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 $SO_2$.

At $600 \ K$,ammonium carbamate decomposes in a closed vessel: $NH_2COONH_{4(s)} \rightleftharpoons 2NH_{3(g)} + CO_{2(g)}$. At equilibrium,the total pressure is $3 \ bar$. Calculate $K_p$. (in $bar^3$)

For the reaction $Br_2 \rightleftharpoons 2Br$,the equilibrium constants at $327\,^oC$ and $527\,^oC$ are $6.1 \times 10^{-12}$ and $1.0 \times 10^{-7}$ respectively. The reaction is ...........

For the reaction $X_{2(g)} + Y_{2(g)} \rightleftharpoons 2XY_{(g)}$,the reaction is studied at a fixed temperature. Initially,$1 \ mol$ of $X_2$ is taken in a $1 \ L$ flask and $2 \ mol$ of $Y_2$ is taken in a $2 \ L$ flask. If the flasks are connected,what are the equilibrium concentrations of $X_2$ and $Y_2$? (Given: Equilibrium concentration of $XY = 0.6 \ mol/L$)

The equilibrium constant $K_c$ for the following equilibrium:
$2 SO_{2(g)} + O_{2(g)} \rightleftharpoons 2 SO_{3(g)}$
at $563 \ K$ is $100$. At equilibrium,the number of moles of $SO_3$ in the $10 \ L$ flask is twice the number of moles of $SO_2$. Calculate the number of moles of oxygen.

$AB_{3(g)}$ dissociates as:
$AB_3(g) \rightleftharpoons AB_2(g) + \frac{1}{2}B_2(g)$
When the initial pressure of $AB_3$ is $800 \ torr$ and the total pressure developed at equilibrium is $900 \ torr$,what fraction of $AB_{3(g)}$ is dissociated? .....$\%$