Question

A solution is obtained by mixing 300 g of \[{\text{25% }}\] solution and 400 g of \[{\text{40% }}\] solution by mass. Calculate the mass percentage of the resulting solution.

Answer 1

Hint: The mass percent of the solution gives the mass of solute present in \[{\text{100 g}}\] of solution. The formula for the mass percent of the solution is as given below:
\[{\text{Mass percent = }}\dfrac{{{\text{Mass of solute}}}}{{{\text{Mass of solution}}}}{\text{ }} \times {\text{ 100 }} \\
{\text{ }} \\\]

Complete step by step answer:
The solution is obtained by mixing 300 g of \[{\text{25% }}\] solution and 400 g of \[{\text{40% }}\] solution by mass.
Calculate the total mass of solution
\[{\text{Mass of solution = 300 g + 400 g}} \\
{\text{Mass of solution}} = 700{\text{ g}} \\
{\text{ }} \\\]
Calculate the mass of solute present in \[{\text{300 g}}\] of \[{\text{25% }}\] solution .
\[{\text{mass of solute = 300 g }} \times {\text{ }}\dfrac{{25}}{{100}} \\
{\text{mass of solute = 75 g}} \\\]
Calculate the mass of solute present in \[{\text{400 g}}\] of \[{\text{40% }}\] solution .
\[{\text{mass of solute = 400 g }} \times {\text{ }}\dfrac{{40}}{{100}} \\
{\text{mass of solute = 160 g}} \\\]
Calculate the total mass of solute
\[{\text{Total mass of solute = 75 g}} + {\text{160 g}} \\
{\text{Total mass of solute = 235 g}} \\\]
Calculate the mass percentage of the resulting solution.
\[{\text{Mass percent = }}\dfrac{{{\text{Mass of solute}}}}{{{\text{Mass of solution}}}}{\text{ }} \times {\text{ 100 }} \\
{\text{Mass percent = }}\dfrac{{{\text{235 g}}}}{{{\text{700 g}}}}{\text{ }} \times {\text{ 100 }} \\
{\text{Mass percent = 33}}{\text{.6% }} \\\]

Hence, the mass percent of the resulting solution is \[{\text{33}}{\text{.6% }}\].

Additional Information: Another formula can be used to calculate the mass percent of the resulting solution.

\[{\text{Mass percent = }}\dfrac{{{\text{Mass of solute}}}}{{{\text{Mass of solute + Mass of solvent}}}}{\text{ }} \times {\text{ 100 }} \\
{\text{ }} \\ \]
Total mass of the solution is the sum of the masses of solute and solvent.

Note: Similar to percentage by mass, another quantity frequently used is percentage by volume. It is the volume of solute present in \[{\text{100 mL}}\] of solution. The formula for the volume percent of the solution is as given below:
\[
{\text{Volume percent = }}\dfrac{{{\text{Volume of solute }}\left( {{\text{mL}}} \right)}}{{{\text{Volume of solution }}\left( {{\text{mL}}} \right)}}{\text{ }} \times {\text{ 100 }} \\
{\text{ }} \\\]