To neutralise 100 mL of 0.1 N `H_(2)SO_(4)`, amount of 2N NaOH required is

Options

A. 5 mL
B. 0.5 mL
C. 0.1 mL
D. 100 mL

Explanation

To solve the problem of how much volume of 2N NaOH is required to neutralize 100 mL of 0.1N H₂SO₄, we can use the concept of normality and the dilution equation. Here’s a step-by-step solution:

### Step 1: Understand the Neutralization Reaction
The neutralization reaction between sulfuric acid (H₂SO₄) and sodium hydroxide (NaOH) can be represented as:
\[ \text{H}_2\text{SO}_4 + 2 \text{NaOH} \rightarrow \text{Na}_2\text{SO}_4 + 2 \text{H}_2\text{O} \]
From this equation, we see that 1 mole of H₂SO₄ reacts with 2 moles of NaOH.

### Step 2: Calculate the Equivalent of H₂SO₄
Normality (N) is defined as the number of equivalents of solute per liter of solution. For H₂SO₄, which can donate 2 protons (H⁺), the equivalents can be calculated as follows:
- Normality (N) = 0.1 N
- Volume (V) = 100 mL = 0.1 L

The number of equivalents of H₂SO₄ is given by:
\[ \text{Equivalents of H}_2\text{SO}_4 = N \times V = 0.1 \, \text{N} \times 0.1 \, \text{L} = 0.01 \, \text{equivalents} \]

### Step 3: Determine the Required Equivalents of NaOH
From the balanced equation, we know that 1 equivalent of H₂SO₄ requires 2 equivalents of NaOH. Therefore, the equivalents of NaOH required will be:
\[ \text{Equivalents of NaOH} = 2 \times \text{Equivalents of H}_2\text{SO}_4 = 2 \times 0.01 = 0.02 \, \text{equivalents} \]

### Step 4: Calculate the Volume of 2N NaOH Required
Now, we need to find out how much volume of 2N NaOH is required to provide 0.02 equivalents. Using the formula:
\[ \text{Equivalents} = N \times V \]
We can rearrange it to find the volume (V):
\[ V = \frac{\text{Equivalents}}{N} \]

Substituting the values:
- Equivalents = 0.02
- Normality of NaOH (N) = 2N

Thus,
\[ V = \frac{0.02 \, \text{equivalents}}{2 \, \text{N}} = 0.01 \, \text{L} = 10 \, \text{mL} \]

### Final Answer
The volume of 2N NaOH required to neutralize 100 mL of 0.1N H₂SO₄ is **10 mL**.

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