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Q1.7:
A solution is obtained by mixing 300 g of 25% solution and 400 g of 40% solution by mass. Calculate the mass percentage of the resulting solution.

Solution :

Step 1: Calculating the Mass of Solute in Each Component

To determine the mass percentage of the final solution, we must first calculate the absolute mass of the solute contributed by each of the individual solutions. The formula for mass of solute is: $Mass_{solute} = \left( \frac{\text{Mass percentage}}{100} \right) \times \text{Total mass of solution}$ [Per the definition of mass percentage].

  • For Solution A: $300\text{ g}$ of $25\%$ solution.
    $Mass_{solute, A} = 0.25 \times 300\text{ g} = 75\text{ g}$
  • For Solution B: $400\text{ g}$ of $40\%$ solution.
    $Mass_{solute, B} = 0.40 \times 400\text{ g} = 160\text{ g}$

Step 2: Calculating Total Mass of Solute and Total Mass of Solution

Upon mixing the two solutions, the total mass of the solute and the total mass of the final solution are the sums of the individual components [Per the Principle of Conservation of Mass].

  • Total Mass of Solute ($m_{total, solute}$):
    $75\text{ g} + 160\text{ g} = 235\text{ g}$
  • Total Mass of Solution ($m_{total, solution}$):
    $300\text{ g} + 400\text{ g} = 700\text{ g}$

Step 3: Calculating Final Mass Percentage

The mass percentage of the resulting solution is calculated as follows:

$Mass\ \%\ = \left( \frac{\text{Total mass of solute}}{\text{Total mass of solution}} \right) \times 100$

$Mass\ \%\ = \left( \frac{235\text{ g}}{700\text{ g}} \right) \times 100$

$Mass\ \%\ = 0.335714... \times 100 \approx 33.57\%$

Visual Representation of Mixing Process

300g (25%) + 400g (40%) = 700g (33.57%)

Final Solution: The mass percentage of the resulting solution is 33.57%.


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