Calculate the mass of potassium sulfate required to prepare its 40% solution in 100g of water.

Options

A. 16.6g
B. 54g
C. 66.6g
D. 20g

Explanation

To calculate the mass of potassium sulfate required to prepare a 40% solution in 100g of water, we can follow these steps:

### Step 1: Understand the Concept of Mass Percentage
The mass percentage of a solution is defined as:
\[ \text{Mass Percentage} = \left( \frac{\text{Mass of Solute}}{\text{Mass of Solution}} \right) \times 100 \]
Where:
- Mass of Solute = Mass of potassium sulfate (let's denote it as \( x \) grams)
- Mass of Solution = Mass of Solute + Mass of Solvent (water)

### Step 2: Set Up the Equation
Given that the mass percentage is 40%, we can set up the equation:
\[ 40 = \left( \frac{x}{100 + x} \right) \times 100 \]

### Step 3: Simplify the Equation
We can simplify the equation:
\[ 40 = \frac{x}{100 + x} \times 100 \]
Dividing both sides by 100:
\[ 0.4 = \frac{x}{100 + x} \]

### Step 4: Cross Multiply to Solve for \( x \)
Cross-multiplying gives us:
\[ 0.4(100 + x) = x \]
Expanding this:
\[ 40 + 0.4x = x \]

### Step 5: Rearrange the Equation
Rearranging the equation to isolate \( x \):
\[ 40 = x - 0.4x \]
\[ 40 = 0.6x \]

### Step 6: Solve for \( x \)
Now, divide both sides by 0.6:
\[ x = \frac{40}{0.6} = \frac{400}{6} \approx 66.67 \text{ grams} \]

### Conclusion
The mass of potassium sulfate required to prepare a 40% solution in 100g of water is approximately **66.67 grams**.

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