If `250 mL` of a solution contains `24.5 g H_(2)SO_(4)` the molarity and normality respectively are:

Options

A. `1M,2N`
B. `1M,0.5M`
C. `0.5M,1N`
D. `2M,1N`

Explanation

To solve the problem of finding the molarity and normality of a solution containing 24.5 g of H₂SO₄ in 250 mL, we can follow these steps:

### Step 1: Calculate the number of moles of H₂SO₄
To find the number of moles, we use the formula:
\[ \text{Number of moles} = \frac{\text{mass of solute (g)}}{\text{molar mass of solute (g/mol)}} \]
The molar mass of H₂SO₄ (sulfuric acid) is calculated as follows:
- Hydrogen (H): 1 g/mol × 2 = 2 g/mol
- Sulfur (S): 32 g/mol × 1 = 32 g/mol
- Oxygen (O): 16 g/mol × 4 = 64 g/mol

Adding these together:
\[ \text{Molar mass of H₂SO₄} = 2 + 32 + 64 = 98 \text{ g/mol} \]

Now, substituting the values:
\[ \text{Number of moles of H₂SO₄} = \frac{24.5 \text{ g}}{98 \text{ g/mol}} \approx 0.25 \text{ moles} \]

### Step 2: Calculate the volume of the solution in liters
The volume of the solution is given as 250 mL. To convert this to liters:
\[ \text{Volume in liters} = \frac{250 \text{ mL}}{1000} = 0.25 \text{ L} \]

### Step 3: Calculate the molarity (M)
Molarity is defined as the number of moles of solute per liter of solution:
\[ \text{Molarity (M)} = \frac{\text{Number of moles of solute}}{\text{Volume of solution in liters}} \]
Substituting the values:
\[ \text{Molarity} = \frac{0.25 \text{ moles}}{0.25 \text{ L}} = 1 \text{ M} \]

### Step 4: Calculate the normality (N)
Normality is calculated using the formula:
\[ \text{Normality (N)} = \text{Molarity (M)} \times n \]
Where \( n \) is the number of equivalents. For H₂SO₄, which can donate 2 protons (H⁺ ions), \( n = 2 \).

Thus:
\[ \text{Normality} = 1 \text{ M} \times 2 = 2 \text{ N} \]

### Final Answer
The molarity and normality of the solution are:
- Molarity = 1 M
- Normality = 2 N