CaCO$₃$(s) $\rightleftharpoons$ CaO(s) + CO$₂$(g), \( K_{p1} = 8 \times 10^{-2} \)
C(s) + CO$₂$(g) $\rightleftharpoons$ 2CO(g), \( K_{p2} = 2 \)
If the partial pressure of CO at equilibrium is \( x \times 10^{-1} \) atm, then find the value of \( x \).
C(s) + CO$₂$(g) $\rightleftharpoons$ 2CO(g), \( K_{p2} = 2 \)
If the partial pressure of CO at equilibrium is \( x \times 10^{-1} \) atm, then find the value of \( x \).
Correct Answer: 4
Solution and Explanation
Step 1: Write the equilibrium expressions for the given reactions.
For the first reaction: \[ K_{p1} = P_{\text{CO}_2} = 8 \times 10^{-2} \] For the second reaction: \[ K_{p2} = \frac{P_{\text{CO}}^2}{P_{\text{CO}_2}} = 2 \]
Step 2: Use the second equation to find \( P_{\text{CO}} \).
\[ \frac{P_{\text{CO}}^2}{8 \times 10^{-2}} = 2 \]
Step 3: Solve for \( P_{\text{CO}} \).
\[ P_{\text{CO}}^2 = 16 \times 10^{-2} \] \[ P_{\text{CO}} = 4 \times 10^{-1} \, \text{atm} \]
Step 4: The value of \( x \) is 4.
Thus, the value of \( x \) is 4.
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