For the reaction $I_{2(g)} \rightleftharpoons 2I_{(g)}$,the equilibrium constant $K_c$ at $1000 \ K$ is $10^{-6}$. If $1 \ mol$ of $I_2$ is added to a $1 \ L$ container,which of the following statements is true at equilibrium?

In a $1.0 \, L$ vessel at $90 \, ^\circ C$,$0.2 \, mol$ of $H_{2(g)}$ and $2.0 \, mol$ of $S_{(s)}$ are mixed. For the reaction $H_{2(g)} + S_{(s)} \rightleftharpoons H_2S_{(g)}$; $K_p = 6.8 \times 10^{-2}$,the partial pressure of $H_2S_{(g)}$ at equilibrium will be ............ $atm$.

If the volume of the container for the reaction $2NO + O_2 \rightleftharpoons 2NO_2$ is reduced to half of its initial volume,the rate of the reaction will become .......

In a closed vessel at $448^{\circ} C$,$0.5 \ mol$ of $H_2$ and $0.5 \ mol$ of $I_2$ react to form hydrogen iodide.
Reaction: $H_{2(g)} + I_{2(g)} \rightleftharpoons 2HI_{(g)}$,$K_c = 50$.
$(i)$ Calculate the moles of $I_2$ that remain unreacted at equilibrium.
$(ii)$ Calculate $K_p$.

For the reaction,$N_2O_{4(g)} \rightleftharpoons 2NO_{2(g)}$,if dinitrogen tetroxide is $50\%$ dissociated at $60^\circ C$,the standard free energy change at this temperature and $1 \ atm$ pressure is:

At $T(K)$,the $K_c$ value of the reaction $AO_{2(g)} + BO_{2(g)} \rightleftharpoons AO_{3(g)} + BO_{(g)}$ is $16$. In a closed $1 \ L$ flask,one mole each of $AO_2, BO_2, AO_3$ and $BO$ are taken and heated to $T(K)$. Identify the correct statements about this equilibrium.
$I)$ Total number of moles at equilibrium is $4$
$II)$ At equilibrium,the ratio of moles of $AO_2$ and $AO_3$ is $1:4$
$III)$ Total number of moles of $AO_2$ and $BO_2$ at equilibrium is $0.8$