Assertion : Number of gram-molecules of `SO_2Cl_2` in 13.5 g of sulphuryl chloride is 0.1.
Reason : Gram molecular mass is equal to one gram molecule.

Options

A. If both assertion and reason are true and reason is the correct explanation of assertion.
B. If both assertion and reason are true but reason is not the correct explanation of assertion.
C. If assertion is true but reason is false.
D. If both assertion and reason are false.

Explanation

To solve the question, we need to analyze the assertion and reason provided:

**Assertion**: The number of gram-molecules of \( SO_2Cl_2 \) in 13.5 g of sulfuryl chloride is 0.1.

**Reason**: Gram molecular mass is equal to one gram molecule.

### Step-by-Step Solution:

1. **Determine the Molecular Mass of \( SO_2Cl_2 \)**:
- The molecular formula for sulfuryl chloride is \( SO_2Cl_2 \).
- To find the molecular mass, we need to sum the atomic masses of all the atoms in the formula:
- Sulfur (S) = 32 g/mol
- Oxygen (O) = 16 g/mol (2 atoms, so \( 2 \times 16 = 32 \) g/mol)
- Chlorine (Cl) = 35.5 g/mol (2 atoms, so \( 2 \times 35.5 = 71 \) g/mol)
- Total molecular mass = \( 32 + 32 + 71 = 135 \) g/mol.

2. **Calculate the Number of Gram-Molecules**:
- The number of gram-molecules can be calculated using the formula:
\[ \text{Number of gram-molecules} = \frac{\text{Mass of substance (g)}}{\text{Molar mass (g/mol)}} \]
- Substituting the values:
\[ \text{Number of gram-molecules} = \frac{13.5 \text{ g}}{135 \text{ g/mol}} = 0.1 \text{ gram-molecules} \]

3. **Evaluate the Assertion**:
- The assertion states that the number of gram-molecules of \( SO_2Cl_2 \) in 13.5 g is 0.1, which we have calculated to be true.

4. **Evaluate the Reason**:
- The reason states that the gram molecular mass is equal to one gram molecule. This is a correct statement because one mole of any substance contains Avogadro's number of molecules (approximately \( 6.022 \times 10^{23} \) molecules), and one gram-molecule is defined as the mass of a substance that contains one mole of its entities.

5. **Conclusion**:
- Both the assertion and the reason are true. However, the reason does not directly explain the assertion, but it is still a true statement.

### Final Answer:
- The assertion is true, and the reason is also true, but they are not directly related.