Question

Why mole fractions sum is equal to one

Answer 1

Explanation:

because we have units of molesmoles ). But for the sum of the moles fractions, χA+χB=nAnA+nB+nBnA+nB=nA+nBnA+nB=1 clearly.

Answer 2

Answer:

Mole fraction are nothing but the quantity of moles of solute/solvent from total moles.

Since we always take this from the total* moles, sum of all mole fractions will always be 1.

Explanation:

Let us consider a solution, which has n moles of solute and m moles of solvent.

Total moles = n + m

moles of solute = n

Mole fraction(solute)= mole of solute/total mole

                           = n/(m + n)

Similarly,

Mole fraction(solvent)= mole of solvent/total

                           = m/(m + n)

On adding total both,

⇒ n/(m + n)  +  m/(m + n)

⇒ (n + m)/(m + n)

⇒ 1

         Hence, sum of mole fractions is 1.

This can be proved even if you have more than 1 solutes.

In case of 3, total mole = m + n + p

sum of mole fractions is:

m/(m+n+p) + n/(m+n+p) + p/(m+n+p)

(m+n+p)/(m+n+p)

1           proved.