Total number of atoms present in 64 gm of `SO_(2)` is -

Options

A. `2 times 6.02 times 10^(23)`
B. `6.02 times 10^(23)`
C. `4 times 6.02 times 10^(23)`
D. `3 times 6.02 times 10^(23)`

Answer

To find the total number of atoms present in 64 g of \( SO_2 \), we can follow these steps:

### Step 1: Calculate the molar mass of \( SO_2 \)
- The molar mass of sulfur (S) is 32 g/mol.
- The molar mass of oxygen (O) is 16 g/mol, and since there are 2 oxygen atoms in \( SO_2 \), we multiply this by 2.

\[ \text{Molar mass of } SO_2 = 32 \, \text{g/mol (S)} + 2 \times 16 \, \text{g/mol (O)} = 32 + 32 = 64 \, \text{g/mol} \]

### Step 2: Calculate the number of moles of \( SO_2 \)
- We use the formula:

\[ \text{Number of moles} = \frac{\text{Given mass}}{\text{Molar mass}} \]

- Given mass = 64 g, Molar mass = 64 g/mol.

\[ \text{Number of moles} = \frac{64 \, \text{g}}{64 \, \text{g/mol}} = 1 \, \text{mol} \]

### Step 3: Calculate the number of molecules in 1 mole of \( SO_2 \)
- We use Avogadro's number (\( N_A \)), which is approximately \( 6.02 \times 10^{23} \) molecules/mol.

\[ \text{Number of molecules} = \text{Number of moles} \times N_A = 1 \, \text{mol} \times 6.02 \times 10^{23} \, \text{molecules/mol} = 6.02 \times 10^{23} \, \text{molecules} \]

### Step 4: Calculate the total number of atoms in \( SO_2 \)
- Each molecule of \( SO_2 \) contains:
- 1 atom of sulfur
- 2 atoms of oxygen

- Therefore, the total number of atoms in one molecule of \( SO_2 \) is:

\[ 1 \, \text{(S)} + 2 \, \text{(O)} = 3 \, \text{atoms} \]

- Now, to find the total number of atoms in 1 mole of \( SO_2 \):

\[ \text{Total number of atoms} = \text{Number of molecules} \times \text{Atoms per molecule} = 6.02 \times 10^{23} \, \text{molecules} \times 3 \, \text{atoms/molecule} = 1.806 \times 10^{24} \, \text{atoms} \]

### Final Answer
The total number of atoms present in 64 g of \( SO_2 \) is \( 1.806 \times 10^{24} \) atoms.

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