The 100 mL of H2SO4 solution having molarity 1M and density 1.5 g/mL is mixed with 400 mL of water. Calculate the final molarity of the H2SO4 solution if the final density is 1.25 g/mL.
(A) 4.4M
(B) 0.145M
(C) 0.52M
(D) 0.227M

To solve this problem, we need to follow these steps:

1. **Calculate the number of moles of \( \text{H}_2\text{SO}_4 \) in the initial solution.**

- Molarity (M) is defined as moles of solute per liter of solution.
- For the initial solution:
\[ \text{Molarity} = 1\, \text{M} \]
\[ \text{Volume} = 100\, \text{mL} = 0.1\, \text{L} \]
\[ \text{Moles of } \text{H}_2\text{SO}_4 = \text{Molarity} \times \text{Volume} \]
\[ \text{Moles of } \text{H}_2\text{SO}_4 = 1\, \text{M} \times 0.1\, \text{L} = 0.1\, \text{moles} \]

2. **Calculate the total volume of the final solution.**

- The initial volume of the \( \text{H}_2\text{SO}_4 \) solution is 100 mL.
- Water added = 400 mL.
- Total final volume = 100 mL + 400 mL = 500 mL = 0.5 L.

3. **Determine the final density of the solution and calculate the total mass of the final solution.**

- Final density of the solution = 1.25 g/mL.
- Total volume of the solution = 500 mL.
- Total mass of the solution = Density × Volume
\[ \text{Total mass} = 1.25\, \text{g/mL} \times 500\, \text{mL} = 625\, \text{g} \]

4. **Determine the mass of the solution that is just water.**

- Density of the initial \( \text{H}_2\text{SO}_4 \) solution = 1.5 g/mL.
- Mass of the initial \( \text{H}_2\text{SO}_4 \) solution = Density × Volume
\[ \text{Mass of initial } \text{H}_2\text{SO}_4 \text{ solution} = 1.5\, \text{g/mL} \times 100\, \text{mL} = 150\, \text{g} \]

5. **Calculate the mass of the water added.**

- Mass of the solution after adding water = 625 g.
- Mass of the water added = Total mass of the final solution - Mass of initial \( \text{H}_2\text{SO}_4 \) solution
\[ \text{Mass of water added} = 625\, \text{g} - 150\, \text{g} = 475\, \text{g} \]

6. **Calculate the final molarity of the \( \text{H}_2\text{SO}_4 \) solution.**

- The number of moles of \( \text{H}_2\text{SO}_4 \) remains the same: 0.1 moles.
- Final volume of the solution = 0.5 L.
- Final Molarity = Number of moles / Volume in liters
\[ \text{Final Molarity} = \frac{0.1\, \text{moles}}{0.5\, \text{L}} = 0.2\, \text{M} \]

However, none of the options provided in the question match the result of 0.2 M. Given this, there may be a mistake in the provided options or an additional factor might need to be considered.

If the answer choices are strictly adhered to, the closest option to our calculated value is 0.227 M (D).