What volume of 0.10 M `H_(2)SO_(4)` must be added to 50 mL of a 0.10 NaOH solution to make a solution in which molarity of the `H_(2)SO_(4)` is 0.050M?

Options

A. 400 mL
B. 50 mL
C. 100 mL
D. 150 mL

Answer

To solve the problem, we need to determine the volume of 0.10 M H₂SO₄ that must be added to 50 mL of 0.10 M NaOH to achieve a final concentration of 0.050 M H₂SO₄.

### Step-by-Step Solution:

1. **Write the Balanced Chemical Equation**:
The reaction between sulfuric acid (H₂SO₄) and sodium hydroxide (NaOH) can be represented as:
\[ H_2SO_4 + 2 NaOH \rightarrow Na_2SO_4 + 2 H_2O \]
From the equation, we see that 1 mole of H₂SO₄ reacts with 2 moles of NaOH.

2. **Determine Moles of NaOH**:
First, we calculate the number of moles of NaOH in the 50 mL solution:
\[ \text{Moles of NaOH} = \text{Molarity} \times \text{Volume (in L)} \]
\[ \text{Moles of NaOH} = 0.10 \, \text{mol/L} \times 0.050 \, \text{L} = 0.005 \, \text{mol} \]

3. **Calculate Moles of H₂SO₄ Required**:
According to the balanced equation, 1 mole of H₂SO₄ is needed for every 2 moles of NaOH. Therefore, the moles of H₂SO₄ required are:
\[ \text{Moles of H₂SO₄} = \frac{\text{Moles of NaOH}}{2} = \frac{0.005}{2} = 0.0025 \, \text{mol} \]

4. **Calculate Volume of H₂SO₄ Needed**:
We know the molarity of H₂SO₄ is 0.10 M. We can find the volume required using the formula:
\[ \text{Volume (in L)} = \frac{\text{Moles}}{\text{Molarity}} = \frac{0.0025 \, \text{mol}}{0.10 \, \text{mol/L}} = 0.025 \, \text{L} \]
Converting to mL:
\[ \text{Volume (in mL)} = 0.025 \, \text{L} \times 1000 \, \text{mL/L} = 25 \, \text{mL} \]

5. **Final Answer**:
The volume of 0.10 M H₂SO₄ that must be added is **25 mL**.