For the reaction $PCl_5 \rightleftharpoons PCl_3 + Cl_2$,the degree of dissociation is inversely proportional to the square root of the system pressure. Assuming constant temperature,if the volume of the system increases to $16$ times its initial volume,the degree of dissociation becomes ....... times.

$3.2 \text{ moles of hydrogen iodide are heated in a closed vessel at } 444^{\circ}C \text{ until equilibrium is reached. If the degree of dissociation at this temperature is } 22\%, \text{ then the number of moles of hydrogen iodide remaining at equilibrium will be:}$

Ammonia is heated in a closed vessel in the presence of a catalyst at $15 \ atm$ pressure and a temperature range of $27 \ ^\circ C$ to $347 \ ^\circ C$. Under these conditions,ammonia undergoes partial dissociation according to the reaction $2NH_3 \rightleftharpoons N_2 + 3H_2$. When the pressure is increased to $50 \ atm$ while keeping the volume of the vessel constant,calculate the percentage of $NH_3$ dissociated.

The vapor density of a gas is $11.2$. At $N.T.P.$,$11.2 \ g$ of this gas occupies a volume of ............. $litres$.

For the reaction $N_2O_{4(g)} \rightleftharpoons 2NO_{2(g)}$,the correct relation between degree of dissociation $(\alpha)$ of $N_2O_{4(g)}$ and equilibrium constant,$K_p$ is $(P=$ total pressure of mixture $)$

$A_{(g)} \rightleftharpoons 2B_{(g)} + C_{(g)}$
For the given reaction,if the initial pressure is $450 \ mm \ Hg$ and the total pressure at time $t$ is $720 \ mm \ Hg$ at a constant temperature $T$ and constant volume $V$. The fraction of $A_{(g)}$ decomposed under these conditions is $x \times 10^{-1}$. The value of $x$ is $......$. (nearest integer)