Deriving pV=NkT from N=Na*n and k=R/Na

[Hannah7h]

I've attempted to use N=N_a*n -where N is that total number of particles of a gas, N_a is the Avogadro constant and n is moles. And then attempted to use k=R/N_a -where k is the Boltzmann constant and R is the molar gas constant. I got as far as N/n=R/k but then not sure how to get from this to the final equation- if this is even the right way

 

[nasu]

You cannot get the ideal gas law by just manipulating the definition of Avogadro number and its relationship with other constants.
Whereas the definition of Avogadro number's is very general, the ideal gas law is valid only for ideal gases. So you need to start with a model of ideal gas and find a relationship between pressure and other parameters.
For example,try to find how the pressure depends on the concentration of particles and their average speed.
You can find the this done in introductory books on kinetic-molecular theory of gases.

 

[ZapperZ]

I've attempted to use N=N_a*n -where N is that total number of particles of a gas, N_a is the Avogadro constant and n is moles. And then attempted to use k=R/N_a -where k is the Boltzmann constant and R is the molar gas constant. I got as far as N/n=R/k but then not sure how to get from this to the final equation- if this is even the right way

Are you trying to convert pV=nRT to pV=NkT?

It would help you are clear on what you want to do, especially on your starting point.

Zz.

 

[Hannah7h]

Are you trying to convert pV=nRT to pV=NkT?

It would help you are clear on what you want to do, especially on your starting point.

Zz.

Ah yeah sorry, it wasn't clear, basically I wanted to know what you would derive pV=nRT from and then how you would derive it from those equations, but also it would be good if you could tell me how to get from pV=nRT to pV=NkT

 

[Khashishi]

The gas constant is just $R=k_B N_a$.

 

[Tazerfish]

I think I know what you are looking for.
First, you make a few assumptions :

• The gas is made up of discrete molecules
  
• These molecules don't interact with one another
  
• The gas molecules collide elastically with the walls of the container
• The gas molecules occupy no relevant Volume
• The gas molecules move equally in all three dimensions

I am just going to stop here because I remembered a video on this:

The derivation starts at 9 minutes

 

[Hannah7h]

I think I know what you are looking for.
First, you make a few assumptions :

• The gas is made up of discrete molecules
  
• These molecules don't interact with one another
  
• The gas molecules collide elastically with the walls of the container
• The gas molecules occupy no relevant Volume
• The gas molecules move equally in all three dimensions

I am just going to stop here because I remembered a video on this:

The derivation starts at 9 minutes

Ohhh ok, I see how its done now, thank you

 

[Tazerfish]

Glad I could help

Tazerfish