$0.1 \ mol$ of $H_2S_{(g)}$ is kept in a $0.4 \ L$ vessel at $1000 \ K$. For the reaction $2 H_2S_{(g)} \rightleftharpoons 2 H_{2(g)} + S_{2(g)}$,$K_c = 10^{-6}$. The percentage dissociation of $H_2S$ is.......$\%$

If $D_T$ and $D_0$ are the theoretical and observed vapour densities at a definite temperature and $\alpha$ is the degree of dissociation of a substance,then $\alpha$ in terms of $D_0, D_T$ and $n$ (number of moles of product formed from $1 \, \text{mole}$ of reactant) is calculated by the formula:

The vapour density of $PCl_5$ at $25^{\circ}C$ is $100$. Calculate the degree of dissociation at this temperature.

The equilibrium constant at a certain temperature for the reaction $A_2 + B_2 \rightleftharpoons 2AB$ is $2$. Calculate the degree of dissociation of either $A_2$ or $B_2$.

At $T$ $K$,consider the following gaseous reaction,which is in equilibrium: $N_2O_5 \rightleftharpoons 2NO_2 + \frac{1}{2}O_2$. What is the fraction of $N_2O_5$ decomposed at constant volume and temperature,if the initial pressure is $300 \ mm \ Hg$ and pressure at equilibrium is $480 \ mm \ Hg$? (Assume all gases as ideal)

For the equilibrium $PCl_{5_{(g)}} \rightleftharpoons PCl_{3_{(g)}} + Cl_{2_{(g)}}$,the observed vapour density of the mixture is $80$. Given atomic masses $P = 31$ and $Cl = 35.5$,the degree of dissociation of $PCl_{5_{(g)}}$ is approximately....$\%$