Flawed logic BR?

[johnwandering]

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A problem asks what the relationship between collision frequency and # particles is.
The answer was LINEAR relationship, and i was fairly confused. But i expected a good mathematical explanation to learn from.

Their answer was: collision frequency affects pressure. Pressure is directly proportional to # of moles via PV=nRT. Because the relationship of pressure to moles is linear, the relationship of collision frequency and nber of moles should also be linear.

Uh hey~ what?
Alright so collision freq affects pressure... But what if collision frequency and pressure are not 1:1 related? What if collision frequency affects pressure like radius affects gravitational force (1/r^2)? Saying that one affects another does not imply linear correlation, only that there is some kind of relationship.


I dont doubt their answer itself, but their process of getting there makes no sense.

 

[MedPR]

Well the question asked specifically what the relationship was, not "why" there is a relationship.

 

[johnwandering]

So the question was asking what kind of relationship it was:

Exponentially inceasing?
Linearly increasing?

 

[MedPR]

So the question was asking what kind of relationship it was:

Exponentially inceasing?
Linearly increasing?

Linear. P is proportional to n. If it were exponential it would look like PV=n^2RT

 

[johnwandering]

Yes, but that would require that collision frequency is first-order proportional to Pressure.

How do you know that?

 

[MedPR]

Yes, but that would require that collision frequency is first-order proportional to Pressure.

How do you know that?

I have no idea what you are saying or asking 😕

The question just asks you what the relationship is between pressure and moles based on the PV=nRT equation. To me it seems like you are asking for a proof of PV=nRT and I don't have the answer for that.

 

[Dasypus]

Yes, but that would require that collision frequency is first-order proportional to Pressure.

How do you know that?

The external pressure (pressure as measured by the container) is basically how hard the gas presses on the container. Every collision with the container wall is another little push, adding to the felt pressure that little bit. At a given temperature, the force of each little push averages out to a certain value, because the average molecular kinetic energy is proportional to the absolute temperature. So we can sum over little pushes to get pressure. Thus, collision frequency is directly related (first-order proportional) to pressure.