In the reaction $PCl_5 \rightleftharpoons PCl_3 + Cl_2$,one mole of $PCl_5$ is started in a $5 \ L$ vessel. If $0.3 \ mol$ of $PCl_5$ is present at equilibrium,find the concentration of $PCl_3$,total moles,and the value of $K_c$.

$1 \ mol$ $N_2$ and $3 \ mol$ $H_2$ are taken in a $4 \ L$ closed vessel at a constant temperature. The reaction is $N_{2(g)} + 3H_{2(g)} \rightleftharpoons 2NH_{3(g)}$. If $0.25\%$ of $N_2$ is converted into ammonia,calculate $K_c$ for this reaction and the $K_c'$ for the reaction $\frac{1}{2}N_{2(g)} + \frac{3}{2}H_{2(g)} \rightleftharpoons NH_{3(g)}$.

For the reaction $PCl_{5(g)} \rightleftharpoons PCl_{3(g)} + Cl_{2(g)}$,at equilibrium,the mole fraction of $PCl_5$ is $0.4$ and the mole fraction of $Cl_2$ is $0.3$. What will be the mole fraction of $PCl_3$?

Equilibrium constants for the following reactions are given (pressure in $atm$) for the reactions at $0\,^{\circ}C$. Select the option mentioning the correct order of True $(T)$ or False $(F)$ statements:
$(A) \ A \cdot 6H_2O_{(s)} \rightleftharpoons A \cdot 2H_2O_{(s)} + 4H_2O_{(g)}; \ K_P = 1.6 \times 10^{-11}$
$(B) \ B \cdot 12H_2O_{(s)} \rightleftharpoons B \cdot 7H_2O_{(s)} + 5H_2O_{(g)}; \ K_P = 2.43 \times 10^{-13}$
$(C) \ C \cdot 10H_2O_{(s)} \rightleftharpoons C_{(s)} + 10H_2O_{(g)}; \ K_P = 10^{-30}$
Aqueous tension of $H_2O$ at $0\,^{\circ}C$ is given as $0.76 \ torr$.
$(I)$ The most effective drying agent will be $C_{(s)}$ out of $C_{(s)}$,$B \cdot 7H_2O_{(s)}$,and $A \cdot 2H_2O_{(s)}$.
$(II)$ At $0\,^{\circ}C$,$A \cdot 6H_2O_{(s)}$ and $B \cdot 12H_2O_{(s)}$ will be efflorescent.
$(III)$ If $R.H.$ is less than $100\%$ in a chamber at $0\,^{\circ}C$,then none of the substances can act as deliquescent.

$1 \ mol$ of $N_2$ and $2 \ mol$ of $H_2$ are allowed to react in a $1 \ dm^3$ vessel. At equilibrium,$0.8 \ mol$ of $NH_3$ is formed. What is the concentration of $H_2$ at equilibrium (in $M$)?

For a reaction,$A \rightleftharpoons P$,the plots of $[A]$ and $[P]$ with time at temperatures $T_1$ and $T_2$ are given below. If $T_2 > T_1$,the correct statement$(s)$ is (are) (Assume $\Delta H^{\ominus}$ and $\Delta S^{\ominus}$ are independent of temperature and ratio of $\ln K$ at $T_1$ to $\ln K$ at $T_2$ is greater than $T_2 / T_1$. Here $H, S, G$ and $K$ are enthalpy,entropy,Gibbs energy and equilibrium constant,respectively.)
$(A)$ $\Delta H^{\ominus} < 0, \Delta S^{\ominus} < 0$
$(B)$ $\Delta G^{\ominus} < 0, \Delta H^{\ominus} > 0$
$(C)$ $\Delta G^{\ominus} < 0, \Delta S^{\ominus} < 0$
$(D)$ $\Delta G^{\ominus} < 0, \Delta S^{\ominus} > 0$