Calculate mass of one molecule of sulphur dioxide `(SO_(2))` in gram.

Answer

To calculate the mass of one molecule of sulfur dioxide (SO₂) in grams, we will follow these steps:

### Step 1: Calculate the Molar Mass of SO₂
The molar mass (or molecular weight) of sulfur dioxide can be calculated using the atomic masses of sulfur and oxygen.

- Atomic mass of sulfur (S) = 32 g/mol
- Atomic mass of oxygen (O) = 16 g/mol

The formula for sulfur dioxide is SO₂, which means it contains:
- 1 sulfur atom
- 2 oxygen atoms

Thus, the molar mass of SO₂ is calculated as follows:
\[ \text{Molar mass of SO₂} = (1 \times 32) + (2 \times 16) = 32 + 32 = 64 \text{ g/mol} \]

### Step 2: Use Avogadro's Number
Avogadro's number (Nₐ) is \(6.022 \times 10^{23}\) molecules/mol. This number tells us how many molecules are present in one mole of a substance.

### Step 3: Calculate the Mass of One Molecule
Since we know that 64 grams of SO₂ corresponds to \(6.022 \times 10^{23}\) molecules, we can find the mass of one molecule by dividing the molar mass by Avogadro's number:

\[ \text{Mass of one molecule of SO₂} = \frac{\text{Molar mass of SO₂}}{Nₐ} = \frac{64 \text{ g}}{6.022 \times 10^{23} \text{ molecules/mol}} \]

### Step 4: Perform the Calculation
Now, we perform the calculation:

\[ \text{Mass of one molecule of SO₂} = \frac{64}{6.022 \times 10^{23}} \approx 1.062 \times 10^{-22} \text{ grams} \]

### Final Answer
The mass of one molecule of sulfur dioxide (SO₂) is approximately:
\[ 1.062 \times 10^{-22} \text{ grams} \]

---