Calculate the concentration (in percentage by weight) of a solution obtained by mixing 300 g `25%` by weight solution of `NH_(4)Cl` and 150 g of `40%` by weight solution of `NH_(4)Cl`

Answer

To calculate the concentration (in percentage by weight) of the solution obtained by mixing 300 g of a 25% by weight solution of NH₄Cl and 150 g of a 40% by weight solution of NH₄Cl, we can follow these steps:

### Step 1: Calculate the mass of NH₄Cl in the first solution
The first solution is 300 g with a concentration of 25% by weight. This means that in every 100 g of the solution, there are 25 g of NH₄Cl.

To find the mass of NH₄Cl in 300 g of this solution:
\[ \text{Mass of NH₄Cl} = \left( \frac{25}{100} \right) \times 300 = 75 \text{ g} \]

### Step 2: Calculate the mass of NH₄Cl in the second solution
The second solution is 150 g with a concentration of 40% by weight. This means that in every 100 g of the solution, there are 40 g of NH₄Cl.

To find the mass of NH₄Cl in 150 g of this solution:
\[ \text{Mass of NH₄Cl} = \left( \frac{40}{100} \right) \times 150 = 60 \text{ g} \]

### Step 3: Calculate the total mass of NH₄Cl
Now, we can find the total mass of NH₄Cl from both solutions:
\[ \text{Total mass of NH₄Cl} = 75 \text{ g} + 60 \text{ g} = 135 \text{ g} \]

### Step 4: Calculate the total mass of the mixed solution
The total mass of the mixed solution is the sum of the masses of the two solutions:
\[ \text{Total mass of solution} = 300 \text{ g} + 150 \text{ g} = 450 \text{ g} \]

### Step 5: Calculate the percentage by weight of NH₄Cl in the mixed solution
To find the concentration of NH₄Cl in the mixed solution, we use the formula:
\[ \text{Percentage by weight} = \left( \frac{\text{Mass of solute}}{\text{Mass of solution}} \right) \times 100 \]
Substituting the values we calculated:
\[ \text{Percentage by weight} = \left( \frac{135 \text{ g}}{450 \text{ g}} \right) \times 100 = 30\% \]

### Final Answer
The concentration of the mixed solution is **30% by weight**.

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