Calculate the mass of potassium sulfate required to prepare its 30% solution in 100g of water.

Options

A. 42.85g
B. 44g
C. 50g
D. 55g

Explanation

To calculate the mass of potassium sulfate required to prepare a 30% solution in 100g of water, 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 solute is potassium sulfate, and the solvent is water.

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

### Step 3: Set Up the Equation
Since we want a 30% solution, we can set up the equation using the mass percentage formula:
\[ 30 = \left( \frac{x}{x + 100} \right) \times 100 \]

### Step 4: Simplify the Equation
Rearranging the equation gives:
\[ 30 = \frac{x}{x + 100} \times 100 \]
Dividing both sides by 100:
\[ 0.30 = \frac{x}{x + 100} \]

### Step 5: Cross Multiply
Cross-multiplying gives:
\[ 0.30(x + 100) = x \]
Expanding the left side:
\[ 0.30x + 30 = x \]

### Step 6: Solve for \( x \)
Rearranging the equation:
\[ 30 = x - 0.30x \]
\[ 30 = 0.70x \]
Now, divide both sides by 0.70:
\[ x = \frac{30}{0.70} = 42.857 \text{ g} \]

### Step 7: Round the Answer
Rounding to two decimal places, we get:
\[ x \approx 42.86 \text{ g} \]

### Conclusion
The mass of potassium sulfate required to prepare a 30% solution in 100 g of water is approximately **42.86 grams**.

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