Calculate the mass of potassium sulfate required to prepare its 50% solution in 100g of water.

Options

A. 100g
B. 150g
C. 200g
D. 10g

Explanation

To calculate the mass of potassium sulfate required to prepare a 50% solution in 100g of water, we can follow these steps:

### Step 1: Understand the definition of a 50% solution
A 50% mass/volume solution means that there are 50 grams of solute (potassium sulfate) in every 100 grams of the solution.

### Step 2: Define the variables
Let the mass of potassium sulfate be \( X \) grams. The total mass of the solution will be the mass of the solute (potassium sulfate) plus the mass of the solvent (water).

### Step 3: Set up the equation
The mass of the solution can be expressed as:
\[ \text{Mass of solution} = \text{Mass of solute} + \text{Mass of solvent} \]
In this case:
\[ \text{Mass of solution} = X + 100 \, \text{g} \]
Since we want a 50% solution, we can use the formula for mass percentage:
\[ \text{Mass percentage} = \left( \frac{\text{Mass of solute}}{\text{Mass of solution}} \right) \times 100 \]
Substituting the values we have:
\[ 50 = \left( \frac{X}{X + 100} \right) \times 100 \]

### Step 4: Solve the equation
Now, we can simplify the equation:
\[ 50 = \frac{X}{X + 100} \times 100 \]
Dividing both sides by 100:
\[ 0.5 = \frac{X}{X + 100} \]
Cross-multiplying gives:
\[ 0.5(X + 100) = X \]
Expanding the left side:
\[ 0.5X + 50 = X \]
Now, rearranging the equation:
\[ 50 = X - 0.5X \]
\[ 50 = 0.5X \]
Dividing both sides by 0.5:
\[ X = 100 \, \text{g} \]

### Step 5: Conclusion
The mass of potassium sulfate required to prepare a 50% solution in 100g of water is **100 grams**.

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