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 find the ratio of the total number of atoms present in the gaseous mixture of \( SO_3 \) and \( CH_4 \) based on their mass ratio of \( 12.5:1 \).

### Step-by-Step Solution:

1. **Identify the Masses**:
- Let the mass of \( CH_4 \) be \( 1 \) g.
- Therefore, the mass of \( SO_3 \) will be \( 12.5 \) g.

2. **Calculate Moles of Each Gas**:
- The molar mass of \( SO_3 \) (Sulfur Trioxide) is calculated as follows:
\[ \text{Molar mass of } SO_3 = 32.07 \, (\text{S}) + 3 \times 16.00 \, (\text{O}) = 80.07 \, \text{g/mol} \]
- The moles of \( SO_3 \) can be calculated using the formula:
\[ \text{Moles of } SO_3 = \frac{\text{mass}}{\text{molar mass}} = \frac{12.5 \, \text{g}}{80.07 \, \text{g/mol}} \approx 0.156 \, \text{mol} \]

- The molar mass of \( CH_4 \) (Methane) is:
\[ \text{Molar mass of } CH_4 = 12.01 \, (\text{C}) + 4 \times 1.008 \, (\text{H}) = 16.04 \, \text{g/mol} \]
- The moles of \( CH_4 \) can be calculated as:
\[ \text{Moles of } CH_4 = \frac{1 \, \text{g}}{16.04 \, \text{g/mol}} \approx 0.062 \, \text{mol} \]

3. **Calculate Total Number of Atoms**:
- Each molecule of \( SO_3 \) contains \( 4 \) atoms (1 S + 3 O).
- Each molecule of \( CH_4 \) contains \( 5 \) atoms (1 C + 4 H).
- Therefore, the total number of atoms in \( SO_3 \) is:
\[ \text{Total atoms from } SO_3 = \text{moles of } SO_3 \times 4 \, \text{atoms/molecule} = 0.156 \, \text{mol} \times 4 = 0.624 \, \text{mol of atoms} \]
- The total number of atoms in \( CH_4 \) is:
\[ \text{Total atoms from } CH_4 = \text{moles of } CH_4 \times 5 \, \text{atoms/molecule} = 0.062 \, \text{mol} \times 5 = 0.310 \, \text{mol of atoms} \]

4. **Calculate the Ratio \( X \)**:
- Now, we can find the ratio \( X \) of the total number of atoms in \( SO_3 \) to that in \( CH_4 \):
\[ X = \frac{\text{Total atoms from } SO_3}{\text{Total atoms from } CH_4} = \frac{0.624}{0.310} \approx 2.016 \]
- Therefore, the ratio \( X \) can be approximated as:
\[ X \approx 2:1 \]

### Final Answer:
The ratio \( X \) of the total number of atoms present in \( SO_3 \) to the total number of atoms present in \( CH_4 \) is \( 2:1 \).