` A 10 L "container at" 300K "contains" CO_(2) "gas at pressure of" 0.2 "atm and excess solid` CaO ("neglect the volume of solid" CaO)`. The volume of container is now decreased by moving the movable piston fitted in the container. What will be the maximum volume of container when pressure of `CO_(2)` attains its maximum value given that `CaCO_(3)(s)hArrCaO(s)+CO_(2)(g) K_(P)=0.800 "atm"`

Options

A. `5L`
B. `2.5L
C. `1L`
D. The information is insufficient.

Explanation

To solve the problem step-by-step, we will analyze the situation involving the equilibrium of calcium carbonate (CaCO₃) with calcium oxide (CaO) and carbon dioxide (CO₂), and how the pressure and volume relate to each other.

### Step 1: Write the Reaction and Equilibrium Constant
The reaction given in the problem is:
\[ \text{CaCO}_3(s) \rightleftharpoons \text{CaO}(s) + \text{CO}_2(g) \]

The equilibrium constant \( K_P \) for this reaction is given as:
\[ K_P = P_{\text{CO}_2} = 0.800 \, \text{atm} \]

### Step 2: Understand the Initial Conditions
Initially, the container has:
- Volume \( V_1 = 10 \, \text{L} \)
- Pressure of CO₂ \( P_2 = 0.2 \, \text{atm} \)

### Step 3: Determine Maximum Pressure of CO₂
The maximum pressure of CO₂ that can be achieved when the system reaches equilibrium is given by \( K_P \):
\[ P_{\text{CO}_2}^{\text{max}} = 0.800 \, \text{atm} \]

### Step 4: Use the Ideal Gas Law Relation
According to Boyle's Law, for a gas at constant temperature, the product of pressure and volume is constant:
\[ P_1 V_1 = P_2 V_2 \]

Where:
- \( P_1 = 0.800 \, \text{atm} \) (maximum pressure of CO₂)
- \( V_1 = 10 \, \text{L} \) (initial volume)
- \( P_2 = 0.2 \, \text{atm} \) (initial pressure of CO₂)
- \( V_2 \) is the volume we need to find when \( P_1 \) is reached.

### Step 5: Rearranging the Equation
We can rearrange the equation to solve for \( V_2 \):
\[ V_2 = \frac{P_1 V_1}{P_2} \]

### Step 6: Substitute the Known Values
Substituting the known values into the equation:
\[ V_2 = \frac{(0.800 \, \text{atm})(10 \, \text{L})}{0.2 \, \text{atm}} \]

### Step 7: Calculate \( V_2 \)
Calculating the above expression:
\[ V_2 = \frac{8.0}{0.2} = 40 \, \text{L} \]

### Step 8: Conclusion
The maximum volume of the container when the pressure of CO₂ attains its maximum value is:
\[ V_2 = 40 \, \text{L} \]