If `CoO(s)+H_2(g)hArr Co(s)+H_2O(g), K_1=60`
`CoO(s)+CO(g)hArrCo(s)+CO_2(g), K_2=180`
then the equilibrium constant of the reaction
`CO_2(g)+H_2(g)hArrCO(g)+H_2O(g)`
will be

Options

A. `0.44`
B. `0.11`
C. `0.22`
D. `0.33`

Explanation

To find the equilibrium constant of the reaction

\[ \text{CO}_2(g) + \text{H}_2(g) \rightleftharpoons \text{CO}(g) + \text{H}_2\text{O}(g) \]

we will use the provided reactions and their equilibrium constants.

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

1. \( \text{CoO}(s) + \text{H}_2(g) \rightleftharpoons \text{Co}(s) + \text{H}_2\text{O}(g) \) with \( K_1 = 60 \)
2. \( \text{CoO}(s) + \text{CO}(g) \rightleftharpoons \text{Co}(s) + \text{CO}_2(g) \) with \( K_2 = 180 \)

### Step 2: Reverse the second reaction.

To use the second reaction, we need to reverse it because we want CO and H2O on the products side:

\[ \text{Co}(s) + \text{CO}_2(g) \rightleftharpoons \text{CoO}(s) + \text{CO}(g) \]

The equilibrium constant for the reversed reaction is:

\[ K_{2,\text{reverse}} = \frac{1}{K_2} = \frac{1}{180} \]

### Step 3: Combine the first reaction and the reversed second reaction.

Now, we will add the first reaction and the reversed second reaction:

1. \( \text{CoO}(s) + \text{H}_2(g) \rightleftharpoons \text{Co}(s) + \text{H}_2\text{O}(g) \) (with \( K_1 = 60 \))
2. \( \text{Co}(s) + \text{CO}_2(g) \rightleftharpoons \text{CoO}(s) + \text{CO}(g) \) (with \( K_{2,\text{reverse}} = \frac{1}{180} \))

When we add these two reactions, we can cancel out the CoO and Co:

\[ \text{CO}_2(g) + \text{H}_2(g) \rightleftharpoons \text{CO}(g) + \text{H}_2\text{O}(g) \]

### Step 4: Calculate the equilibrium constant for the combined reaction.

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

\[ K = K_1 \times K_{2,\text{reverse}} = K_1 \times \frac{1}{K_2} \]

Substituting the values:

\[ K = 60 \times \frac{1}{180} = \frac{60}{180} = \frac{1}{3} \]

### Final Answer:

Thus, the equilibrium constant for the reaction

\[ \text{CO}_2(g) + \text{H}_2(g) \rightleftharpoons \text{CO}(g) + \text{H}_2\text{O}(g) \]

is

\[ K = \frac{1}{3} \approx 0.33 \]

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