How much water is needed to dilute 10 ml of 10 N hydrochloric acid to make it exactly decinormal (0.1 N) ?

Options

A. 990 ml
B. 1000 ml
C. 1010 ml
D. 100 ml

Answer

To solve the problem of how much water is needed to dilute 10 ml of 10 N hydrochloric acid (HCl) to make it exactly decinormal (0.1 N), we can use the dilution formula which relates the normalities and volumes before and after dilution.

### Step-by-Step Solution:

1. **Identify the Given Values**:
- Initial Normality (N1) = 10 N
- Initial Volume (V1) = 10 ml
- Final Normality (N2) = 0.1 N
- Final Volume (V2) = V1 + V (where V is the volume of water to be added)

2. **Set Up the Dilution Equation**:
The dilution equation is given by:
\[ N1 \times V1 = N2 \times V2 \]
Substituting the known values into the equation:
\[ 10 \, \text{N} \times 10 \, \text{ml} = 0.1 \, \text{N} \times (10 \, \text{ml} + V) \]

3. **Calculate the Left Side**:
\[ 10 \times 10 = 100 \, \text{N ml} \]

4. **Set Up the Right Side**:
\[ 0.1 \times (10 + V) = 0.1 \times 10 + 0.1V = 1 + 0.1V \]

5. **Equate Both Sides**:
\[ 100 = 1 + 0.1V \]

6. **Isolate V**:
Subtract 1 from both sides:
\[ 100 - 1 = 0.1V \implies 99 = 0.1V \]
Now, divide both sides by 0.1:
\[ V = \frac{99}{0.1} = 990 \, \text{ml} \]

7. **Conclusion**:
Therefore, the amount of water needed to dilute the solution is **990 ml**.