How many sulphur atom will be present in 2 litre of centi normal aq. Solution of `H_(2)SO_(4)` ?

Answer

To find the number of sulfur atoms present in a 2-liter solution of centi-normal \( H_2SO_4 \), we can follow these steps:

### Step 1: Understand the Normality
Given that the solution is centi-normal, we know that:
- Centi-normal (cN) means \( 10^{-2} \) normal.
- Therefore, the normality of the solution is \( 0.01 \, N \) (since \( 10^{-2} = 0.01 \)).

### Step 2: Calculate Molarity from Normality
The relationship between normality (N) and molarity (M) is given by:
\[ M = \frac{N}{n} \]
where \( n \) is the number of equivalents. For \( H_2SO_4 \):
- It has 2 acidic hydrogens, so \( n = 2 \).

Now substituting the values:
\[ M = \frac{0.01}{2} = 0.005 \, M \]

### Step 3: Calculate Moles of \( H_2SO_4 \) in 2 Liters
Molarity is defined as the number of moles of solute per liter of solution. Therefore, in 2 liters:
\[ \text{Moles of } H_2SO_4 = M \times \text{Volume in liters} = 0.005 \, \text{mol/L} \times 2 \, \text{L} = 0.01 \, \text{mol} \]

### Step 4: Determine the Number of Sulfur Atoms
Each molecule of \( H_2SO_4 \) contains 1 sulfur atom. Thus, the number of moles of sulfur will be equal to the number of moles of \( H_2SO_4 \):
\[ \text{Moles of sulfur} = 0.01 \, \text{mol} \]

### Step 5: Convert Moles of Sulfur to Atoms
Using Avogadro's number (\( 6.022 \times 10^{23} \) atoms/mol), we can find the total number of sulfur atoms:
\[ \text{Number of sulfur atoms} = \text{Moles of sulfur} \times \text{Avogadro's number} = 0.01 \, \text{mol} \times 6.022 \times 10^{23} \, \text{atoms/mol} \]
\[ = 6.022 \times 10^{21} \, \text{atoms} \]

### Final Answer
Thus, the number of sulfur atoms present in 2 liters of centi-normal aqueous solution of \( H_2SO_4 \) is:
\[ \boxed{6.022 \times 10^{21}} \]