Calculate the mass of potassium sulfate required to prepare its 25% solution in 100g of water.

Options

A. 15g
B. 22.2g
C. 33.3g
D. 20g

Explanation

To calculate the mass of potassium sulfate (K₂SO₄) required to prepare a 25% solution in 100g of water, we can follow these steps:

### Step 1: Understand the Definition of Mass Percentage
The mass percentage of a solution is defined as:
\[ \text{Mass percentage} = \left( \frac{\text{Mass of solute}}{\text{Mass of solution}} \right) \times 100 \]
In this case, the mass percentage is given as 25%.

### Step 2: Define the Variables
Let:
- \( x \) = mass of potassium sulfate (solute) in grams.
- Mass of water (solvent) = 100 g.
- Therefore, the mass of the solution = mass of solute + mass of solvent = \( x + 100 \) g.

### Step 3: Set Up the Equation
Using the mass percentage formula:
\[ 25 = \left( \frac{x}{x + 100} \right) \times 100 \]

### Step 4: Simplify the Equation
To simplify, divide both sides by 100:
\[ 0.25 = \frac{x}{x + 100} \]

### Step 5: Cross-Multiply
Cross-multiply to eliminate the fraction:
\[ 0.25(x + 100) = x \]

### Step 6: Distribute and Rearrange
Distributing \( 0.25 \):
\[ 0.25x + 25 = x \]
Now, rearranging the equation gives:
\[ 25 = x - 0.25x \]
\[ 25 = 0.75x \]

### Step 7: Solve for \( x \)
Now, solve for \( x \):
\[ x = \frac{25}{0.75} = \frac{25 \times 100}{75} = \frac{2500}{75} \approx 33.33 \text{ g} \]

### Conclusion
The mass of potassium sulfate required to prepare a 25% solution in 100 g of water is approximately **33.33 grams**.

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