Calculate the mass of potassium sulfate required to prepare its 15% solution in 100g of water.

Options

A. 17.6g
B. 21g
C. 37.6g
D. 15g

Explanation

To calculate the mass of potassium sulfate required to prepare a 15% 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:
\[ \text{Mass percentage} = \left( \frac{\text{mass of solute}}{\text{mass of solution}} \right) \times 100 \]
In this case, the solute is potassium sulfate (K₂SO₄) and the solvent is water.

### Step 2: Define the variables
Let the mass of potassium sulfate be \( x \) grams. The mass of the solvent (water) is given as 100 grams.

### Step 3: Calculate the mass of the solution
The mass of the solution is the sum of the mass of the solute and the mass of the solvent:
\[ \text{Mass of solution} = \text{mass of solute} + \text{mass of solvent} = x + 100 \text{ grams} \]

### Step 4: Set up the equation using the mass percentage
We know the mass percentage is 15%, so we can set up the equation:
\[ 15 = \left( \frac{x}{x + 100} \right) \times 100 \]

### Step 5: Simplify the equation
To eliminate the percentage, we can rewrite the equation:
\[ 15 = \frac{x}{x + 100} \times 100 \]
Dividing both sides by 100:
\[ 0.15 = \frac{x}{x + 100} \]

### Step 6: Cross-multiply to solve for \( x \)
Cross-multiplying gives:
\[ 0.15(x + 100) = x \]
Expanding the left side:
\[ 0.15x + 15 = x \]

### Step 7: Rearrange the equation
Rearranging the equation to isolate \( x \):
\[ 15 = x - 0.15x \]
\[ 15 = 0.85x \]

### Step 8: Solve for \( x \)
Now, divide both sides by 0.85:
\[ x = \frac{15}{0.85} \approx 17.65 \text{ grams} \]

### Conclusion
The mass of potassium sulfate required to prepare a 15% solution in 100g of water is approximately **17.65 grams**.

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