Calculate the mass of potassium sulfate required to prepare its 13% solution in 100g of water.

Options

A. 15g
B. 18g
C. 20g
D. 21g

Explanation

To calculate the mass of potassium sulfate required to prepare a 13% solution in 100 g of water, we can follow these steps:

### Step 1: Understand the Definition of Mass Percentage
The mass percentage of a solution is defined as:
\[ \text{Mass \%} = \left( \frac{\text{Mass of solute}}{\text{Mass of solution}} \right) \times 100 \]
In this case, the mass percentage is given as 13%.

### Step 2: Define Variables
Let:
- \( x \) = mass of potassium sulfate (solute) in grams
- The mass of water (solvent) = 100 g
- 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:
\[ 13 = \left( \frac{x}{x + 100} \right) \times 100 \]

### Step 4: Simplify the Equation
To eliminate the percentage, we can rewrite the equation:
\[ \frac{x}{x + 100} = \frac{13}{100} \]

### Step 5: Cross-Multiply
Cross-multiplying gives us:
\[ 100x = 13(x + 100) \]

### Step 6: Expand and Rearrange
Expanding the right side:
\[ 100x = 13x + 1300 \]
Now, rearranging the equation:
\[ 100x - 13x = 1300 \]
\[ 87x = 1300 \]

### Step 7: Solve for \( x \)
Now, divide both sides by 87:
\[ x = \frac{1300}{87} \approx 14.94 \text{ g} \]

### Step 8: Round to Appropriate Significant Figures
Rounding to two significant figures, we find:
\[ x \approx 15 \text{ g} \]

### Final Answer
The mass of potassium sulfate required to prepare a 13% solution in 100 g of water is approximately **15 g**.

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