How many `g "of" KCl` would have to be dissolved in `60 g H_(2)O` to give `20%` by weight of solution?

Options

A. `15 g`
B. `1.5 g`
C. `11.5 g`
D. `31. 5 g`

Explanation

To solve the problem of how many grams of KCl must be dissolved in 60 g of water to create a solution that is 20% by weight, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Concept of Weight Percent**:
The weight percent (w/w%) of a solution is defined as the mass of the solute divided by the total mass of the solution, multiplied by 100. The formula is:
\[ \text{Weight percent} = \frac{W_A}{W_A + W_B} \times 100 \]
where \(W_A\) is the weight of the solute (KCl) and \(W_B\) is the weight of the solvent (water).

2. **Identify Known Values**:
- Weight percent of the solution = 20%
- Weight of water (solvent), \(W_B = 60 \, \text{g}\)

3. **Set Up the Equation**:
We need to find \(W_A\) (the weight of KCl). Plugging the known values into the weight percent formula:
\[ 20 = \frac{W_A}{W_A + 60} \times 100 \]

4. **Rearrange the Equation**:
To eliminate the percentage, divide both sides by 100:
\[ 0.2 = \frac{W_A}{W_A + 60} \]
Now, cross-multiply to solve for \(W_A\):
\[ 0.2(W_A + 60) = W_A \]

5. **Distribute and Simplify**:
Expanding the left side gives:
\[ 0.2W_A + 12 = W_A \]
Rearranging this equation to isolate \(W_A\):
\[ W_A - 0.2W_A = 12 \]
\[ 0.8W_A = 12 \]

6. **Solve for \(W_A\)**:
Divide both sides by 0.8:
\[ W_A = \frac{12}{0.8} = 15 \, \text{g} \]

### Final Answer:
Thus, **15 grams of KCl** must be dissolved in 60 grams of water to create a 20% by weight solution.