Calculate the mass of potassium sulfate required to prepare its 20% solution in 100g of water.

Options

A. 25g
B. 15g
C. 10g
D. 5g

Explanation

To calculate the mass of potassium sulfate required to prepare a 20% solution in 100g of water, we can follow these steps:

### Step 1: Understand the definition of a percentage solution
A 20% (w/w) solution means that there are 20 grams of solute (potassium sulfate) in every 100 grams of the solution.

### Step 2: Define the variables
Let:
- \( x \) = mass of potassium sulfate (solute) in grams
- Total mass of the solution = mass of solute + mass of solvent (water)

Given:
- Mass of water (solvent) = 100 grams
- Mass of solution = mass of solute + mass of solvent = \( x + 100 \) grams

### Step 3: Set up the equation using the percentage definition
According to the percentage formula:
\[ \text{Percentage (w/w)} = \left( \frac{\text{mass of solute}}{\text{mass of solution}} \right) \times 100 \]
For our case:
\[ 20 = \left( \frac{x}{x + 100} \right) \times 100 \]

### Step 4: Simplify the equation
Dividing both sides by 100:
\[ 0.20 = \frac{x}{x + 100} \]

### Step 5: Cross-multiply to solve for \( x \)
Cross-multiplying gives:
\[ 0.20(x + 100) = x \]
Expanding the left side:
\[ 0.20x + 20 = x \]

### Step 6: Rearrange the equation
Rearranging the equation to isolate \( x \):
\[ 20 = x - 0.20x \]
\[ 20 = 0.80x \]

### Step 7: Solve for \( x \)
Dividing both sides by 0.80:
\[ x = \frac{20}{0.80} = 25 \text{ grams} \]

### Conclusion
The mass of potassium sulfate required to prepare a 20% solution in 100g of water is **25 grams**.

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