For a binary solution, why is the sum of the mole fractions, $χ_{n}$ $chi_n$ , of each component ALWAYS equal to ONE?

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For a binary solution, why is the sum of the mole fractions, $χ_{n}$ $chi_n$ , of each component ALWAYS equal to ONE?

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Answer 1 · 2017-03-03T19:12:40

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

Explanation:

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

Now the total number of moles of stuff is $n_{A} + n_{B}$ $n_A+n_B$ , but the mole fraction of $A = χ_{A} = \frac{n_{A}}{n_{A} + n_{B}}$ $A=chi_A=n_A/(n_A+n_B)$ , and likewise, $χ_{B} = \frac{n_{B}}{n_{A} + n_{B}}$ $chi_B=n_B/(n_A+n_B)$ ,

Each $χ$ $chi$ value is dimensionless (why? because we have units of $\frac{moles}{moles}$ $"moles"/"moles"$ ). But for the sum of the moles fractions,

$χ_{A} + χ_{B} = \frac{n_{A}}{n_{A} + n_{B}} + \frac{n_{B}}{n_{A} + n_{B}} = \frac{n_{A} + n_{B}}{n_{A} + n_{B}} = 1$ $chi_A+chi_B=n_A/(n_A+n_B)+n_B/(n_A+n_B)=(n_A+n_B)/(n_A+n_B)=1$ 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 $n$ .

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For a binary solution, why is the sum of the mole fractions, $χ_{n}$ $chi_n$ , of each component ALWAYS equal to ONE?

1 Answer

Explanation:

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

1 Answer

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For a binary solution, why is the sum of the mole fractions, $χ_{n}$ $chi_n$ , of each component ALWAYS equal to ONE?