a' moles of `PCI_(5)`, undergoes, thermal dissociation as: `PCI(5)hArrPCI_(3)+CI_(2)`, the mole of `PCI_(3)` equilibrium is `0.25` and the total pressure is `2.0` atmosphere. The partial pressure of `CI_(2)` at equilibrium is:

Options

A. `2.5`
B. `1.0`
C. `0.5`
D. None

Answer

To solve the problem step by step, we can follow these instructions:

### Step 1: Write the balanced chemical equation
The thermal dissociation of PCl5 can be represented by the following equation:
\[ \text{PCl}_5 \rightleftharpoons \text{PCl}_3 + \text{Cl}_2 \]

### Step 2: Define the initial moles and changes
Let \( a \) be the initial moles of PCl5. At equilibrium, let \( x \) be the number of moles of PCl5 that dissociate. Therefore, the changes in moles can be represented as:
- Moles of PCl5 at equilibrium = \( a - x \)
- Moles of PCl3 at equilibrium = \( x \)
- Moles of Cl2 at equilibrium = \( x \)

### Step 3: Use the mole fraction of PCl3
It is given that the mole fraction of PCl3 at equilibrium is 0.25. The mole fraction can be defined as:
\[ \text{Mole fraction of PCl}_3 = \frac{\text{Moles of PCl}_3}{\text{Total moles at equilibrium}} \]

The total moles at equilibrium can be expressed as:
\[ \text{Total moles} = (a - x) + x + x = a + x \]

Thus, the mole fraction of PCl3 can be written as:
\[ \frac{x}{a + x} = 0.25 \]

### Step 4: Solve for x in terms of a
From the equation above, we can rearrange it to find:
\[ x = 0.25(a + x) \]
\[ x = 0.25a + 0.25x \]
\[ x - 0.25x = 0.25a \]
\[ 0.75x = 0.25a \]
\[ x = \frac{0.25a}{0.75} = \frac{a}{3} \]

### Step 5: Calculate total moles at equilibrium
Substituting \( x \) back into the total moles:
\[ \text{Total moles} = a + x = a + \frac{a}{3} = \frac{4a}{3} \]

### Step 6: Calculate the mole fraction of Cl2
Since the moles of Cl2 at equilibrium is equal to \( x \):
\[ \text{Mole fraction of Cl}_2 = \frac{x}{\text{Total moles}} = \frac{\frac{a}{3}}{\frac{4a}{3}} = \frac{1}{4} \]

### Step 7: Calculate the partial pressure of Cl2
The partial pressure of Cl2 can be calculated using the total pressure:
\[ \text{Partial pressure of Cl}_2 = \text{Mole fraction of Cl}_2 \times \text{Total pressure} \]
Given that the total pressure is 2.0 atm:
\[ \text{Partial pressure of Cl}_2 = \frac{1}{4} \times 2.0 \, \text{atm} = 0.5 \, \text{atm} \]

### Final Answer
The partial pressure of Cl2 at equilibrium is **0.5 atm**.

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