`5N H_(2)SO_(4)` was diluted from 1 litre to 10 litres. Normality of the solution obtained is

Options

A. 10 N
B. 5 N
C. 1 N
D. 0.5 N

Answer

To solve the problem of finding the normality of a diluted solution of \( H_2SO_4 \), we can use the dilution formula:

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Initial Normality (\( n_1 \)) = 5 N
- Initial Volume (\( V_1 \)) = 1 L
- Final Volume (\( V_2 \)) = 10 L

2. **Use the Dilution Formula:**
The relationship between the initial and final normalities and volumes is given by the formula:
\[ n_1 \times V_1 = n_2 \times V_2 \]
where:
- \( n_1 \) = initial normality
- \( V_1 \) = initial volume
- \( n_2 \) = final normality (which we need to find)
- \( V_2 \) = final volume

3. **Substitute the Known Values:**
Plugging in the known values into the equation:
\[ 5 \, \text{N} \times 1 \, \text{L} = n_2 \times 10 \, \text{L} \]

4. **Calculate \( n_2 \):**
Rearranging the equation to solve for \( n_2 \):
\[ n_2 = \frac{5 \, \text{N} \times 1 \, \text{L}}{10 \, \text{L}} = \frac{5}{10} = 0.5 \, \text{N} \]

5. **Conclusion:**
The normality of the diluted solution is \( 0.5 \, \text{N} \).

### Final Answer:
The normality of the solution obtained after dilution is **0.5 N**.

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