The volume of water to be added to 200 mL of seminormal HCl solution to make it decinormal is

Options

A. 200 mL
B. 400 mL
C. 600 mL
D. 800 mL

Answer

To solve the problem of how much water needs to be added to 200 mL of a semi-normal (0.5 N) HCl solution to make it decinormal (0.1 N), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Initial Conditions**:
- Initial volume (V1) = 200 mL
- Initial normality (N1) = 0.5 N (which is semi-normal)
- Final normality (N2) = 0.1 N (which is decinormal)

2. **Use the Dilution Formula**:
The dilution formula states that:
\[ N_1V_1 = N_2V_2 \]
Where:
- \(N_1\) = initial normality
- \(V_1\) = initial volume
- \(N_2\) = final normality
- \(V_2\) = final volume after dilution

3. **Substitute the Known Values**:
Plugging in the values we have:
\[ 0.5 \, \text{N} \times 200 \, \text{mL} = 0.1 \, \text{N} \times V_2 \]

4. **Calculate \(V_2\)**:
Rearranging the equation to solve for \(V_2\):
\[ V_2 = \frac{0.5 \, \text{N} \times 200 \, \text{mL}}{0.1 \, \text{N}} = \frac{100}{0.1} = 1000 \, \text{mL} \]

5. **Determine the Volume of Water to be Added**:
Now, to find out how much water needs to be added, we subtract the initial volume from the final volume:
\[ \text{Volume of water to be added} = V_2 - V_1 = 1000 \, \text{mL} - 200 \, \text{mL} = 800 \, \text{mL} \]

### Final Answer:
The volume of water to be added to 200 mL of semi-normal HCl solution to make it decinormal is **800 mL**.

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