At constant temperature,the equilibrium constant $(K_p)$ for the decomposition reaction $N_2O_4 \rightleftharpoons 2NO_2$ is expressed by $K_p = \frac{4x^2P}{1 - x^2}$,where $P = \text{pressure}$,$x = \text{extent of decomposition}$. Which one of the following statements is true?

  • A
    $K_p$ increases with increase of $P$
  • B
    $K_p$ increases with increase of $x$
  • C
    $K_p$ increases with decrease of $x$
  • D
    $K_p$ remains constant with change in $P$ and $x$

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The reaction,$CO_{(g)} + 3H_{2(g)} \longleftrightarrow CH_{4(g)} + H_{2}O_{(g)}$ is at equilibrium at $1300 \, K$ in a $1 \, L$ flask. It also contains $0.30 \, mol$ of $CO$,$0.10 \, mol$ of $H_{2}$,and $0.02 \, mol$ of $H_{2}O$ and an unknown amount of $CH_{4}$ in the flask. Determine the concentration of $CH_{4}$ in the mixture. The equilibrium constant,$K_{c}$ for the reaction at the given temperature is $3.90$.

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For the reactions $A \rightleftharpoons B; K_c = 2$,$B \rightleftharpoons C; K_c = 4$,and $C \rightleftharpoons D; K_c = 6$,the value of $K_c$ for the reaction $A \rightleftharpoons D$ is:

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