For a binary solution, why is the sum of the mole fractions, #chi_n#, of each component ALWAYS equal to ONE?

Answer 1

Because of the way we define the mole fraction..........

Let's make it simple: consider a 2 component mixture, with #n_A# and #n_B# moles of #A# and #B#.

Now the total number of moles of stuff is #n_A+n_B#, but the mole fraction of #A=chi_A=n_A/(n_A+n_B)#, and likewise, #chi_B=n_B/(n_A+n_B)#,

Each #chi# value is dimensionless (why? because we have units of #"moles"/"moles"#). But for the sum of the moles fractions,

#chi_A+chi_B=n_A/(n_A+n_B)+n_B/(n_A+n_B)=(n_A+n_B)/(n_A+n_B)=1# clearly.

I could do the same for ternary mixtures, or however many species there are in the mixtures. #Sigmachi_n=1# for whatever value we have for #n#.

Capisce?

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Answer 2

Naomi Aronson

The sum of mole fractions in a binary solution is always one due to the conservation of mass principle.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.