From the following data at 1000 K
`COCl_2 (g) Leftrightarrow CO(g)+Cl_2 (g) , K_(1)=0.329`
`2CO(g)+O_(2) (g) Leftrightarrow 2CO_(2) (g) , K_(2)=2.24 xx 10^(22)`
Calculate equilibrium constant at 1000 K for
`2COCl_2 (g) +O_(2) (g) Leftrightarrow 2CO_(2) (g) +2Cl_(2) (g)`

Answer

To calculate the equilibrium constant for the reaction:

\[ 2COCl_2 (g) + O_2 (g) \leftrightarrow 2CO_2 (g) + 2Cl_2 (g) \]

we will use the given equilibrium constants \( K_1 \) and \( K_2 \) for the reactions provided.

### Step 1: Write the given reactions and their equilibrium constants.

1. For the reaction:
\[ COCl_2 (g) \leftrightarrow CO(g) + Cl_2 (g) \]
The equilibrium constant is:
\[ K_1 = 0.329 \]

2. For the reaction:
\[ 2CO(g) + O_2 (g) \leftrightarrow 2CO_2 (g) \]
The equilibrium constant is:
\[ K_2 = 2.24 \times 10^{22} \]

### Step 2: Modify the first reaction.

To use \( K_1 \) for our desired reaction, we need to multiply the first reaction by 2:

\[ 2COCl_2 (g) \leftrightarrow 2CO(g) + 2Cl_2 (g) \]

When we multiply a reaction by a coefficient, the equilibrium constant is raised to that power:

\[ K_1' = K_1^2 = (0.329)^2 \]

### Step 3: Calculate \( K_1' \).

Calculating \( K_1' \):

\[ K_1' = (0.329)^2 = 0.108241 \]

### Step 4: Combine the modified first reaction with the second reaction.

Now we can add the modified first reaction to the second reaction:

\[ 2COCl_2 (g) \leftrightarrow 2CO(g) + 2Cl_2 (g) \quad (K_1' = 0.108241) \]
\[ 2CO(g) + O_2 (g) \leftrightarrow 2CO_2 (g) \quad (K_2 = 2.24 \times 10^{22}) \]

When we add these two reactions, the \( 2CO(g) \) cancels out:

\[ 2COCl_2 (g) + O_2 (g) \leftrightarrow 2CO_2 (g) + 2Cl_2 (g) \]

### Step 5: Calculate the overall equilibrium constant \( K \).

The overall equilibrium constant for the combined reaction is the product of the individual equilibrium constants:

\[ K = K_1' \times K_2 \]

Substituting the values we calculated:

\[ K = (0.108241) \times (2.24 \times 10^{22}) \]

### Step 6: Perform the multiplication.

Calculating \( K \):

\[ K = 0.108241 \times 2.24 \times 10^{22} \approx 2.43 \times 10^{22} \]

### Final Answer:

The equilibrium constant \( K \) for the reaction

\[ 2COCl_2 (g) + O_2 (g) \leftrightarrow 2CO_2 (g) + 2Cl_2 (g) \]

at 1000 K is approximately:

\[ K \approx 2.43 \times 10^{22} \]