Question

Shobha dissolved \[{\mathbf{42g}}\] of sugar in \[{\mathbf{150g}}\] of water. She stirred the solution well and then filtered it. She obtained \[{\mathbf{12g}}\] of sugar as the residue. Find the solubility of sugar.
A. \[{\mathbf{2}}.{\mathbf{4}}\% \]
B. \[{\mathbf{20}}\% \]
C. \[{\mathbf{21}}.{\mathbf{1}}\% \]
D. \[{\mathbf{36}}\% \]

Answer 1

Hint: Now the solubility of the product is found out by different quantities. In the above question, as the solvent and solution are given in grams, we will find the solubility in gram per \[100grams\]. Now to find the solubility of the solution, simply divide the mass of solute in grams upon the mass of solvent in grams and multiply it by \[100grams\].

Complete step by step answer:
- Solubility is a phenomenon which states how much amount of solute (the substance which needs to be dissolved) is soluble in a solvent (the substance which dissolves another substance).
- According to the solubility of a compound, it is differentiated in different terms such as freely soluble, soluble, sparingly soluble, slightly soluble, or insoluble. In labs, in the preliminary test of quality analysis solubility is an essential phenomenon to check them upon the given compound.
- Now in the above question, we can simply find the solubility of the solvent by dividing the mass of solute in grams with solvent in grams and multiplying it with \[100grams\].
- In the above question, one can observe that \[{\mathbf{42g}}\] of sugar was used, but \[{\mathbf{12g}}\] of that sugar was remained residue, means only $30g$ of sugar was consumed in the solution.
Total mass of solute taken;
\[ = 42g\]
Total mass of solute residue;
\[ = 12g\]
Total mass of solute used in solution;
\[ = 42g - 12g\]
\[ = 30g\]
Total mass of solvent;
\[ = 150g\]
Using the formula, we get;
\[ = \left[ {\dfrac{30g}{150}} \right] \times 100g\]
\[ = 0.2 \times 100g\]
\[ = 20\]
Therefore the total percentage of sugar that was dissolved in $150g$ of water is \[20\% \]

Hence, option B is correct.

Note:
Solubility of a compound can depend on various factors, and it can also change by changing various factors. Increasing temperature increases the solubility of a solute in the solution. Increasing the vapour pressure upon solution can decrease the solubility of a product.