Calculate the mass of potassium sulfate required to prepare its 35% solution in 100g of water.

Options

A. 28g
B. 40g
C. 48.53g
D. 53.84g

Explanation

To solve the problem of calculating the mass of potassium sulfate required to prepare a 35% solution in 100g of water, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Problem**: We need to prepare a 35% solution of potassium sulfate (K₂SO₄) in 100g of water. A 35% solution means that 35g of solute (K₂SO₄) is present in 100g of the total solution.

2. **Define Variables**:
- Let the mass of potassium sulfate (solute) be \( x \) grams.
- The mass of water (solvent) is given as 100g.
- Therefore, the total mass of the solution will be \( x + 100 \) grams.

3. **Set Up the Percentage Formula**:
- The mass percentage formula is given by:
\[ \text{Mass \%} = \left( \frac{\text{Mass of solute}}{\text{Mass of solution}} \right) \times 100 \]
- For our case, we know the mass percentage is 35%, so we can write:
\[ 35 = \left( \frac{x}{x + 100} \right) \times 100 \]

4. **Rearrange the Equation**:
- To eliminate the percentage, we can simplify the equation:
\[ 35 = \frac{x}{x + 100} \times 100 \]
- Dividing both sides by 100 gives:
\[ 0.35 = \frac{x}{x + 100} \]

5. **Cross Multiply**:
- Cross multiplying gives:
\[ 0.35(x + 100) = x \]

6. **Expand and Simplify**:
- Expanding the left side:
\[ 0.35x + 35 = x \]
- Rearranging the equation:
\[ x - 0.35x = 35 \]
\[ 0.65x = 35 \]

7. **Solve for \( x \)**:
- Dividing both sides by 0.65:
\[ x = \frac{35}{0.65} \approx 53.85 \text{ grams} \]

8. **Conclusion**:
- The mass of potassium sulfate required to prepare a 35% solution in 100g of water is approximately **53.85 grams**.