A 25mL HCl solution containing 3.65g HCl/L is neutralized by 50mL of NaOH solution. Again, 25mL of an `H_(2)SO_(4)` solution of unknow strenght. The normally of the `H_(2)SO_(4)` solution is :

Options

A. 0.25N
B. 0.025N
C. 0.05N
D. 0.05N

Answer

To find the normality of the \( H_2SO_4 \) solution, we can follow these steps:

### Step 1: Calculate the number of equivalents of HCl in the first reaction

1. **Given Data**:
- Concentration of HCl = 3.65 g/L
- Volume of HCl solution = 25 mL

2. **Calculate the number of grams of HCl in 25 mL**:
\[ \text{Mass of HCl} = \frac{3.65 \, \text{g}}{1000 \, \text{mL}} \times 25 \, \text{mL} = 0.09125 \, \text{g} \]

3. **Calculate the number of equivalents of HCl**:
- Molecular weight of HCl = 36.5 g/mol
- Number of equivalents of HCl = \(\frac{\text{mass}}{\text{molecular weight}}\)
\[ \text{Equivalents of HCl} = \frac{0.09125 \, \text{g}}{36.5 \, \text{g/mol}} = 0.0025 \, \text{equivalents} \]

### Step 2: Relate the equivalents of HCl to the equivalents of NaOH

1. **Using the neutralization reaction**:
- The reaction between HCl and NaOH is a 1:1 reaction.
- Therefore, equivalents of NaOH = equivalents of HCl = 0.0025 equivalents.

### Step 3: Calculate the normality of NaOH

1. **Given Volume of NaOH**:
- Volume of NaOH = 50 mL

2. **Using the formula for normality**:
\[ \text{Normality (N)} = \frac{\text{equivalents}}{\text{volume in L}} \]
\[ N_{NaOH} = \frac{0.0025 \, \text{equivalents}}{0.050 \, \text{L}} = 0.050 \, \text{N} \]

### Step 4: Use the normality of NaOH to find the normality of \( H_2SO_4 \)

1. **In the second neutralization reaction**:
- Volume of NaOH used = 25 mL
- Volume of \( H_2SO_4 \) = 50 mL

2. **Set up the equation for normality**:
\[ \text{Equivalents of NaOH} = \text{Equivalents of } H_2SO_4 \]
\[ 0.025 \, \text{L} \times 0.050 \, \text{N} = 0.050 \, \text{L} \times N_{H_2SO_4} \]

3. **Calculate the normality of \( H_2SO_4 \)**:
\[ 0.00125 = 0.050 \, \text{L} \times N_{H_2SO_4} \]
\[ N_{H_2SO_4} = \frac{0.00125}{0.050} = 0.025 \, \text{N} \]

### Final Answer:
The normality of the \( H_2SO_4 \) solution is **0.025 N**.

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