Write the applications of equilibrium constants.

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(N/A) The equilibrium constant $(K)$ provides valuable information about a chemical reaction:
$1$. Predicting the extent of a reaction: If $K_c > 10^3$,the product predominates; if $K_c < 10^{-3}$,the reactant predominates; if $K_c$ is between $10^{-3}$ and $10^3$,both reactants and products are present in significant amounts.
$2$. Predicting the direction of the reaction: By comparing the reaction quotient $(Q_c)$ with the equilibrium constant $(K_c)$: if $Q_c < K_c$,the reaction proceeds in the forward direction; if $Q_c > K_c$,it proceeds in the reverse direction; if $Q_c = K_c$,the system is at equilibrium.
$3$. Calculating equilibrium concentrations: Given the initial concentrations and the value of $K_c$,the equilibrium concentrations of reactants and products can be calculated.

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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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