The normality of solution obtained by mixing 100 ml of 0.2 M `H_(2) SO_(4)` with 100 ml of 0.2 M NaOH is

Options

A. 0.1
B. 0.2
C. 0.5
D. 0.3

Answer

To find the normality of the solution obtained by mixing 100 mL of 0.2 M \( H_2SO_4 \) with 100 mL of 0.2 M \( NaOH \), we can follow these steps:

### Step 1: Calculate the number of equivalents of \( H_2SO_4 \)

1. **Determine the number of equivalents of \( H_2SO_4 \)**:
- The formula for calculating equivalents is:
\[ \text{Number of equivalents} = \text{Molarity} \times \text{Volume (in L)} \times \text{n} \]
- For \( H_2SO_4 \), the normality factor \( n \) is 2 because it can donate 2 protons (H⁺ ions).
- Convert the volume from mL to L:
\[ 100 \text{ mL} = 0.1 \text{ L} \]
- Now calculate the equivalents:
\[ \text{Number of equivalents of } H_2SO_4 = 0.2 \, \text{M} \times 0.1 \, \text{L} \times 2 = 0.04 \, \text{equivalents} \]

### Step 2: Calculate the number of equivalents of \( NaOH \)

2. **Determine the number of equivalents of \( NaOH \)**:
- For \( NaOH \), the normality factor \( n \) is 1 because it can donate 1 hydroxide ion (OH⁻).
- Use the same formula:
\[ \text{Number of equivalents of } NaOH = 0.2 \, \text{M} \times 0.1 \, \text{L} \times 1 = 0.02 \, \text{equivalents} \]

### Step 3: Determine the limiting reagent

3. **Determine the limiting reagent**:
- Since \( H_2SO_4 \) has 0.04 equivalents and \( NaOH \) has 0.02 equivalents, \( NaOH \) is the limiting reagent.

### Step 4: Calculate the total volume of the solution

4. **Calculate the total volume of the solution**:
- The total volume after mixing is:
\[ 100 \text{ mL} + 100 \text{ mL} = 200 \text{ mL} = 0.2 \text{ L} \]

### Step 5: Calculate the normality of the resulting solution

5. **Calculate the normality of the resulting solution**:
- Normality (N) is given by:
\[ \text{Normality} = \frac{\text{Number of equivalents}}{\text{Total volume (in L)}} \]
- Since \( NaOH \) is the limiting reagent, we use its equivalents:
\[ \text{Normality} = \frac{0.02 \, \text{equivalents}}{0.2 \, \text{L}} = 0.1 \, \text{N} \]

### Final Answer:
The normality of the solution obtained by mixing 100 mL of 0.2 M \( H_2SO_4 \) with 100 mL of 0.2 M \( NaOH \) is **0.1 N**.

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