A mixture of `HCl(g), PCl_(3)(g)` and `PCl_(5)(s)` each have
equal number of CI-atom then their molar ratio in the mixture is :

Options

A. `1 : 3 : 5`
B. `1 : 1 : 1`
C. `15 : 2 : 3`
D. `15 : 5 : 3`

Explanation

To solve the problem of finding the molar ratio of HCl(g), PCl₃(g), and PCl₅(s) in a mixture where each component has an equal number of chlorine atoms, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the number of chlorine atoms in each compound**:
- HCl has 1 Cl atom.
- PCl₃ has 3 Cl atoms.
- PCl₅ has 5 Cl atoms.

2. **Let the equal number of chlorine atoms be represented by \( n \)**:
- This means that the total number of chlorine atoms contributed by each gas must equal \( n \).

3. **Calculate the moles of each compound based on the number of chlorine atoms**:
- For HCl: Since there is 1 Cl atom per molecule, the number of moles of HCl contributing to \( n \) Cl atoms is \( \frac{n}{1} = n \).
- For PCl₃: Since there are 3 Cl atoms per molecule, the number of moles of PCl₃ contributing to \( n \) Cl atoms is \( \frac{n}{3} \).
- For PCl₅: Since there are 5 Cl atoms per molecule, the number of moles of PCl₅ contributing to \( n \) Cl atoms is \( \frac{n}{5} \).

4. **Write the ratio of the moles of each compound**:
- The ratio of moles of HCl : PCl₃ : PCl₅ can be expressed as:
\[ n : \frac{n}{3} : \frac{n}{5} \]

5. **Eliminate \( n \) from the ratio**:
- This simplifies to:
\[ 1 : \frac{1}{3} : \frac{1}{5} \]

6. **Convert to a common denominator**:
- The least common multiple (LCM) of 1, 3, and 5 is 15. Multiply each term by 15 to eliminate the fractions:
\[ 15 : 5 : 3 \]

7. **Final Molar Ratio**:
- Thus, the molar ratio of HCl : PCl₃ : PCl₅ is:
\[ 15 : 5 : 3 \]

### Conclusion:
The molar ratio in the mixture is **15 : 5 : 3**.