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

Hint: 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 $ .