The equilibrium constant of a reaction at $298 \ K$ is $5 \times 10^{-3}$ and at $1000 \ K$ is $2 \times 10^{-5}$. What is the sign of $\Delta H$ for the reaction?

$13.8 \,g$ of $N_{2}O_{4}$ was placed in a $1 \,L$ reaction vessel at $400 \,K$ and allowed to attain equilibrium.
$N_{2}O_{4(g)} \rightleftharpoons 2NO_{2(g)}$
The total pressure at equilibrium was found to be $9.15 \,bar$. Calculate $K_{c}$,$K_{p}$,and the partial pressures at equilibrium.

At $T$ $(K)$,$K_c$ for the dissociation of $PCl_5$ is $2 \times 10^{-2} \ mol \ L^{-1}$. The number of moles of $PCl_5$ that must be taken in a $1.0 \ L$ flask at the same temperature to get $0.2 \ mol$ of chlorine at equilibrium is:

$2SO_2 + O_2 \to$ product. If the pressure of the reaction increases $3$ times, then the rate will be (in $\times$)?

In reaction $A + 2B \rightleftharpoons 2C + D$,the initial concentration of $B$ was $1.5$ times that of $[A]$,but at equilibrium,the concentrations of $A$ and $B$ became equal. The equilibrium constant for the reaction is:

At high temperature,$2 \, \text{mol}$ of $NH_3$ is placed in a $500 \, \text{mL}$ vessel. For the decomposition reaction $2NH_{3(g)} \rightleftharpoons N_{2(g)} + 3H_{2(g)}$,if $1 \, \text{mol}$ of $NH_3$ remains at equilibrium,then $K_c$ is equal to: