What is the volume (in litres) of `0.1 M H_(2)SO_(4)` required to completely neutralize 1 litre of 0.5 M NaOH ?

Options

A. 5
B. `2.5`
C. `0.5`
D. 10

Explanation

To solve the question of what volume (in liters) of `0.1 M H2SO4` is required to completely neutralize 1 liter of `0.5 M NaOH`, we can follow these steps:

### Step 1: Write the neutralization reaction
The neutralization reaction between sodium hydroxide (NaOH) and sulfuric acid (H2SO4) can be written as:
\[ \text{H}_2\text{SO}_4 + 2 \text{NaOH} \rightarrow \text{Na}_2\text{SO}_4 + 2 \text{H}_2\text{O} \]
This shows that one mole of H2SO4 reacts with two moles of NaOH.

### Step 2: Calculate the number of moles of NaOH
Given that the concentration of NaOH is `0.5 M` and the volume is `1 L`, we can calculate the number of moles of NaOH using the formula:
\[ \text{Number of moles} = \text{Molarity} \times \text{Volume} \]
Substituting the values:
\[ \text{Number of moles of NaOH} = 0.5 \, \text{mol/L} \times 1 \, \text{L} = 0.5 \, \text{mol} \]

### Step 3: Determine the number of moles of H2SO4 required
From the balanced equation, we see that 2 moles of NaOH react with 1 mole of H2SO4. Therefore, the number of moles of H2SO4 required to neutralize 0.5 moles of NaOH is:
\[ \text{Number of moles of H2SO4} = \frac{0.5 \, \text{mol NaOH}}{2} = 0.25 \, \text{mol H2SO4} \]

### Step 4: Calculate the volume of H2SO4 required
We know the molarity of H2SO4 is `0.1 M`. We can use the molarity formula again to find the volume required:
\[ \text{Molarity} = \frac{\text{Number of moles}}{\text{Volume in liters}} \]
Rearranging this gives us:
\[ \text{Volume} = \frac{\text{Number of moles}}{\text{Molarity}} \]
Substituting the values:
\[ \text{Volume of H2SO4} = \frac{0.25 \, \text{mol}}{0.1 \, \text{mol/L}} = 2.5 \, \text{L} \]

### Final Answer
The volume of `0.1 M H2SO4` required to completely neutralize `1 L` of `0.5 M NaOH` is **2.5 liters**.

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