A bottle contains 500 ml of 2.4 M HC1 solution. How much water should he added to dilute it to 1.6 M HC1 solution ?

Explanation

To solve the problem of how much water should be added to dilute a 500 ml solution of 2.4 M HCl to a final concentration of 1.6 M, we can use the dilution formula, which relates the initial and final molarity and volume of a solution. The formula is:

\[ M_1 V_1 = M_2 V_2 \]

Where:
- \( M_1 \) = initial molarity (2.4 M)
- \( V_1 \) = initial volume (500 ml)
- \( M_2 \) = final molarity (1.6 M)
- \( V_2 \) = final volume (unknown)

### Step-by-Step Solution:

1. **Identify the known values:**
- \( M_1 = 2.4 \, \text{M} \)
- \( V_1 = 500 \, \text{ml} \)
- \( M_2 = 1.6 \, \text{M} \)

2. **Set up the dilution equation:**
\[ M_1 V_1 = M_2 V_2 \]

3. **Substitute the known values into the equation:**
\[ 2.4 \, \text{M} \times 500 \, \text{ml} = 1.6 \, \text{M} \times V_2 \]

4. **Calculate the left side:**
\[ 2.4 \times 500 = 1200 \]

5. **Now, substitute this value into the equation:**
\[ 1200 = 1.6 \times V_2 \]

6. **Solve for \( V_2 \):**
\[ V_2 = \frac{1200}{1.6} \]
\[ V_2 = 750 \, \text{ml} \]

7. **Determine the amount of water to be added:**
- The final volume \( V_2 \) is 750 ml, and the initial volume \( V_1 \) is 500 ml.
- Therefore, the amount of water to be added is:
\[ \text{Water to be added} = V_2 - V_1 = 750 \, \text{ml} - 500 \, \text{ml} = 250 \, \text{ml} \]

### Final Answer:
You should add **250 ml** of water to dilute the solution to 1.6 M HCl.