PASSAGE-IV : 10 g of NaOH required certain amount of `H_(2)SO_(4)` for complete neutralisation.
Calculate the absolute mass of one molecule of `H_(2)SO_(4)`.

Options

A. `1.67xx10^(-27)g`
B. `9.2xx10^(-28)g`
C. `16.27xx10^(-23)g`
D. `3.4xx10^(-20)g`

Explanation

To solve the problem, we need to calculate the absolute mass of one molecule of \( H_2SO_4 \) (sulfuric acid). Here’s a step-by-step solution:

### Step 1: Calculate the molar mass of \( H_2SO_4 \)
To find the molar mass of sulfuric acid (\( H_2SO_4 \)), we need to sum the atomic masses of all the atoms in the molecule.

- 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

Now, add these values together:
\[ \text{Molar mass of } H_2SO_4 = 2 + 32 + 64 = 98 \text{ g/mol} \]

### Step 2: Use Avogadro's number to find the mass of one molecule
Avogadro's number (\( N_A \)) is \( 6.022 \times 10^{23} \) molecules/mol. To find the mass of one molecule of \( H_2SO_4 \), we divide the molar mass by Avogadro's number:

\[ \text{Mass of one molecule of } H_2SO_4 = \frac{\text{Molar mass}}{N_A} = \frac{98 \text{ g/mol}}{6.022 \times 10^{23} \text{ molecules/mol}} \]

### Step 3: Calculate the mass of one molecule
Now, perform the calculation:

\[ \text{Mass of one molecule of } H_2SO_4 = \frac{98}{6.022 \times 10^{23}} \approx 1.63 \times 10^{-25} \text{ g} \]

### Step 4: Final result
Thus, the absolute mass of one molecule of \( H_2SO_4 \) is approximately \( 1.63 \times 10^{-25} \) grams.