12 g of a saturated solution of potassium chloride at `20^@C`, when evaporated to dryness, leaves a solid residue of 3 g. Calculate the solubility of potassium chloride.

Explanation

To calculate the solubility of potassium chloride (KCl) from the given data, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the total weight of the saturated solution**:
The total weight of the saturated solution of potassium chloride is given as 12 g.

2. **Determine the weight of the solid residue**:
After evaporation, the solid residue left is 3 g.

3. **Calculate the weight of water in the solution**:
To find the weight of water in the solution, subtract the weight of the solid residue from the total weight of the saturated solution:
\[ \text{Weight of water} = \text{Total weight of solution} - \text{Weight of solid residue} \]
\[ \text{Weight of water} = 12 \, \text{g} - 3 \, \text{g} = 9 \, \text{g} \]

4. **Use the unitary method to find solubility**:
We know that 9 g of water can dissolve 3 g of KCl. We want to find out how much KCl can be dissolved in 100 g of water. Using the unitary method, we set up the proportion:
\[ \text{If } 9 \, \text{g of water} \text{ dissolves } 3 \, \text{g of KCl, then } 100 \, \text{g of water will dissolve } x \, \text{g of KCl} \]
\[ \frac{9 \, \text{g}}{3 \, \text{g}} = \frac{100 \, \text{g}}{x \, \text{g}} \]
Cross-multiplying gives:
\[ 9x = 300 \implies x = \frac{300}{9} \approx 33.33 \, \text{g} \]

5. **Conclusion**:
The solubility of potassium chloride at 20°C is approximately 33.33 g per 100 g of water.

### Final Answer:
The solubility of potassium chloride at 20°C is approximately **33.33 g per 100 g of water**.