Force Exerted by Individual Molecules

In summary, to find the average force-magnitude exerted on the walls of a spherical flask containing 0.075 mol of an ideal gas at 342 K, you need to first find the pressure using the ideal gas law and then calculate the force due to a single molecule using the partial pressure and the area of the flask's walls. This does not involve internal energy.
  • #1
vworange
9
0
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:
[itex]P = (1/3)*(N/V)*2*((3/2)kT)[/itex]

Then using the idea that:
[itex]P = F/A[/itex]

No luck. I think I'm doing things wrong. Does this have something to do with internal energy? ([itex]U = (3/2)nRT[/itex])
 
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  • #2
vworange said:
I have absolutely no idea how to do this question. I've tried several different ways.. tried using the equation:
[itex]P = (1/3)*(N/V)*2*((3/2)kT)[/itex]

Then using the idea that:
[itex]P = F/A[/itex]

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

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
 
  • #3


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.
 

Related to Force Exerted by Individual Molecules

1. What is the force exerted by individual molecules?

The force exerted by individual molecules, also known as intermolecular forces, is the attractive or repulsive force between molecules. It is caused by the interactions between the positively charged nuclei and the negatively charged electrons of neighboring molecules.

2. How is the force exerted by individual molecules measured?

The force exerted by individual molecules can be measured using various techniques such as atomic force microscopy, surface force apparatus, or optical tweezers. These methods allow for the measurement of forces on the nanoscale level.

3. What factors affect the force exerted by individual molecules?

The force exerted by individual molecules is influenced by several factors, including the type of molecule, the distance between molecules, and the temperature. Polar molecules tend to have stronger intermolecular forces, while nonpolar molecules have weaker forces.

4. How does the force exerted by individual molecules impact physical properties?

The force exerted by individual molecules plays a significant role in determining the physical properties of a substance. For example, substances with strong intermolecular forces tend to have higher melting and boiling points, while substances with weak forces have lower melting and boiling points.

5. Can the force exerted by individual molecules be manipulated?

Yes, the force exerted by individual molecules can be manipulated through the use of external forces such as pressure or temperature. Additionally, chemical modifications can also alter the strength of intermolecular forces.

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