Force exerted by one molecule on container wall

[Himanshu_6174]

I came across this problem in University Physics:

(a) Oxygen 1O22 has a molar mass of 32.0 g>mol. What
is the average translational kinetic energy of an oxygen molecule
at a temperature of 300 K? (b) What is the average value of the
square of its speed? (c) What is the root-mean-square speed? (d)
What is the momentum of an oxygen molecule traveling at this
speed? (e) Suppose an oxygen molecule traveling at this speed
bounces back and forth between opposite sides of a cubical vessel
0.10 m on a side. What is the average force the molecule exerts on
one of the walls of the container? (Assume that the molecule’s
velocity is perpendicular to the two sides that it strikes.) (f ) What
is the average force per unit area? (g) How many oxygen mole-
cules traveling at this speed are necessary to produce an average
pressure of 1 atm? (h) Compute the number of oxygen molecules
that are actually contained in a vessel of this size at 300 K and
atmospheric pressure. (i) Your answer for part (h) should be three
times as large as the answer for part (g). Where does this discrep-
ancy arise?


For the part (e) the solution says that 1st we calculate the change in momentum which is 2m*V_rms then to find time taken to travel between walls which is 0.20/V_rms and then ΔP/t gives the average force! Now I think what if I considered the molecule to be moving from the center of the container to the side, in that case the time reduces and the av force increases. So I find this a little illogical! Is my thinking right? Can we determine the actual force considering the wall to be perfectly rigid and collisions elastic? TIA

 

[Simon Bridge]

The idea is to compute the average force on the container over a great many bounces.
The time that is important, therefore, is the time between bounces not the time to get to a wall from some arbitrary position in the container.