How Do You Calculate the Average Force Exerted by a Gas Molecule in a Flask?

[dalitwil]

I have been having a hard time with the following question:

A 400 mL spherical flask contains 0.075 mol of an ideal gas at a temperature of 300 K. What is the average force-magnitude exerted on the walls of the flask by a single molecule?

I couldn't really start the problem because I have two unknowns: m and v. I need m to find v, and i need v to find F. Because it doesn't give me a molar mass, i am lost on how to find v, wondering if there is another approach I could take? Please help!

 

[dextercioby]

U can find the pressure (in Pa) and then compute the average force by multiplying the pressure in Pa with the surface area in m^{2}...U can't use kinetic theory,because computing the momentum transfer by a molecule would require knowledge of the average magnitude of velocity and the molecule's mass...

Daniel.

 

[what]

Think ideal gas law to find the pressure, then do as dextercioby said.

 

[dalitwil]

Ok so I used PV=nRT to find pressure:

P*(.4L) = (0.075)*(8.31)*(300)
=467.43Pa

Then I calculated the surface area by setting the volume equal to 3/4pi r^3:

find the radius (=.45708) and finding surface A=4pi*r^2 =2.6

Now calculating the F from F=PA gave me 1227. This was incorrect.
I also tried subsituting the volume with .0004m^3 (1L=10^-3m^3) and recalculating the P and A and it was still incorrect.

I don't understand what i did wrong, I understand the logic behind finding F this way, but my calculations are wrong. Can anyone please help me?

 

[dextercioby]

It can't be right.U got to be consistent with your units...Use SI-mKgs...

$$p=\frac{\nu RT}{V} \ [Pa]$$

$$p=\frac{0.075\cdot 10^{-3} \ \mbox{Kmol} \cdot 8314 \ \frac{\mbox{J}}{\mbox{Kmol}\cdot\mbox{K}} \cdot 300 \ \mbox{K}}{0.4\cdot 10^{-3} \ \mbox{m}^{3}}$$

and get that #.

Daniel.