Which of the following statements is/are true about equilibrium?
$(a)$ Equilibrium is possible only in a closed system at a given temperature.
$(b)$ All the measurable properties of the system remain constant at equilibrium.
$(c)$ Equilibrium constant for the reverse reaction is the inverse of the equilibrium constant for the reaction in the forward direction.

$CH_3COOH_{(l)} + C_2H_5OH_{(l)} \rightleftharpoons CH_3COOC_2H_{5_{(l)}} + H_2O_{(l)}$. In the above reaction,one mole of each of acetic acid and alcohol are heated in the presence of a little conc. $H_2SO_4$. On equilibrium being attained:

The number of correct statement$(s)$ involving equilibria in physical processes from the following is:
$A$. Equilibrium is possible only in a closed system at a given temperature.
$B$. Both the opposing processes occur at the same rate.
$C$. When equilibrium is attained at a given temperature,the value of all its parameters becomes constant.
$D$. For dissolution of solids in liquids,the solubility is constant at a given temperature.

In a $10 \ L$ vessel,$SO_3, SO_2$,and $O_2$ gases are present at a definite temperature with $K_c = 100$. For the reaction $2SO_{2(g)} + O_{2(g)} \rightleftharpoons 2SO_{3(g)}$,if $SO_3$ and $SO_2$ are present in the same number of moles at equilibrium,find the moles of $O_2$. If $SO_3$ is double the moles of $SO_2$,what is the number of moles of $O_2$?

For the reaction $A_{(g)} + 3B_{(g)} \rightleftharpoons 2C_{(g)}$ at $27 \, ^oC$,$2 \, moles$ of $A$,$4 \, moles$ of $B$ and $6 \, moles$ of $C$ are present in a $2 \, litre$ vessel. If $K_C$ for the reaction is $1.2$,the reaction will proceed in

For the reaction $X_{(g)} + Y_{(g)} \rightleftharpoons Z_{(g)}$ at $550 \ K$,the value of $K_c$ is $10^{-4} \ mol^{-1} \ L$. If at equilibrium $[X] = \frac{1}{2}[Y] = \frac{1}{2}[Z]$,then the value of $[Z]$ at equilibrium will be: