The volume of 0.1 M `H_(2)SO_(4)` that is needed to completely neutralise 40 ml of 0.2 M NaOH is

Options

A. 10 ml
B. 20 ml
C. 40 ml
D. 80 ml

Explanation

To find the volume of 0.1 M \( H_2SO_4 \) needed to completely neutralize 40 ml of 0.2 M NaOH, we can follow these steps:

### Step 1: Write the balanced chemical equation
The balanced chemical reaction between sulfuric acid (\( H_2SO_4 \)) and sodium hydroxide (\( NaOH \)) is:
\[ H_2SO_4 + 2 NaOH \rightarrow Na_2SO_4 + 2 H_2O \]
From the equation, we can see that 1 mole of \( H_2SO_4 \) reacts with 2 moles of \( NaOH \).

### Step 2: Calculate the number of moles of NaOH
We can calculate the number of moles of \( NaOH \) using the formula:
\[ \text{Moles} = \text{Molarity} \times \text{Volume (in L)} \]
Given that the volume of \( NaOH \) is 40 ml (which is 0.040 L) and the molarity is 0.2 M:
\[ \text{Moles of NaOH} = 0.2 \, \text{mol/L} \times 0.040 \, \text{L} = 0.008 \, \text{mol} \]

### Step 3: Determine the number of moles of \( H_2SO_4 \) required
From the balanced equation, we know that 1 mole of \( H_2SO_4 \) reacts with 2 moles of \( NaOH \). Therefore, the moles of \( H_2SO_4 \) required can be calculated as:
\[ \text{Moles of } H_2SO_4 = \frac{\text{Moles of NaOH}}{2} = \frac{0.008 \, \text{mol}}{2} = 0.004 \, \text{mol} \]

### Step 4: Calculate the volume of \( H_2SO_4 \) needed
Now, we can find the volume of \( H_2SO_4 \) needed using its molarity. The formula for volume is:
\[ \text{Volume} = \frac{\text{Moles}}{\text{Molarity}} \]
Given that the molarity of \( H_2SO_4 \) is 0.1 M:
\[ \text{Volume of } H_2SO_4 = \frac{0.004 \, \text{mol}}{0.1 \, \text{mol/L}} = 0.04 \, \text{L} = 40 \, \text{ml} \]

### Final Answer
The volume of 0.1 M \( H_2SO_4 \) needed to completely neutralize 40 ml of 0.2 M NaOH is **40 ml**.

---