Calculate the partial pressure of carbon monoxide from the following data’s
`CaCO_(3)(s) overset(Delta)to CaO(s) + CO_(2)(g), K_(p) = 8 xx 10^(-2)`
`CO_(2)(g) + C(s) rarr 2CO(g), K_(p) = 2`

Options

A. 0.2
B. 0.4
C. 1.6
D. 4

Explanation

To calculate the partial pressure of carbon monoxide (CO) from the given data, we will follow these steps:

### Step 1: Write the Equations and Equilibrium Constants
We have two reactions with their respective equilibrium constants (Kp):

1. **For the decomposition of calcium carbonate:**
\[ \text{CaCO}_3(s) \rightleftharpoons \text{CaO}(s) + \text{CO}_2(g) \quad K_p = 8 \times 10^{-2} \]

2. **For the reaction of carbon dioxide with carbon:**
\[ \text{CO}_2(g) + \text{C}(s) \rightleftharpoons 2\text{CO}(g) \quad K_p = 2 \]

### Step 2: Relate Kp to Partial Pressures
From the first reaction, we can express the Kp in terms of the partial pressure of CO2:
\[ K_{p1} = P_{\text{CO}_2} = 8 \times 10^{-2} \]

From the second reaction, we can express Kp in terms of the partial pressures of CO:
\[ K_{p2} = \frac{(P_{\text{CO}})^2}{P_{\text{CO}_2}} = 2 \]

### Step 3: Substitute the Value of P_CO2 into the Second Equation
Substituting \( P_{\text{CO}_2} = 8 \times 10^{-2} \) into the second equation:
\[ 2 = \frac{(P_{\text{CO}})^2}{8 \times 10^{-2}} \]

### Step 4: Solve for \( P_{\text{CO}}^2 \)
Rearranging the equation gives:
\[ (P_{\text{CO}})^2 = 2 \times (8 \times 10^{-2}) = 16 \times 10^{-2} \]

### Step 5: Calculate \( P_{\text{CO}} \)
Taking the square root of both sides:
\[ P_{\text{CO}} = \sqrt{16 \times 10^{-2}} = \sqrt{16} \times \sqrt{10^{-2}} = 4 \times 0.1 = 0.4 \]

### Final Answer
The partial pressure of carbon monoxide (CO) is:
\[ P_{\text{CO}} = 0.4 \, \text{atm} \]

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