m s))=(2 xx 1.013 xx 10^5)/(2 xx 7.64 xx 10^-26 xx 423)`
= `3.1 xx 10^27`.