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 a 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, follow these steps:

### Step 1: Calculate the amount of NH₄Cl in the first solution (25% solution)
- The first solution is 25% NH₄Cl by weight. This means that in 100 g of the solution, there are 25 g of NH₄Cl.
- For 300 g of this solution:
\[ \text{Amount of NH₄Cl} = \left( \frac{25 \text{ g}}{100 \text{ g}} \right) \times 300 \text{ g} = 75 \text{ g} \]

### Step 2: Calculate the amount of NH₄Cl in the second solution (40% solution)
- The second solution is 40% NH₄Cl by weight. This means that in 100 g of the solution, there are 40 g of NH₄Cl.
- For 150 g of this solution:
\[ \text{Amount of NH₄Cl} = \left( \frac{40 \text{ g}}{100 \text{ g}} \right) \times 150 \text{ g} = 60 \text{ g} \]

### Step 3: Calculate the total amount of NH₄Cl in the mixed solution
- Total NH₄Cl from both solutions:
\[ \text{Total NH₄Cl} = 75 \text{ g} + 60 \text{ g} = 135 \text{ g} \]

### Step 4: Calculate the total mass of the mixed solution
- Total mass of the mixed solution:
\[ \text{Total mass} = 300 \text{ g} + 150 \text{ g} = 450 \text{ g} \]

### Step 5: Calculate the percentage by weight of NH₄Cl in the mixed solution
- Percentage by weight of NH₄Cl:
\[ \text{Percentage} = \left( \frac{\text{Total NH₄Cl}}{\text{Total mass}} \right) \times 100 = \left( \frac{135 \text{ g}}{450 \text{ g}} \right) \times 100 \]
- Simplifying this:
\[ = \frac{135}{450} \times 100 = 30\% \]

### Final Answer
The concentration of the solution obtained by mixing the two solutions is **30% by weight**.

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