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 HCl solution to make it decinormal, we can follow these steps:

### Step 1: Understand the Given Information
- We have a semi-normal HCl solution, which means its normality (N1) is \( \frac{N}{2} \).
- We want to dilute this solution to make it decinormal, which means the final normality (N2) will be \( \frac{N}{10} \).
- The initial volume (V1) of the semi-normal HCl solution is 400 ml.

### Step 2: Set Up the Dilution Equation
For dilution, we use the formula:
\[ N1 \times V1 = N2 \times V2 \]
Where:
- \( N1 = \frac{N}{2} \)
- \( N2 = \frac{N}{10} \)
- \( V1 = 400 \, \text{ml} \)
- \( V2 \) is the final volume we need to find.

### Step 3: Substitute the Values into the Equation
Substituting the values into the dilution equation:
\[ \left(\frac{N}{2}\right) \times 400 = \left(\frac{N}{10}\right) \times V2 \]

### Step 4: Simplify the Equation
We can cancel \( N \) from both sides (assuming \( N \neq 0 \)):
\[ \frac{400}{2} = \frac{V2}{10} \]
This simplifies to:
\[ 200 = \frac{V2}{10} \]

### Step 5: Solve for V2
To find \( V2 \), multiply both sides by 10:
\[ V2 = 200 \times 10 = 2000 \, \text{ml} \]

### Step 6: Calculate the Volume of Water to be Added
Now, we need to find the volume of water to be added. The volume of water added is given by:
\[ \text{Volume of water added} = V2 - V1 \]
Substituting the values:
\[ \text{Volume of water added} = 2000 \, \text{ml} - 400 \, \text{ml} = 1600 \, \text{ml} \]

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

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