Question

In aqueous solution of urea is 20% by mass of solution. Molarity of the solution when density of the solution is 1.2gram per ml is:
A.4M
B.3.5M
C.5M
D.None of these

Answer 1

Hint: We can calculate molarity of the solution from the volume of the solution and moles of urea. The volume of the solution is calculated using the density of the solution and mass. We can calculate the moles of urea using the molar mass and mass of urea.

Formula used: We can define Molarity as the mass of solute in one liter of solution. Molarity is the desired concentration unit for stoichiometry calculations. The formula is,
${\text{Molarity}} = \dfrac{{{\text{Mass of solute}}\left( {{\text{in moles}}} \right)}}{{{\text{Volume of solution}}\left( {{\text{in liters}}} \right)}}$

Complete step by step answer:
Given data contains,
Density of the solution is 1.2gram per ml.
Mass percent of urea solution is 20%.
Mass percent of urea solution is 20%, which means 20grams of urea in 100gram of the solution.
We know that density and mass, so let us now calculate the volume of the solution. We know the formula to obtain the density of the solution.
${\text{Density}} = \dfrac{{{\text{Mass}}}}{{{\text{Volume}}}}$
Let us rearrange the formula of density to calculate the volume of the solution,
${\text{Volume}} = \dfrac{{{\text{Mass}}}}{{{\text{Density}}}}$
The mass of the solution is 100gram and density of the solution is 1.2gram per ml. Let us now substitute these values in the formula of volume.
${\text{Volume}} = \dfrac{{{\text{Mass}}}}{{{\text{Density}}}}$
$ \Rightarrow {\text{Volume}} = \dfrac{{100g}}{{1.2g/mL}}$
$ \Rightarrow {\text{Volume}} = 83.33ml$
${\text{Volume}} = 0.083L$
The volume of the solution is $0.083L$.
We know the molar mass of urea is 60g/mol and the mass of urea is 20g. From this we can calculate the moles of urea.
Moles of urea = $ = \dfrac{{{\text{Mass of urea}}}}{{{\text{Molar mass of urea}}}}$
Moles of urea = $\dfrac{{20g}}{{60g/mol}}$
Moles of urea = $0.3333mol$
The moles of urea are $0.3333{\text{mol}}$.
From the calculated moles of urea and volume of the solution, we can calculate the molarity of the solution. The formula to calculate the molarity is,
${\text{Molarity}} = \dfrac{{{\text{Mass of solute}}\left( {{\text{in moles}}} \right)}}{{{\text{Volume of solution}}\left( {{\text{in liters}}} \right)}}$
Let us substitute the values of mass of urea and volume of the solution in the equation to calculate the molarity of the solution.
The moles of urea are $0.3333$mol.
The volume of the solution is $0.083L$.
${\text{Molarity}} = \dfrac{{0.3333mol}}{{0.083L}}$
${\text{Molarity}} = 4.01mol/L$
${\text{Molarity}} = 4.01M$
The molarity of the solution is $4.0M$.

So, the correct answer is Option A.

Note:
From molarity, we can also calculate the mass percentage, molality. An example of calculation of mass percentage from molarity is shown below.
Example:
The concentration of the phosphoric acid expressed in mass percentage has to be calculated.
Given,
Molarity of the solution is $0.631M$
Density of the solution is $1.031g/ml$
The grams of the phosphoric acid are calculated using the molar mass.
Grams of phosphoric acid = \[0.631mol \times \dfrac{{97.994g}}{{1mol}} = 61.8342g\]
The mass of the solution is calculated from the density of solution
Mass of the solution = $1L \times \dfrac{{1.031g}}{{1ml}} \times \dfrac{{1000ml}}{{1L}} = 1031g$
The concentration of the solution is,
${\text{Mass percentage}} = \dfrac{{{\text{Grams of solute}}}}{{{\text{Grams of solution}}}} \times 100\% $
Concentration of the solution = \[\dfrac{{61.8342g}}{{1031g}} \times 100\% \]
Concentration of the solution = $5.9974\% $
The concentration of the solution expressed in mass percentage is $5.9974\% $.