Question

Shobha dissolved 42g of sugar in 150g water. She stirred the solution well and then filtered it. She obtained $12g$ of sugar as the residue. Find the solubility of sugar.
A. $2.4\% $
B. $20\% $
C. $21.1\% $
D. $36\% $

Answer 1

Hint: Solubility is the ratio between the mass of solute which dissolved in a solvent to the mass of the solvent. Since a residue is obtained, this means that all the solute which was initially added hasn’t been dissolved. The difference between the sugar added initially and the residue obtained will give us the amount of sugar which dissolved. This divided by the weight of water given will give us solubility.

Formulas used: $S = \dfrac{{{W_B}}}{{{W_A}}} \times 100$
Where $S$ is the percentage solubility, ${W_B}$ is the mass of the solute which dissolved and ${W_A}$ is the mass of the solvent given.

Complete step by step answer:
A given amount of solvent will only be able to dissolve a given solute up to a certain value. Beyond this, the addition of more solute will just lead to the solute being deposited at the bottom.
This extra solute is what Shobha got as her residue after filtration. Thus, as we can see, the amount of sugar which actually dissolved will be the difference between the total sugar added and the mass of the sugar obtained as the residue. Here, the total sugar added is $42g$ and the residue is $12g$. Thus, we have:
Mass of sugar which actually dissolved $ = 42 - 12 = 30g$
Thus, only $30g$ of the sugar was able to dissolve in the water. We know that:
$S = \dfrac{{{W_B}}}{{{W_A}}} \times 100$
Where $S$ is the percentage solubility, ${W_B}$ is the mass of the solute which dissolved and ${W_A}$ is the mass of the solvent given.
Here as we have seen, ${W_B} = 30g$ and it is given that ${W_A} = 150g$. Substituting these values, we get:
$S = \dfrac{{30}}{{150}} \times 100 = \dfrac{{100}}{5}$
$ \Rightarrow S = 20\% $
Thus, the solubility of the given amount of sugar is $20\% $

So, the correct answer is Option B .

Note: The maximum amount of solute that can be dissolved in a particular solvent at a particular temperature is given by the saturation solubility level.
Note that solubility of most salts increases with temperature, since dissolution is a process which releases heat (endothermic process).