At equilibrium for the reaction $A_{2(g)} + B_{2(g)} \rightleftharpoons 2 AB_{(g)}$,the concentrations of $A_2$,$B_2$,and $AB$ respectively are $1.5 \times 10^{-3} \ M$,$2.1 \times 10^{-3} \ M$,and $1.4 \times 10^{-3} \ M$ in a sealed vessel at $800 \ K$. What will be $K_p$ for the decomposition of $AB$ at the same temperature?

$N_2O_{4(g)}$ at $300 \ K$ is kept in a closed container under $1 \ atm$. At equilibrium,$20\%$ of $N_2O_{4(g)}$ is converted to $NO_{2(g)}$.
$N_2O_{4(g)} \rightleftharpoons 2NO_{2(g)}$
Hence,the resultant pressure is: (in $atm$)

From the given data of equilibrium constants for the following reactions:
$(1) \ CO_{2(g)} + H_{2(g)} \rightleftharpoons CO_{(g)} + H_2O_{(g)} \ ; \ K_1$
$(2) \ CO_{(g)} + H_2O_{(g)} \rightleftharpoons CO_{2(g)} + H_{2(g)} \ ; \ K_2$
Wait,the provided question text has a typo in the reaction equations. Assuming the standard problem format where we relate equilibrium constants for reverse or combined reactions,if the target reaction is the same as reaction $(1)$,the answer is $K_1$. However,based on the options provided,this is likely a question asking for the relationship between $K_1$ and $K_2$ where reaction $(2)$ is the reverse of reaction $(1)$. If reaction $(2)$ is the reverse of reaction $(1)$,then $K_2 = \frac{1}{K_1}$. Given the options,please re-verify the input. Assuming the question asks for the equilibrium constant of a reaction derived from these,if the target reaction is $CO_{(g)} + H_2O_{(g)} \rightleftharpoons CO_{2(g)} + H_{2(g)}$,the answer is $K_1^{-1}$. Given the options,if we assume the target reaction is the reverse of reaction $(1)$,then $K = \frac{1}{K_1}$.

For the reaction $2SO_3 \rightleftharpoons 2SO_2 + O_2$,if $K_c = 100$ and the degree of dissociation $\alpha = 1$,determine the concentration of $O_2$ when the concentration of $SO_3$ is equal to the concentration of $SO_2$.

$13.8 \,g$ 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.

Fill in the blanks:
$a$. If a reaction is in equilibrium,then the rate of the forward reaction and the rate of the backward reaction will be ....... .
$b$. If $\Delta G$ is negative,then thermodynamically the reaction takes place in the ...... direction.
$c$. The equilibrium constant gives ........ information for a reaction.