Calculate the volume of water to be added to 400 ml of seminormal HCl solution to make it decinormal

Options

A. 1000 ml
B. 1200 ml
C. 1600 ml
D. 2000 ml

Answer

To solve the problem of calculating the volume of water to be added to 400 ml of semi-normal (0.5 N) HCl solution to make it decinormal (0.1 N), we can follow these steps:

### Step 1: Understand the relationship between normality, volume, and dilution
The dilution formula can be expressed as:
\[ N_1 \times V_1 = N_2 \times V_2 \]
where:
- \( N_1 \) is the initial normality (0.5 N for semi-normal HCl),
- \( V_1 \) is the initial volume (400 ml),
- \( N_2 \) is the final normality (0.1 N for decinormal HCl),
- \( V_2 \) is the final volume after adding water.

### Step 2: Substitute the known values into the formula
We can rearrange the equation to solve for \( V_2 \):
\[ V_2 = \frac{N_1 \times V_1}{N_2} \]

Substituting the known values:
\[ V_2 = \frac{0.5 \, \text{N} \times 400 \, \text{ml}}{0.1 \, \text{N}} \]

### Step 3: Calculate \( V_2 \)
Now, perform the calculation:
\[ V_2 = \frac{200 \, \text{N} \cdot \text{ml}}{0.1 \, \text{N}} = 2000 \, \text{ml} \]

### Step 4: Calculate the volume of water to be added
To find the volume of water to be added, subtract the initial volume from the final volume:
\[ \text{Volume of water} = V_2 - V_1 \]
\[ \text{Volume of water} = 2000 \, \text{ml} - 400 \, \text{ml} = 1600 \, \text{ml} \]

### Final Answer
The volume of water to be added is **1600 ml**.

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