My textbook shows that pressure fraction is equal to mole fraction because the same volume cancels: enter image description here

But it violates (if I am not mistaken) the law in this example it gives:

the main components of dry air, by volume, are N2, 78.08%, O2, 20.95%, Ar, 0.93%, and CO2, 0.04%. What is the partial pressure of each gas in a sample of air at 1atm.

The strategy it gives for solving this problem is by treating the volume percent as mole percent, and in turn as pressure percent. But obviously, each gas occupies a different volume, the law of partial pressure doesn't apply. does it?

Also, is it possible for different components of air to occupy different amounts of space in atmosphere? If atmosphere is a container, doesn't all components just occupy the same amount of space-the size of container?

  • $\begingroup$ I'd guess that you have something confused. Textbook? page? Need to see whole problem to understand the context. In general though PV=nRT, so P of a particular gas component would be nRT/V and the pressures of the individual components would sum to the total pressure. Note that for some container at some temperature R, T and V will all be constants. $\endgroup$ – MaxW Oct 22 '15 at 2:19
  • $\begingroup$ "If atmosphere is a container, doesn't all components just occupy the same amount of space-the size of container?" Yes, but consider having a liter container with 200 ml of oxygen and 800 ml of nitrogen. Now there is also a "force field" between the nitrogen and oxygen. If the temperature was exactly the same and the pressure was exactly 760 mm in both, then the ideal gas laws tell us that releasing the force field would yield 1000 ml mixture of oxygen and nitrogen at 760 mm, and the same temperature. $\endgroup$ – MaxW Oct 22 '15 at 4:36
  • $\begingroup$ Whenever they use the term "by volume," they always mean mole fraction (particularly in atmospheric science). So, when I see the words "by volume," I mentally translate it into the words "mole fraction." It has never made sense to me why they use this terminology because all the components of the gas occupy the same volume. $\endgroup$ – Chet Miller Oct 29 '15 at 2:38

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