Question

Mole fraction of solvent in aqueous solution of NaOH having molarity of $3$ is
(A) $0.3$
(B) $0.05$
(C) $0.7$
(D) $0.95$

Answer 1

To find the mole fraction of solvent we need to find the number of moles of solvent (water if the given solution is aqueous) in solution. The mole fraction of a component (solute or solvent) is the ratio of the number of moles of a component to the total number of moles of a solution. Hence using this definition/formula we find the mole fraction of solvent.

Complete answer:
Let $X$ be the mole fraction of solvent.
Given molality of NaOH solution $= 3$ $m$ . It means that $3$ moles of $NaOH$ are present in $1000\,g$ ( $1kg$ ) of solvent.
It implies number of moles of $NaOH$ (solute) $= 3$ $m$ ---(1)
Since the solution is aqueous solution in nature, which means that the given solvent is water.
Calculating the number moles of water in the solution, by using the formula
$Number\,of\,moles = \dfrac{{Mass}}{{Molar\,mass\,}}$ ------(2)
Given mass of water $= 1000\,g$
We know that the Molar mass of water $= 18\,g/mol$
Putting values in the equation (1), we get
$Number\,of\,moles\;of\;water = \dfrac{{1000g}}{{18\,g/mol\,}} = 55.55$ mol----(3)
To calculate the mole fraction of solvent, we use the formula
$Mole\,fraction\,of\,solvent(water)X = \dfrac{{Number\,of\,moles\,of\,water}}{{sum\;of\,moles\,of\,water\,and\,NaOH(solute)}}$
Using the equations (1) and (3), we get
$X = \dfrac{{55.55}}{{55.55 + 3}} = 0.95$
Thus, the mole fraction of solvent is $0.95$ .
Hence the correct option is (D) $0.95$ .

Note:
Note that molarity is defined as the number moles of solute per $1000\,g$ of solvent. The S.I unit of molarity is $m$ or $mol/kg$ . Also note that if $n$ moles of solution present in $1000\,g$ of solvent, then the molality of that solution is $n$ .