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 $(\ln \ 20 = 2.99)$.

$0.5 \ mol$ of $CaCO_3(s)$ is heated in a $500 \ mL$ closed vessel at $400 \ K$. The reaction is $CaCO_{3(s)} \rightleftharpoons CaO(s) + CO_{2(g)}$. If the equilibrium constant $K_c = 0.9 \ mol \ L^{-1}$,calculate the amount of $CO_2$ in $mol$ at equilibrium and the percentage of the reaction completed.

In the reaction $CH_3COOH + C_2H_5OH \rightleftharpoons CH_3COOC_2H_5 + H_2O$,one mole of each of acetic acid and ethanol is heated in the presence of a little concentrated $H_2SO_4$. When equilibrium is reached,which of the following is true?

Which of the following statements is/are wrong?
$(a)$ At equilibrium,concentrations of reactants and products become constant because the reaction stops.
$(b)$ Addition of catalyst speeds up the forward reaction more than the backward reaction.
$(c)$ Equilibrium constant of an exothermic reaction decreases with increase of temperature.
$(d)$ $K_p$ is always greater than $K_c$.

When $5.1 \ g$ of solid $NH_4HS$ is introduced into a two litre evacuated flask at $27^{\circ}C$,$20\%$ of the solid decomposes into gaseous ammonia and hydrogen sulphide. The $K_p$ for the reaction at $27^{\circ}C$ is $x \times 10^{-2}$.
The value of $x$ is ....... . (Integer answer)
[Given $R=0.082 \ L \ atm \ K^{-1} \ mol^{-1}$]

At $67\,^{\circ}C$ and $1\ bar$ pressure,dinitrogen tetraoxide is $50\%$ dissociated into nitrogen dioxide. $\Delta G^{\circ}$ for the process $N_2O_{4(g)} \rightleftharpoons 2NO_{2(g)}$ is $(R = \frac{25}{3} \ J \ K^{-1} \ mol^{-1}, \ln 2 = 0.7, \ln 3 = 1.1)$.