Dalton's law of partial pressure

  • I
  • Thread starter dRic2
  • Start date
  • #1
dRic2
Gold Member
813
198
Does anyone know a rigorous proof for Dalton's law ? I think I saw it once, but I can not find it again anywhere.

Thanks
Ric
 

Answers and Replies

  • #2
319
64
Dalton's "law" is not a real law but only an approximation. In the case of ordinary gases, the molecules or atoms do not collide very often, and the partial pressures add (as I am sure you know). It can be derived by neglecting the forces between these particles, and the volume occupied by them. A paragraph about it can be found at https://en.wikipedia.org/wiki/Dalton's_law

You can start with a discussion of the kinetic theory of gases. I just read about it in Halliday, Resnick and Walker's "Fundamentals of Physics", fifth edition. They assume that the particles do not collide with one another, but only with the walls of whatever contains them. They derive an expression for the pressure based on the number of particles per unit volume and their average speed. Although they do not explicitly treat the case where the gas is a mixture, the concept can be extended to that case.

I hope that helps.
 
  • Like
Likes dRic2
  • #3
dRic2
Gold Member
813
198
Wikipedia only says the total pressure for a mixture of gases can be expressed as ##p_{tot} = \sum p_i##, but it doesn't say why.

I do not know very much about kinetic theory of gasses, but if you say the answer lies there, then I'll study it. :wink::biggrin:
 
  • #4
FactChecker
Science Advisor
Gold Member
6,059
2,343
Wikipedia only says the total pressure for a mixture of gases can be expressed as ##p_{tot} = \sum p_i##, but it doesn't say why.
Because there is so little interaction of any type between the gas molecules that the forces from each can just be added together for a good approximation. So the pressures are added to get a total pressure.
 
  • Like
Likes dRic2
  • #5
dRic2
Gold Member
813
198
good approximation
Yes, but I remember that, for ideal gasses, it not an approximation. Maybe it just comes from the fact that ideal gasses are supposed to have no interaction between their molecules, but I remember my professor showed this with math... Maybe I remember wrong.
 
  • #6
FactChecker
Science Advisor
Gold Member
6,059
2,343
Yes, but I remember that, for ideal gasses, it not an approximation. Maybe it just comes from the fact that ideal gasses are supposed to have no interaction between their molecules, but I remember my professor showed this with math... Maybe I remember wrong.
I just said "good approximation" out of an over-abundance of caution. It's probably good enough to be called exact. Yes, the assumption of no interaction is key.
 
  • Like
Likes dRic2
  • #7
sophiecentaur
Science Advisor
Gold Member
2020 Award
25,525
5,034
So the pressures are added to get a total pressure.
A very noddy way of looking at the way pressures can add up would be to consider several small people banging against a wall with hammers. The effect of this (including the rate of hammering) is a pressure. Then take several larger people with bigger hammers, also banging on the wall. They will also have the effect of pressure and the two will just add together.
Instead of people, imagine large and small ballbearings in a steel box, all hitting the wall and bouncing against each other occasionally. The ball / ball collisions make no difference to the total momentum in the direction of the wall and you can think in terms of the frequency of collisions of the big balls and small balls against the wall. Collisions between big and small balls will even out the distribution of Kinetic energies of the balls (corresponding to the temperature in the gas) and the pressure on a wall will be the sum of the pressures (rate of collisions times average momentum). If you were to have just small balls in the box (same number), with the same mean speed (aka temperature) the pressure against the wall will be the same as the contribution of the small balls when they are part of the mixture. Ditto for the big balls.
That's just Kinetic Theory put into everyday words.
 
  • Like
Likes FactChecker and dRic2

Related Threads on Dalton's law of partial pressure

  • Last Post
Replies
1
Views
949
  • Last Post
Replies
5
Views
1K
  • Last Post
Replies
17
Views
2K
  • Last Post
Replies
6
Views
5K
  • Last Post
Replies
11
Views
3K
Replies
12
Views
10K
Replies
1
Views
2K
Replies
3
Views
779
Replies
4
Views
6K
Replies
1
Views
644
Top