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 can follow these steps:

### Step 1: Identify Initial Conditions
- The initial pressure of \( \text{COCl}_2 \) is given as 1000 torr.
- The initial pressures of \( \text{CO} \) and \( \text{Cl}_2 \) are both 0 torr since they are products formed from the decomposition of \( \text{COCl}_2 \).

### Step 2: Write the Change in Pressure
Let \( p \) be the change in pressure of \( \text{COCl}_2 \) that decomposes at equilibrium. Therefore:
- At equilibrium, the pressure of \( \text{COCl}_2 \) will be \( 1000 - p \) torr.
- The pressure of \( \text{CO} \) will be \( p \) torr.
- The pressure of \( \text{Cl}_2 \) will also be \( p \) torr.

### Step 3: Write the Total Pressure at Equilibrium
The total pressure at equilibrium is given as 1500 torr. Therefore, we can write the equation:
\[ (1000 - p) + p + p = 1500 \]
Simplifying this gives:
\[ 1000 + p = 1500 \]

### Step 4: Solve for \( p \)
Now, we can solve for \( p \):
\[ p = 1500 - 1000 = 500 \text{ torr} \]

### Step 5: Determine Partial Pressures at Equilibrium
Now that we have \( p \):
- The pressure of \( \text{COCl}_2 \) at equilibrium is:
\[ 1000 - p = 1000 - 500 = 500 \text{ torr} \]
- The pressure of \( \text{CO} \) at equilibrium is:
\[ p = 500 \text{ torr} \]
- The pressure of \( \text{Cl}_2 \) at equilibrium is:
\[ p = 500 \text{ torr} \]

### Step 6: Write the Expression for \( K_p \)
The expression for 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:
\[ K_p = \frac{(500)(500)}{500} = \frac{250000}{500} = 500 \]

### Final Answer
Thus, the value of \( K_p \) is **500**.

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