What volume of 2 N HCI be taken to form 500 mL `N/10` solution of HCl?

Answer

To solve the problem of finding the volume of 2 N HCl required to prepare 500 mL of a 1/10 N (or 0.1 N) HCl solution, we can use the dilution equation:

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Normality of the concentrated solution (N1) = 2 N
- Normality of the diluted solution (N2) = 1/10 N = 0.1 N
- Final volume of the diluted solution (V2) = 500 mL

2. **Use the Dilution Equation:**
The dilution equation is given by:
\[ N1 \times V1 = N2 \times V2 \]
Where:
- \(N1\) = Normality of the concentrated solution
- \(V1\) = Volume of the concentrated solution we need to find
- \(N2\) = Normality of the diluted solution
- \(V2\) = Volume of the diluted solution

3. **Substitute the Known Values:**
Substitute the known values into the equation:
\[ 2 \, \text{N} \times V1 = \left(\frac{1}{10} \, \text{N}\right) \times 500 \, \text{mL} \]

4. **Calculate the Right Side:**
Calculate \(N2 \times V2\):
\[ \frac{1}{10} \times 500 = 50 \, \text{N mL} \]

5. **Set Up the Equation:**
Now we have:
\[ 2 \, \text{N} \times V1 = 50 \, \text{N mL} \]

6. **Solve for \(V1\):**
Rearranging the equation to solve for \(V1\):
\[ V1 = \frac{50}{2} = 25 \, \text{mL} \]

### Final Answer:
The volume of 2 N HCl required to form 500 mL of a 1/10 N solution is **25 mL**.

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