The neutralization of 50 ml of 0.25N `H_2SO_4` will require ____ ml of
0.50 N NaOH.

Options

A. 2.5
B. 0.25
C. 50
D. 25

Explanation

To solve the problem of how many milliliters of 0.50 N NaOH are required to neutralize 50 ml of 0.25 N H₂SO₄, we can follow these steps:

### Step 1: Understand the 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 the balanced equation, we see that 1 mole of H₂SO₄ reacts with 2 moles of NaOH.

### Step 2: Calculate the Equivalents of H₂SO₄
Normality (N) is defined as the number of equivalents of solute per liter of solution. The formula for calculating equivalents is:
\[ \text{Equivalents} = \text{Normality} \times \text{Volume (L)} \]

For H₂SO₄:
- Normality (N) = 0.25 N
- Volume = 50 ml = 0.050 L

Calculating the equivalents of H₂SO₄:
\[ \text{Equivalents of H}_2\text{SO}_4 = 0.25 \, \text{N} \times 0.050 \, \text{L} = 0.0125 \, \text{equivalents} \]

### Step 3: Determine the Equivalents of NaOH Required
From the balanced equation, we know that 1 equivalent of H₂SO₄ reacts with 2 equivalents of NaOH. Therefore, the equivalents of NaOH required will be:
\[ \text{Equivalents of NaOH} = 2 \times \text{Equivalents of H}_2\text{SO}_4 \]
\[ \text{Equivalents of NaOH} = 2 \times 0.0125 = 0.025 \, \text{equivalents} \]

### Step 4: Calculate the Volume of NaOH Required
Now we can use the normality of NaOH to find the volume needed. We know:
\[ \text{Equivalents} = \text{Normality} \times \text{Volume (L)} \]

Let \( V \) be the volume of NaOH in liters. We have:
- Normality of NaOH = 0.50 N
- Equivalents of NaOH = 0.025

Setting up the equation:
\[ 0.025 = 0.50 \times V \]

Solving for \( V \):
\[ V = \frac{0.025}{0.50} = 0.050 \, \text{L} \]

Converting liters to milliliters:
\[ V = 0.050 \, \text{L} \times 1000 \, \text{ml/L} = 25 \, \text{ml} \]

### Conclusion
The volume of 0.50 N NaOH required to neutralize 50 ml of 0.25 N H₂SO₄ is **25 ml**.

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