At a given temperature,the equilibrium constant for the reaction $PCl_{5(g)} \rightleftharpoons PCl_{3(g)} + Cl_{2(g)}$ is $2.4 \times 10^{-3}$. At the same temperature,the equilibrium constant for the reaction $PCl_{3(g)} + Cl_{2(g)} \rightleftharpoons PCl_{5(g)}$ is:

  • A
    $2.4 \times 10^{-3}$
  • B
    $-2.4 \times 10^{-3}$
  • C
    $4.17 \times 10^{2}$
  • D
    $4.8 \times 10^{-2}$

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$A$ sample of pure $PCl_{5}$ was introduced into an evacuated vessel at $473 \, K$. After equilibrium was attained,the concentration of $PCl_{5}$ was found to be $0.5 \times 10^{-1} \, mol \, L^{-1}$. If the value of $K_{c}$ is $8.3 \times 10^{-3}$,what are the concentrations of $PCl_{3}$ and $Cl_{2}$ at equilibrium?
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