Force Exerted by Individual Molecules

[vworange]

A 390 mL spherical flask contains 0.075 mol of an ideal gas at a temperature of 342 K. What is the average force-magnitude exerted on the walls of the flask by a single molecule?

I have absolutely no idea how to do this question. I've tried several different ways.. tried using the equation:
P = (1/3)*(N/V)*2*((3/2)kT)

Then using the idea that:
P = F/A

No luck. I think I'm doing things wrong. Does this have something to do with internal energy? (U = (3/2)nRT)

 

[learningphysics]

I have absolutely no idea how to do this question. I've tried several different ways.. tried using the equation:
P = (1/3)*(N/V)*2*((3/2)kT)

Then using the idea that:
P = F/A

No luck. I think I'm doing things wrong. Does this have something to do with internal energy? (U = (3/2)nRT)

First find the pressure P using PV=nRT.

Now find the partial pressure due to a single molecule, p=P/(total number of molecules)

Now you can calculate the force due to a single molecule on the walls using p=f/A =>f=pA

 

[thepatientmental]

The force exerted by individual molecules on the walls of the flask is a result of their random motion and collisions with the walls. This force can be calculated using the ideal gas law, which relates the pressure of the gas to its temperature, volume, and number of moles. However, since we are interested in the force exerted by a single molecule, we need to rearrange the equation to solve for force (F) instead of pressure (P). This can be done by multiplying both sides of the equation by the area (A) of the flask, which cancels out the pressure term.

F = P*A = (1/3)*(N/V)*2*((3/2)kT)*A

Since we are given the volume (V) and number of moles (n) of the gas, we can calculate the total number of molecules (N) using Avogadro's number (6.022x10^23). We can also calculate the area (A) of the flask using its volume and the formula for the surface area of a sphere.

Substituting these values into the equation, we get:

F = (1/3)*(0.075*6.022x10^23)/(0.390/2)^2*2*((3/2)*1.38x10^-23*342)*4*pi*(0.390/2)^2

= 1.48x10^-21 N

This is the average force exerted by a single molecule on the walls of the flask. Keep in mind that this force is constantly changing as molecules collide with the walls at different speeds and angles. So, this is just an average value.