The total number of gm-molecules of `SO_(2)Cl_(2)` in 13.5 g of sulphuryl chloride is

Options

A. `0.1`
B. `0.2`
C. `0.3`
D. `0.4`

Explanation

To find the total number of gram-molecules of \( SO_2Cl_2 \) in 13.5 g of sulphuryl chloride, we will follow these steps:

### Step 1: Calculate the molar mass of \( SO_2Cl_2 \)

1. **Identify the atomic masses:**
- Sulfur (S) = 32 g/mol
- Oxygen (O) = 16 g/mol
- Chlorine (Cl) = 35.5 g/mol

2. **Calculate the molar mass:**
\[ \text{Molar mass of } SO_2Cl_2 = \text{mass of S} + 2 \times \text{mass of O} + 2 \times \text{mass of Cl} \]
\[ = 32 + 2 \times 16 + 2 \times 35.5 \]
\[ = 32 + 32 + 71 = 135 \text{ g/mol} \]

### Step 2: Calculate the number of moles of \( SO_2Cl_2 \)

3. **Use the formula for moles:**
\[ \text{Number of moles} = \frac{\text{Given weight}}{\text{Molar mass}} \]
\[ = \frac{13.5 \text{ g}}{135 \text{ g/mol}} \]

4. **Perform the calculation:**
\[ = 0.1 \text{ moles} \]

### Step 3: Convert moles to gram-molecules

5. **Since 1 mole is equivalent to 1 gram-molecule:**
\[ \text{Number of gram-molecules} = 0.1 \text{ gram-molecules} \]

### Final Answer:
The total number of gram-molecules of \( SO_2Cl_2 \) in 13.5 g of sulphuryl chloride is **0.1**.

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