Question

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

Answer 1

Mass percentage is a way of expressing the concentration of a solution. Mass percentage of a solution represents the mass of solute present per cent, i.e. per 100g of the solution.
Formula used: ${\text{Mass percent}} = \dfrac{{{\text{Mass of solute}}}}{{{\text{Mass of solution}}}} \times 100$

Complete step by step answer:
We are given in the question that the solution obtained is made by mixing $300{\text{g}}$of $25\%$ by mass solution and $400{\text{g}}$of $40\%$ by mass solution of the same solute. First we calculate the mass of the solution which can be simply given by the sum of the masses of the two solutions added, i.e.,
${\text{Mass of solution}} = 300{\text{g}} + 400{\text{g}}$
${\text{Mass of solution}} = 700{\text{g}}$
Now to calculate the mass of solute in the mixture, we need to find the masses of the solute present in the initial two solutions. In the first solution, that is, $300{\text{g}}$ of $25\%$ solution, the mass of the solute is given as, ${\text{Mass of solute}} = 300 \times \dfrac{{25}}{{100}}$
${\text{Mass of solute}} = 75{\text{g}}$
In the second solution, that is, $400{\text{g}}$ of $40\%$ solution, the mass of the solute is given as,
${\text{Mass of solute}} = 400 \times \dfrac{{40}}{{100}}$
${\text{Mass of solute}} = 160{\text{g}}$
So the total mass of solute in the mixture formed by mixing the above two solution will be ${\text{Total mass of solute}} = 75{\text{g}} + 160{\text{g}} = 235{\text{g}}$
The mass percentage of the solution can be calculated by finding the ratio between the mass of solute in the solution and the mass of the total solution and then multiplying it by 100. So we can write, ${\text{Mass percent}} = \dfrac{{{\text{Mass of solute}}}}{{{\text{Mass of solution}}}} \times 100$
${\text{Mass percentage}} = \dfrac{{235{\text{g}}}}{{700{\text{g}}}} \times 100$
${\text{Mass percent}} = 33.6\%$

Thus, the mass percentage of the resulting solution obtained by mixing $300{\text{g}}$of $25\%$by mass solution and $400{\text{g}}$of $40\%$ by mass solution is $33.6\%$.
Note:
Similar to the mass percentage, another quantity used to determine concentration of a mixture commonly is percentage by volume. It gives us the volume of the solute present per cent, i.e., per 100 units of volume of the solution.