Hydrogen gas is contained in a closed vessel at 1atm(100kPa) and 300K. Calculate the mean speed of the molecules.

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)`