`100ml` of `2.45 % (w//v) H_(2)SO_(4)` solution is mixed with `200ml` of `7% (w//w) H_(2)SO_(4)` solution `("density" = 1.4 gm//ml)` and the mixture is diluted to `500ml`. What is the molarity of the diluted solution ?

Options

A. `0.25 M`
B. `1.0 M`
C. `0.75 M`
D. `0.45 M`

Answer

To find the molarity of the diluted solution, we will follow these steps:

### Step 1: Calculate the mass of H₂SO₄ in the first solution (2.45% w/v)
- The formula for weight/volume percentage is:
\[ \text{Mass of solute (g)} = \left(\frac{\text{Percentage}}{100}\right) \times \text{Volume of solution (mL)} \]
- For the first solution:
\[ \text{Mass of H₂SO₄} = \left(\frac{2.45}{100}\right) \times 100 \, \text{mL} = 2.45 \, \text{g} \]

### Step 2: Calculate the mass of H₂SO₄ in the second solution (7% w/w)
- The formula for weight/weight percentage is:
\[ \text{Mass of solute (g)} = \left(\frac{\text{Percentage}}{100}\right) \times \text{Total mass of solution (g)} \]
- First, we need to find the total mass of the 200 mL solution using its density (1.4 g/mL):
\[ \text{Total mass of solution} = \text{Volume} \times \text{Density} = 200 \, \text{mL} \times 1.4 \, \text{g/mL} = 280 \, \text{g} \]
- Now, calculate the mass of H₂SO₄:
\[ \text{Mass of H₂SO₄} = \left(\frac{7}{100}\right) \times 280 \, \text{g} = 19.6 \, \text{g} \]

### Step 3: Calculate the total mass of H₂SO₄ in the mixture
- Total mass of H₂SO₄ from both solutions:
\[ \text{Total mass of H₂SO₄} = 2.45 \, \text{g} + 19.6 \, \text{g} = 22.05 \, \text{g} \]

### Step 4: Calculate the number of moles of H₂SO₄
- The molar mass of H₂SO₄ is approximately 98 g/mol.
- Calculate the number of moles:
\[ \text{Number of moles} = \frac{\text{Mass (g)}}{\text{Molar mass (g/mol)}} = \frac{22.05 \, \text{g}}{98 \, \text{g/mol}} \approx 0.2255 \, \text{mol} \]

### Step 5: Calculate the molarity of the diluted solution
- The final volume of the solution after dilution is 500 mL or 0.5 L.
- Molarity (M) is calculated using the formula:
\[ \text{Molarity (M)} = \frac{\text{Number of moles}}{\text{Volume of solution (L)}} \]
- Therefore:
\[ \text{Molarity} = \frac{0.2255 \, \text{mol}}{0.5 \, \text{L}} = 0.451 \, \text{M} \]

### Final Answer
The molarity of the diluted solution is approximately **0.45 M**.

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