If 100 ml of a solution contains 10 g of `H_(2)SO_(4)`, normality of the solution is

Options

A. 4.04 N
B. 3.04 N
C. 2.04 N
D. 1.04 N

Explanation

To find the normality of a solution containing 10 g of \( H_2SO_4 \) in 100 ml, we will follow these steps:

### Step 1: Calculate the number of moles of \( H_2SO_4 \)

The number of moles can be calculated using the formula:
\[ \text{Number of moles} = \frac{\text{Weight of solute (g)}}{\text{Molecular weight of solute (g/mol)}} \]

The molecular weight of \( H_2SO_4 \) is calculated as follows:
- Hydrogen (H): 2 atoms × 1 g/mol = 2 g/mol
- Sulfur (S): 1 atom × 32 g/mol = 32 g/mol
- Oxygen (O): 4 atoms × 16 g/mol = 64 g/mol

Adding these together:
\[ \text{Molecular weight of } H_2SO_4 = 2 + 32 + 64 = 98 \text{ g/mol} \]

Now, substituting the values:
\[ \text{Number of moles of } H_2SO_4 = \frac{10 \text{ g}}{98 \text{ g/mol}} \approx 0.102 \text{ moles} \]

### Step 2: Convert the volume of the solution from ml to liters

Since normality is typically expressed in terms of liters, we need to convert 100 ml to liters:
\[ \text{Volume in liters} = \frac{100 \text{ ml}}{1000} = 0.1 \text{ L} \]

### Step 3: Calculate the molarity of the solution

Molarity (M) is defined as the number of moles of solute per liter of solution:
\[ \text{Molarity} = \frac{\text{Number of moles}}{\text{Volume of solution in L}} = \frac{0.102 \text{ moles}}{0.1 \text{ L}} = 1.02 \text{ M} \]

### Step 4: Determine the n-factor for \( H_2SO_4 \)

The n-factor for an acid is equal to its basicity, which is the number of \( H^+ \) ions it can furnish. For \( H_2SO_4 \):
- It can furnish 2 \( H^+ \) ions.

Thus, the n-factor for \( H_2SO_4 \) is 2.

### Step 5: Calculate the normality of the solution

Normality (N) is calculated using the formula:
\[ \text{Normality} = \text{Molarity} \times n \text{-factor} \]
Substituting the values:
\[ \text{Normality} = 1.02 \text{ M} \times 2 = 2.04 \text{ N} \]

### Conclusion

The normality of the solution is \( 2.04 \text{ N} \).

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