Calculate $\Delta G^o$ (in $kcal/mole$) for the decomposition of $Cl_{2(g)} \rightleftharpoons 2Cl_{(g)}$,if chlorine molecules are $50\%$ dissociated at $1000 \ K$ at a pressure of $15 \ atm$ at equilibrium $(\ln \ 20 = 2.99)$.

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.

For the reaction $A_{(g)} \rightleftharpoons B_{(g)} + C_{(g)}$,$A$ is $33 \%$ dissociated at a total pressure $P$. The correct relation between $P$ and $K_{p}$ is

At a certain temperature,$2HI \rightleftharpoons H_2 + I_2$. If only $50\%$ of $HI$ is dissociated at equilibrium,the equilibrium constant $(K_c)$ is:

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 $O_2$?

$15 \ mol$ of $H_2$ and $5.2 \ mol$ of $I_2$ are mixed and allowed to attain equilibrium at $773 \ K$. At equilibrium,the number of moles of $HI$ is found to be $10$. The equilibrium constant for the dissociation of $HI$ is