`{:("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 \( PCl_5 \rightleftharpoons PCl_3 + Cl_2 \), we will follow these steps:

### Step 1: Define Initial Moles
Let:
- Initial moles of \( PCl_5 = a \)
- Initial moles of \( PCl_3 = b \)
- Initial moles of \( Cl_2 = c \)

### Step 2: Define Degree of Dissociation
Let \( \alpha \) be the degree of dissociation of \( PCl_5 \). This means that a fraction \( \alpha \) of \( PCl_5 \) will dissociate.

### Step 3: Calculate Moles at Equilibrium
At equilibrium:
- Moles of \( PCl_5 \) remaining = \( a - a\alpha = a(1 - \alpha) \)
- Moles of \( PCl_3 \) formed = Initial moles + Moles formed from dissociation = \( b + a\alpha \)
- Moles of \( Cl_2 \) formed = \( c + a\alpha \)

### Step 4: Total Moles at Equilibrium
Total moles at equilibrium can be calculated as:
\[ \text{Total moles} = \text{Moles of } PCl_5 + \text{Moles of } PCl_3 + \text{Moles of } Cl_2 \]
\[ = a(1 - \alpha) + (b + a\alpha) + (c + a\alpha) \]
\[ = a(1 - \alpha) + b + c + 2a\alpha \]
\[ = a + b + c + a\alpha \]

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

### Step 6: Calculate Partial Pressure of \( PCl_3 \)
The partial pressure of \( PCl_3 \) can be calculated using the formula:
\[ \text{Partial pressure of } PCl_3 = \text{Mole fraction of } PCl_3 \times P \]
Substituting the mole fraction we found:
\[ = \left( \frac{b + a\alpha}{a + b + c + a\alpha} \right) \times P \]

### Final Result
Thus, the partial pressure of \( PCl_3 \) is:
\[ \text{Partial pressure of } PCl_3 = \frac{(b + a\alpha) \times P}{a + b + c + a\alpha} \]