How much water should be mixed with 12 mL of alcohol so as to obtain 12 % alcohol solution ?

Answer

To solve the problem of how much water should be mixed with 12 mL of alcohol to obtain a 12% alcohol solution, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Problem**: We need to find out how much water (let's call this volume \( x \)) should be added to 12 mL of alcohol to create a solution that has 12% alcohol concentration.

2. **Define the Variables**:
- Volume of alcohol (solute) = 12 mL
- Volume of water (solvent) = \( x \) mL
- Total volume of the solution = Volume of alcohol + Volume of water = \( 12 + x \) mL
- Desired concentration of alcohol = 12%

3. **Set Up the Concentration Equation**:
The formula for concentration is given by:
\[ \text{Concentration} = \left( \frac{\text{Volume of solute}}{\text{Total volume of solution}} \right) \times 100 \]
Plugging in the values we have:
\[ 12\% = \left( \frac{12}{12 + x} \right) \times 100 \]

4. **Solve the Equation**:
- First, convert the percentage to a decimal:
\[ 12\% = \frac{12}{100} = 0.12 \]
- Now, set up the equation:
\[ 0.12 = \frac{12}{12 + x} \]
- Cross-multiply to eliminate the fraction:
\[ 0.12(12 + x) = 12 \]
- Distribute \( 0.12 \):
\[ 1.44 + 0.12x = 12 \]
- Rearranging gives:
\[ 0.12x = 12 - 1.44 \]
\[ 0.12x = 10.56 \]
- Now, divide both sides by \( 0.12 \):
\[ x = \frac{10.56}{0.12} = 88 \, \text{mL} \]

5. **Conclusion**: Therefore, the volume of water that should be mixed with 12 mL of alcohol to obtain a 12% alcohol solution is **88 mL**.