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

Click For Summary

Discussion Overview

The discussion revolves around the relationship between Dalton's law of partial pressures and the volume ratio of gas components in a mixture. Participants explore whether the partial pressure of an ideal gas can be derived from volume ratios instead of the standard formulation of Dalton's law.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Conceptual clarification

Main Points Raised

  • One participant questions the validity of using the volume ratio to determine partial pressures, seeking a derivation or explanation.
  • Another participant suggests that the ideal gas law (PV=nRT) is fundamental to understanding the relationship between moles and volume.
  • A participant attempts to derive the mole fraction (xi) in terms of volumes and pressures, indicating a connection between mole fractions and volume ratios.
  • One participant clarifies that summing partial pressures assumes all gases occupy the same volume, while summing partial volumes assumes they are under the same pressure.
  • A later reply expresses curiosity about the general relationship between moles, volume, and pressure, indicating a desire for deeper understanding.

Areas of Agreement / Disagreement

The discussion contains multiple viewpoints regarding the relationship between Dalton's law and volume ratios, with no consensus reached on the validity of the alternative formulation.

Contextual Notes

Participants express uncertainty about the derivation of the proposed relationship and the assumptions underlying the use of volume ratios in this context.

Syrus
Messages
213
Reaction score
0

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?



Homework Equations







The Attempt at a Solution

 
Physics news on Phys.org
PV=nRT is all you need. How does n depend on V?

Well, perhaps adding obvious

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
 
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
 

Similar threads

  • · Replies 3 ·
Replies
3
Views
3K
  • · Replies 16 ·
Replies
16
Views
4K
  • · Replies 2 ·
Replies
2
Views
3K
  • · Replies 1 ·
Replies
1
Views
4K
Replies
4
Views
2K
  • · Replies 5 ·
Replies
5
Views
4K
  • · Replies 2 ·
Replies
2
Views
3K
  • · Replies 4 ·
Replies
4
Views
2K
  • · Replies 7 ·
Replies
7
Views
3K
  • · Replies 3 ·
Replies
3
Views
2K