Calculate the mass of potassium sulfate required to prepare its 10% solution in 100g of water.

Options

A. 11.1g
B. 22.2g
C. 33.3g
D. 44.4g

Explanation

To calculate the mass of potassium sulfate (K₂SO₄) required to prepare a 10% solution in 100g of water, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Definition of Mass Percentage**:
The mass percentage of a solution is defined as:
\[ \text{Mass Percentage} = \left( \frac{\text{Mass of Solute}}{\text{Mass of Solution}} \right) \times 100 \]

2. **Identify the Given Values**:
- Mass percentage of the solution = 10%
- Mass of water (solvent) = 100g

3. **Set Up the Equation**:
Let \( x \) be the mass of potassium sulfate (solute) required. The mass of the solution is the sum of the mass of the solute and the mass of the solvent:
\[ \text{Mass of Solution} = \text{Mass of Solute} + \text{Mass of Solvent} = x + 100g \]
Now, substituting the values into the mass percentage formula:
\[ 10 = \left( \frac{x}{x + 100} \right) \times 100 \]

4. **Solve the Equation**:
Rearranging the equation gives:
\[ 10 = \frac{x}{x + 100} \times 100 \]
Dividing both sides by 100:
\[ 0.1 = \frac{x}{x + 100} \]
Cross-multiplying gives:
\[ 0.1(x + 100) = x \]
Expanding the left side:
\[ 0.1x + 10 = x \]
Rearranging the equation:
\[ 10 = x - 0.1x \]
\[ 10 = 0.9x \]
Dividing both sides by 0.9:
\[ x = \frac{10}{0.9} \approx 11.11g \]

5. **Conclusion**:
The mass of potassium sulfate required to prepare a 10% solution in 100g of water is approximately **11.11 grams**.