Ideal Gas Mixtures: Dalton vs Amagat Models

[Saladsamurai]

Hello all! You know, I thought I knew something about ideal gas mixtures, but now I am not so sure. I am reading through a section of a text that discusses the Dalton and the Agamat models of ideal gas mixtures. I will briefly describe each:

Dalton Model: The underlying assumption is that each mixture component behaves as an ideal gas as if it were alone at the temperature T and volume V of the mixture. Hence, can apply the ideal gas relation to both the mixture and each component to arrive at

$$\frac{p_i}{p} = \frac{n_iRT/V}{nRT/V} = \frac{n_i}{n} = y_i \qquad(1)$$


Agamat Mode: The underling assumption is that each mixture component behaves as an ideal gas as if it existed separately at the pressure P and temperature T of the mixture. Hence,

$$\frac{V_i}{V} = \frac{n_iRT/P_i}{nRT/P} = \frac{n_i}{n} = y_i \qquad(2)$$


Now the 2 models just described are based on 2 different assumptions and it would seem as though the 2 assumptions are conflicting with each other. That is, since the Dalton model assumes common T and V, it gives rise to the concept of a partial pressure. And again, since the Agamat model assumes common T and P, it gives rise to the concept of partial volumes.

This would suggest that if I am doing calculations with an ideal gas mixture, I can only talk about partial pressures OR partial volumes and not both.

Does this make sense to anyone? I would like to clarify this because I am doing some experimental work, and I need to converto from an equivalence ratio to a percent volume and that is how all of this confusion started.

 

[Andrew Mason]

Makes sense to me. Conceptually, I don't see how partial volumes would correspond to reality, since the molecules are free to move anywhere within the confines of the container. But as a model it works fine.

AM