In the equilibrium , `PCl_(5)hArr PCl_(3)+Cl_(2)` starting with 2 mol of `PCl_(5)` in 5 L flask at `350K`, there is `80%` dissociation. Hence the equilibrium pressure is

Options

A. 1150 atm
B. 132. 2 atm
C. 20.7 atm
D. 13.8 atm

Explanation

To find the equilibrium pressure of the reaction \( PCl_5 \rightleftharpoons PCl_3 + Cl_2 \) starting with 2 moles of \( PCl_5 \) in a 5 L flask at 350 K with 80% dissociation, we can follow these steps:

### Step 1: Determine the initial moles of \( PCl_5 \)
We start with 2 moles of \( PCl_5 \).

### Step 2: Calculate the amount dissociated
Given that there is 80% dissociation:
\[ \text{Moles dissociated} = 80\% \text{ of } 2 \text{ moles} = \frac{80}{100} \times 2 = 1.6 \text{ moles} \]

### Step 3: Calculate the moles at equilibrium
At equilibrium:
- Moles of \( PCl_5 \) remaining = Initial moles - Moles dissociated
\[ \text{Moles of } PCl_5 = 2 - 1.6 = 0.4 \text{ moles} \]
- Moles of \( PCl_3 \) formed = Moles dissociated = 1.6 moles
- Moles of \( Cl_2 \) formed = Moles dissociated = 1.6 moles

Thus, at equilibrium, the total moles are:
\[ \text{Total moles} = \text{Moles of } PCl_5 + \text{Moles of } PCl_3 + \text{Moles of } Cl_2 = 0.4 + 1.6 + 1.6 = 3.6 \text{ moles} \]

### Step 4: Use the ideal gas law to find the equilibrium pressure
Using the ideal gas law \( PV = nRT \):
- \( n = 3.6 \) moles (total moles at equilibrium)
- \( R = 0.0821 \, \text{L atm K}^{-1} \text{mol}^{-1} \)
- \( T = 350 \, \text{K} \)
- \( V = 5 \, \text{L} \)

Rearranging the ideal gas law to find pressure \( P \):
\[ P = \frac{nRT}{V} \]
Substituting the values:
\[ P = \frac{3.6 \times 0.0821 \times 350}{5} \]

### Step 5: Calculate the pressure
Calculating the above expression:
\[ P = \frac{3.6 \times 0.0821 \times 350}{5} = \frac{103.074}{5} = 20.6148 \, \text{atm} \]

### Final Result
The equilibrium pressure is approximately \( 20.6 \, \text{atm} \).