Hydrogen gas is contained ina closed vessel at 1atm(100kPa) and 300K.(a) Calculate the mean speed pf the molecules. (b) Suppose the molecules strike the wall with this speed making an average angle of `45^(@)`with it. How many molecules strike each squre metre ifj the wall per second?

Explanation

`P= 1 atm =10^5 pascal`
`T = 300K`
` M= 2g= 2 xx 10^-3kg `
(a) V_avg = (sqrt (8 RT)/ (sqrt(pi M)))`
` = (sqrt (8 xx 8.3 xx 300)/(sqrt(3.14 xx 2 xx (10^-3))))`
` = (sqrt (8 xx 8.3 xx 300 xx (10^3))/ (sqrt(3.14 xx 2)))`
`= 1781.004 =1780 m//s`
(b) When the molecules strike at an angle
`45^@,`
force exerted
`=mV(cos 45^@)-(-mV(cos 45^@))`
` = 2 m V (cos 45^@)`
= `(2mV/(sqrt 2)) = (sqrt 2)mV`
Number of molecules striking per unit
area
`= force/((sqrt 2)mV xx Area)`
` = Pressure/((sqrt 2)m V)`
` (10^5)/(((sqrt 2)xx 2 xx (10^-3) xx 1780)/(6 xx (10^23))`
` =(3 xx (10^31)/2516.92)`
` =1.19 xx (10^-3) xx (10^31)`
` = 1.19 xx (10^28) xx =1.2 xx (10^28)`