A gaseous mixture contains `SO_(3)(g)` and `CH_(4)(g)` in `12.5 : 1` ratio by mass. Calculate `X ` where `X =` Ratio of total number of atoms present in `SO_(3)(g)` to total number of atoms presents in `CH_(4)(g)` in the mixure.

Explanation

To solve the problem, we need to calculate the ratio of the total number of atoms present in \( SO_3 \) to the total number of atoms present in \( CH_4 \) in the given mixture.

### Step-by-Step Solution:

1. **Identify the Mass Ratio**:
The mass ratio of \( SO_3 \) to \( CH_4 \) is given as \( 12.5 : 1 \).

2. **Calculate Molar Masses**:
- Molar mass of \( SO_3 \):
\[ S: 32 \, \text{g/mol} + 3 \times O: 16 \, \text{g/mol} = 32 + 48 = 80 \, \text{g/mol} \]
- Molar mass of \( CH_4 \):
\[ C: 12 \, \text{g/mol} + 4 \times H: 1 \, \text{g/mol} = 12 + 4 = 16 \, \text{g/mol} \]

3. **Convert Mass Ratio to Moles**:
To find the number of moles, we can use the mass ratio:
\[ \text{Moles of } SO_3 = \frac{12.5}{80} \quad \text{and} \quad \text{Moles of } CH_4 = \frac{1}{16} \]

4. **Calculate Moles**:
- Moles of \( SO_3 \):
\[ n_{SO_3} = \frac{12.5}{80} = 0.15625 \, \text{mol} \]
- Moles of \( CH_4 \):
\[ n_{CH_4} = \frac{1}{16} = 0.0625 \, \text{mol} \]

5. **Calculate the Mole Ratio**:
Now we can find the mole ratio of \( SO_3 \) to \( CH_4 \):
\[ \text{Mole Ratio} = \frac{n_{SO_3}}{n_{CH_4}} = \frac{0.15625}{0.0625} = 2.5 \]

6. **Calculate Total Atoms in Each Compound**:
- Each molecule of \( SO_3 \) contains 4 atoms (1 Sulfur + 3 Oxygens).
- Each molecule of \( CH_4 \) contains 5 atoms (1 Carbon + 4 Hydrogens).
- Total atoms in \( SO_3 \):
\[ \text{Total atoms in } SO_3 = n_{SO_3} \times 4 = 0.15625 \times 4 = 0.625 \]
- Total atoms in \( CH_4 \):
\[ \text{Total atoms in } CH_4 = n_{CH_4} \times 5 = 0.0625 \times 5 = 0.3125 \]

7. **Calculate the Ratio of Total Atoms**:
Finally, we find the ratio \( X \):
\[ X = \frac{\text{Total atoms in } SO_3}{\text{Total atoms in } CH_4} = \frac{0.625}{0.3125} = 2 \]

### Final Answer:
The value of \( X \) is \( 2 \).

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