For the following equilibrium in a closed container

${\mathrm{PCl}}_5\left(\mathrm{g}\right)\rightleftharpoons {\mathrm{PCl}}_3\left(\mathrm{g}\right)+{\mathrm{Cl}}_2\left(\mathrm{g}\right)$

At a constant temperature, the volume of the container is halved suddenly, which of the following is correct for ${\mathrm{K}}_{\mathrm{p}}$ and $\mathrm{\alpha }$ ?

Using the data provided, find the value of equilibrium constant for the following reaction at $298 \mathrm{K}$ and $1$ atm pressure. ${\mathrm{NO}}_{\left(\mathrm{g}\right)}+\frac{1}{2}{\mathrm{O}}_2( \mathrm{g})\rightleftharpoons {\mathrm{NO}}_2( \mathrm{g})$
${\mathrm{\Delta }}_{\mathrm{f}}{\mathrm{H}}^0\left({\mathrm{NO}}_{\left(\mathrm{g}\right)}\right)=90.4\mathrm{kJ}.{\mathrm{mol}}^{-1}$

${\mathrm{\Delta }}_{\mathrm{f}}{\mathrm{H}}^0\left({\mathrm{NO}}_2\left(\mathrm{g}\right)\right)=32.48\mathrm{kJ}\cdot {\mathrm{mol}}^{-1}$

${\mathrm{\Delta S}}^{\circ }\mathrm{at} 298\mathrm{K}=-70.8\mathrm{J}\cdot {\mathrm{K}}^{-1}\cdot {\mathrm{mol}}^{-1}$

$\mathrm{antilog}(0.50)=3162$

The reaction

${\mathrm{CaCO}}_3\left(\mathrm{s}\right)\rightleftharpoons \mathrm{CaO}\left(\mathrm{s}\right)+{\mathrm{CO}}_2\left(\mathrm{g}\right)$

is in equilibrium in a closed vessel at $298 \mathrm{K}.$ The partial pressure (in atm) of ${\mathrm{CO}}_2\left(\mathrm{g}\right)$ in the reaction vessel is closest to:

[Given: The change in Gibbs energies of formation at $298 \mathrm{K}$ and $1$ bar for

$\mathrm{CaO}\left(\mathrm{s}\right)=-603.501 \mathrm{kJ} {\mathrm{mol}}^{-1}$

${\mathrm{CO}}_2\left(\mathrm{g}\right)=-394.389 \mathrm{kJ} {\mathrm{mol}}^{-1}$

${\mathrm{CaCO}}_3\left(\mathrm{s}\right)=-1128.79 \mathrm{kJ} {\mathrm{mol}}^{-1}$

Gas constant $\mathrm{R}=8.314 \mathrm{J} {\mathrm{K}}^{-1} {\mathrm{mol}}^{-1}$]

The value of ${\mathrm{K}}_{\mathrm{c}} \mathrm{us} 64 \mathrm{at} 800 \mathrm{K}$ for the reaction

${\mathrm{N}}_2\left(\mathrm{g}\right)+3{\mathrm{H}}_2\left(\mathrm{g}\right)\to 2 {\mathrm{NH}}_3 \left(\mathrm{g}\right)$

The value of ${\mathrm{K}}_{\mathrm{c}}$ for the following reaction is :

${\mathrm{NH}}_3 \left(\mathrm{g}\right)\to \frac{1}{2} {\mathrm{N}}_2 \left(\mathrm{g}\right)+\frac{3}{2} {\mathrm{H}}_2 \left(\mathrm{g}\right)$

Find equilibrium constant ${\mathrm{K}}_{\mathrm{C}}$ for given condition: starting from $2\mathrm{ }\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{e}\mathrm{s}$ of ${\mathrm{P}\mathrm{C}\mathrm{l}}_5$ in $1\mathrm{ }\mathrm{l}\mathrm{i}\mathrm{t}\mathrm{r}\mathrm{e}$ container,$\mathrm{ }0.5\mathrm{ }\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{e}\mathrm{s}$ of ${\mathrm{P}\mathrm{C}\mathrm{l}}_5$ dissociates till equilibrium at $25°\mathrm{C}$.