Find the weight of `H_(2)SO_(4)` in `1200mL` of a solution of `0.4N` strength.

Options

A. 23.52 g
B. 2.53 g
C. 2.53 g
D. 29.52g

Answer

To find the weight of \( H_2SO_4 \) in 1200 mL of a solution with a normality of 0.4N, we can follow these steps:

### Step 1: Calculate the number of milliequivalents
We know that:
\[ \text{Milliequivalents} = \text{Normality} \times \text{Volume (in mL)} \]
Given:
- Normality (N) = 0.4N
- Volume (V) = 1200 mL

So,
\[ \text{Milliequivalents} = 0.4 \times 1200 = 480 \text{ milliequivalents} \]

### Step 2: Determine the equivalent weight of \( H_2SO_4 \)
The equivalent weight of an acid is calculated as:
\[ \text{Equivalent Weight} = \frac{\text{Molar Mass}}{n} \]
where \( n \) is the number of replaceable hydrogen ions. For \( H_2SO_4 \):
- Molar Mass of \( H_2SO_4 \) = 98 g/mol
- \( n = 2 \) (since it can donate 2 protons)

Thus,
\[ \text{Equivalent Weight of } H_2SO_4 = \frac{98}{2} = 49 \text{ g/equiv} \]

### Step 3: Relate milliequivalents to weight
We can express the milliequivalents in terms of weight:
\[ \text{Milliequivalents} = \frac{\text{Weight}}{\text{Equivalent Weight}} \times 1000 \]

Substituting the values we have:
\[ 480 = \frac{\text{Weight}}{49} \times 1000 \]

### Step 4: Solve for weight
Rearranging the equation to find the weight:
\[ \text{Weight} = \frac{480 \times 49}{1000} \]

Calculating this gives:
\[ \text{Weight} = \frac{23520}{1000} = 23.52 \text{ grams} \]

### Final Answer
The weight of \( H_2SO_4 \) in 1200 mL of a 0.4N solution is **23.52 grams**.

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