Question

Given, $\dfrac{w}{v}\% $ of urea solution is $6.3\% $ its density is $1.05\;gm\;m{l^{ - 1}}$. Mole fraction of urea is nearly
A.$0.018$
B.$0.019$
C.$0.024$
D.$0.030$

Answer 1

Hint: The quantity of molecules of a specific component in a mixture divided by the total quantity of moles in the given mixture is represented by mole fraction. It is one process which expresses the concentration of a solution.
Mole Fraction formula:
$mole\;fraction\;of\,solute = \dfrac{{moles\;of\;solute}}{{mole\;of\;solute + mole\;of\,solvent}}$
$ = \dfrac{{{n_A}}}{{{n_A} + {n_B}}}$

 Complete answer:
In chemistry, the amount of component ${n_i}$ divided by the total amount of all component of the mixture ${n_{tot}}$ is referred to mole fraction or molar fraction ${x_i}$ or ${X_i}$.
${x_i} = \dfrac{{{n_i}}}{{{n_{tot}}}}$
The summation of all the mole fraction is equal to $1$:
$\sum\limits_{i = 1}^N {{n_i}} = {n_{tot}}$ , $\sum\limits_{i = 1}^N {{x_i}} = 1$
Another term used for mole fraction is amount fraction. It is similar to the number fraction which can be explained as the number of molecules of a constituent ${N_i}$ divided by the total number of all molecules ${N_{tot}}$. The composition of a mixture with a dimensionless quantity; mass fraction and volume fraction are others is expressed by one method which is mole fraction.
Mass fraction ${w_i}$ is the product of the ratio of mass of one component to the total mass of the all component and mole fraction.
It can be found by using the formula,
${w_i} = {x_i}\dfrac{{{M_i}}}{{\overline M }} = {x_I}\dfrac{{{M_i}}}{{\sum\nolimits_j {{x_j}} {M_j}}}$
Here, ${M_i}$ is the molar mass of the component $i$ and $\overline M $ is the average molar mass of the mixture.
According to the question:
$\dfrac{w}{v}\% = 6.3\% $
This means that $6.3\;g$ urea in $100\;ml$ solution
since,
$mass\,of\,solution = density \times volume$
$ = 1.05 \times 100$
$ = 105\;g$
Thus,
$mass\,of\,water\left( {solvent} \right) = 105 - 6.3$
$ = 98.7\;g$
$moles\;of\;urea = \dfrac{{mass}}{{molar\;mass}}$
$ = \dfrac{{6.3}}{{60}}$
$ = 0.105$
$moles\,\,of\,water = \dfrac{{98.7}}{{18}}$
$ = 5.483$
${X_{urea}} = \dfrac{{{n_{urea}}}}{{{n_{urea}} + {n_{water}}}}$
\[ = \dfrac{{0.105}}{{0.105 + 5.483}}\]
${X_{urea}} = 0.0187$
Thus, this is the required answer.

 Note:
Please remember that mole fraction stands in for a fraction of molecules. As different molecules consist of different masses and there is the difference in mole fraction from the mass fraction.