Question

Find the weight of solvent in \[24\% {\text{ }}\left( {w/v} \right)\]of the solution, if the density of the solution is\[1.06{\text{ }}gm{l^{ - 1}}\].
A.\[82{\text{ }}g\]
B.\[80{\text{ }}g\]
C.\[72{\text{ }}g\]
D.\[60{\text{ }}g\]

Answer 1

Hint: Weight by volume percentage is given in the question which is defined as weight of solute present in 100 mL of the solution and density is also given. So, by using density formula mass of solution could be calculated and mass of solute is given from the weight by volume percentage and their difference will give weight of solvent.

Complete step by step answer:
In the question, the weight by volume percentage of the solution is given and the density of solution is given and we have to find out the weight of solvent. For this we need to know the weight of solution and weight of solute and difference of these will give us weight of solvent.
Because weight of solute + solvent = weight of solution
Percentage weight by volume is defined as the number of grams of solute present in 100 mL of the solution. So, in the question it is given as \[24\% \] it means \[24{\text{ }}gm\]of solute is present in the \[100{\text{ }}mL\]of solution.
So, total volume of solution is \[100{\text{ }}mL\] and weight of solute is \[24{\text{ }}g\]
Now, Density of solution is the mass of the solution divided by the volume of solution. From the question, we know density of solution is given as\[1.03{\text{ }}gm{L^{ - 1}}\], therefore mass of solution could be calculated as: -
\[Density = \dfrac{{mass}}{{volume}}\]
\[1.06{\text{ }}gm{L^{ - 1}} = \frac{{mass}}{{100{\text{ }}mL}}\]
Mass = \[1.06{\text{ }} \times 100{\text{ }}g\]
Mass of solution = \[106{\text{ }}g\]
Now, we have weight of solution and weight of solute and therefore, we can calculate weight of solvent as: -
Weight of solute + weight of solvent = weight of solution
\[24{\text{ }} + \] weight of solvent \[ = {\text{ }}106\]
Weight of solvent = \[106{\text{ }}-{\text{ }}24\]
Weight of solvent = \[82{\text{ }}g\]

Therefore, the correct answer is A i.e. \[82{\text{ }}g\]

Note:
In this specific question, weight by volume percentage is given and there are several other terms as well which are used to express concentration like Mass percentage, Molarity, Molality, Normality, PPM and others.