# Dalton's law of partial pressure

• I
Gold Member
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

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.

dRic2
Gold Member
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.

FactChecker
Gold Member
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.

dRic2
Gold Member
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.

FactChecker
Gold Member
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.

dRic2
sophiecentaur