The initial pressure of `COCI_2` is 1000 torr. The total pressure of the system becomes 1500 torr, when the equilibrium `COCI_2(g) hArr CO(g) +CI_2(g)` is attained at constant temperature . The value of `K_p` of a reaction.

Options

A. 1500
B. 1000
C. 2500
D. 500

Answer

To find the equilibrium constant \( K_p \) for the reaction

\[ \text{COCl}_2(g) \rightleftharpoons \text{CO}(g) + \text{Cl}_2(g) \]

we start with the given data:

- Initial pressure of \( \text{COCl}_2 = 1000 \, \text{torr} \)
- Total pressure at equilibrium = 1500 torr

### Step 1: Set up the initial and equilibrium conditions

Initially, we have:
- \( P_{\text{COCl}_2} = 1000 \, \text{torr} \)
- \( P_{\text{CO}} = 0 \)
- \( P_{\text{Cl}_2} = 0 \)

At equilibrium, we can express the pressures in terms of a change \( x \):
- \( P_{\text{COCl}_2} = 1000 - x \)
- \( P_{\text{CO}} = x \)
- \( P_{\text{Cl}_2} = x \)

### Step 2: Write the expression for total pressure at equilibrium

The total pressure at equilibrium is given by the sum of the partial pressures:

\[ P_{\text{total}} = P_{\text{COCl}_2} + P_{\text{CO}} + P_{\text{Cl}_2 \]

Substituting the equilibrium pressures:

\[ 1500 = (1000 - x) + x + x \]

### Step 3: Simplify and solve for \( x \)

This simplifies to:

\[ 1500 = 1000 + x \]

Now, solving for \( x \):

\[ x = 1500 - 1000 = 500 \, \text{torr} \]

### Step 4: Calculate the equilibrium pressures

Now we can find the equilibrium pressures:

- \( P_{\text{COCl}_2} = 1000 - x = 1000 - 500 = 500 \, \text{torr} \)
- \( P_{\text{CO}} = x = 500 \, \text{torr} \)
- \( P_{\text{Cl}_2} = x = 500 \, \text{torr} \)

### Step 5: Write the expression for \( K_p \)

The equilibrium constant \( K_p \) is given by:

\[ K_p = \frac{P_{\text{CO}} \cdot P_{\text{Cl}_2}}{P_{\text{COCl}_2}} \]

Substituting the equilibrium pressures:

\[ K_p = \frac{(500)(500)}{500} \]

### Step 6: Solve for \( K_p \)

Calculating \( K_p \):

\[ K_p = \frac{250000}{500} = 500 \]

### Final Answer

Thus, the value of \( K_p \) for the reaction is:

\[ \boxed{500} \]