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## Homework Statement

If mole fraction, pressure fraction and volume fraction are denoted by X

_{mol}, X

_{p}, X

_{V}respectively, of a gaseous component, then what is the relation between them?

## Homework Equations

mole fraction = mole of component / total moles

pressure fraction = pressure of component / total pressure

volume fraction = volume of component / total volume

## The Attempt at a Solution

Well, to be honest, I simply don't know where to start from. But still, have a look at my method (even if it is stupid) :

Let's assume there are 3 gaseous components.

mole fraction of 1st component (at const. temp.) = n1 / n1+n2+n3

= P1V1 /( P1V1+P2V2+P3V3) (cancelling the RT terms, T being constant) (equation 1)

=P1 / (P1+P2+P3) ..........pressure fraction assuming constant volume (from eq.1)

=V1 / (V1+V2+V3) ...........volume fraction assuming constant pressure (from eq. 1 )

So, my answer is that all three are same, which happens to be the correct answer according to my book. But i still need some clarifications, is it justified to assume volume to be constant for calculating pressure fraction? please help me out. If you find my answer to be incorrect, please give me the correct proof.