Question

Mole fraction of solute in aqueous solution of 30% NaOH is:
A. 0.16
B. 0.05
C. 0.22
D. 0.95

Answer 1

Hint: We should recall the concepts of finding mole fraction. To find answers for these types of questions assume that there is a solution of 100 gram.

Complete step by step answer:

So, first of all let us assume that there is 100 gram of solution.
Then, a solution of 30% NaOH, means 30 gm. of NaOH is present in 100 g solution.
Then, Mass of water =70 gm.
Now, we will find number of moles of NaOH
$Number\,of\,moles=\dfrac{Given\,\,mass}{Molar\,mass}$
We know that the given mass that we had found from the concentration of NaOH solution is 30 gram. And molar mass we can find that will be
Molar mass of NaOH= (23+16+1) =40 gram
Moles of NaOH=
= $\dfrac{40}{30}=0.75$moles
Similarly, we can find a number of moles of water.
Moles of water = $\dfrac{Given\,mass\,of\,water}{Molar\,mass\,of\,water}=\dfrac{70}{18}=3.89$Moles

As we can see, NaOH is present in small quantities that will be our solute and rest is our solvent.
Mole fraction of solute
=$\dfrac{moles\,of\,solute}{moles\,of\,solute+\,moles\,of\,solvent}$=$\dfrac{{{x}_{a}}}{{{x}_{a}}+{{x}_{b}}}$= $\dfrac{0.75}{0.75+3.89}$=0.16
So, our correct option will be option A.

Note: We should know about mole fraction. Molar fraction of a compound is another measure of concentration. Mole fraction is simply the number of moles of a particular substance compared to the total number of moles. Since the number of moles of one substance in a mixture can never be more than the total number of moles, the mole fraction for a substance always ranges between 0 and 1. The mole fraction is typically given the symbol “x”.