`{:("For the reaction",PCl_(5)hArrPCl_(3)+Cl_(2)),("Initial moles are"," a b c"):}`
If `alpha` is the degree of dissociation and P is the total pressure. The partial pressure of `PCl_(3)` is

Options

A. `(b+a alpha)/(a+b+c+a alpha)"P atm"`
B. `(a+a alpha)/(a+b+c+a alpha)"P atm"`
C. `(a(a -alpha))/(a+b+c+a alpha)"P atm"`
D. `(a+b+c+a alpha)/(b+a alpha)"P atm"`

Answer

To find the partial pressure of \( PCl_3 \) in the reaction \( PCl_5 \rightleftharpoons PCl_3 + Cl_2 \) with given initial moles and degree of dissociation, we can follow these steps:

### Step-by-Step Solution:

1. **Identify Initial Moles**:
- Let the initial moles of \( PCl_5 \) be \( a \).
- Let the initial moles of \( PCl_3 \) be \( b \).
- Let the initial moles of \( Cl_2 \) be \( c \).

2. **Define Degree of Dissociation**:
- Let \( \alpha \) be the degree of dissociation of \( PCl_5 \). This means that \( \alpha \) fraction of \( PCl_5 \) dissociates.

3. **Calculate Moles at Equilibrium**:
- At equilibrium, the moles of each species will be:
- Moles of \( PCl_5 \) = \( a - a\alpha = a(1 - \alpha) \)
- Moles of \( PCl_3 \) = \( b + a\alpha \)
- Moles of \( Cl_2 \) = \( c + a\alpha \)

4. **Calculate Total Moles at Equilibrium**:
- The total moles at equilibrium will be:
\[ \text{Total moles} = (a(1 - \alpha)) + (b + a\alpha) + (c + a\alpha) \]
Simplifying this gives:
\[ \text{Total moles} = a + b + c + a\alpha \]

5. **Calculate Mole Fraction of \( PCl_3 \)**:
- The mole fraction of \( PCl_3 \) is given by:
\[ \text{Mole fraction of } PCl_3 = \frac{\text{Moles of } PCl_3}{\text{Total moles}} = \frac{b + a\alpha}{a + b + c + a\alpha} \]

6. **Use Dalton's Law to Find Partial Pressure**:
- According to Dalton's Law, the partial pressure of \( PCl_3 \) is:
\[ P_{PCl_3} = \text{Mole fraction of } PCl_3 \times P \]
- Substituting the mole fraction we found:
\[ P_{PCl_3} = \left(\frac{b + a\alpha}{a + b + c + a\alpha}\right) \times P \]

### Final Expression:
The partial pressure of \( PCl_3 \) is:
\[ P_{PCl_3} = \frac{(b + a\alpha)}{(a + b + c + a\alpha)} \times P \]