# Dalton's law of partial pressures equivalent to volume ratio?

## Homework Statement

I had a general inquiry about a relation in my physical chemistry textbook. It stated that when determining the partial pressure of an ideal gas component in a mixture/solution, instead of using the standard Dalton's law: Pi = xiPtot, one can simply use the relation Pi = (volume i : volume mixture or solution)Ptot.

I am having a hard time convincing myself of this and have not been able to find a derivation of this in either my book or online. Can someone please help me get started?

## The Attempt at a Solution

Borek
Mentor
PV=nRT is all you need. How does n depend on V?

$$n_{total} = \sum n_i$$

will help.

Assuming we are dealing with a binary solution, that gets me here...(still stuck)

xi = ni/ntot

ni = PiVi/RT

ntot = PiVi/RT + PjVj/RT

ni/ntot = PiVi/(PiVi + PjVj)

.....?

Obviously we want xi to somehow equal Vi/ Vtot

Borek
Mentor
You don't have separate PiVi pairs. If you sum partial pressures Pi it is equivalent to assuming all gases occupy the same volume Vtotal, if you sum partial volumes Vi it is equivalent to assuming all gases are under the same pressure Ptotal.

Ah, i see what you are saying now.

If we write ni = ViPtot/RT this leads us to the conclusion.

I am curious now why ni = ViPtot/RT = VtotPi/RT in general