Question

Please help with question, stuck on it. Please show all work of solution to comprehend it.

1.) In the simple kinetic theory of a gas, the molecules are assumed to be point-like objects (without any volume) so that they rarely collide with one another. In reality, each molecule has a small volume and so there are collisions. Let's assume that a molecule is a hard sphere of radius r. Then the molecules will occasionally collide with each other. The average distance traveled between two successive collisions (called mean free path) is λ = V/(4π √2 r²N) where V is the volume of the gas containing N molecules.

a)Calculate the mean free path of a H₂ molecule in a hydrogen gas tank at STP. Assume the molecular radius to be 10^-10m.

b)The rms speed at temperature T is √(3k_BT/m). The average speed is slightly different:

v_avg = √(8k_BT/πm)

     What is v_avg for a H₂ molecule at STP?

c) Assuming that an average molecule travels with v_avg, what would be the average time between two successive collisions?

Answer 1

a) The mean free path λ:V USIn ks Balt3mann Constent At sTP ''Temperature Teo.こ273.IS k and pressure P=los Pa < molecular adius λ = 1-3&X) 23x 273.is A2.12 Xio 7mmean free path averoge speed Vavg mass of H olecule m 332xiskg -23 So Vavj- The average speed for a H2 nalecule at i STP-1700- c) The averoge time bejween the CoMisions 700.