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.

$0.5 \ mol$ 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.

From the given data of equilibrium constants for the following reactions:
$(1) \ CO_{2(g)} + H_{2(g)} \rightleftharpoons CO_{(g)} + H_2O_{(g)} \ ; \ K_1$
$(2) \ CO_{(g)} + H_2O_{(g)} \rightleftharpoons CO_{2(g)} + H_{2(g)} \ ; \ K_2$
Wait,the provided question text has a typo in the reaction equations. Assuming the standard problem format where we relate equilibrium constants for reverse or combined reactions,if the target reaction is the same as reaction $(1)$,the answer is $K_1$. However,based on the options provided,this is likely a question asking for the relationship between $K_1$ and $K_2$ where reaction $(2)$ is the reverse of reaction $(1)$. If reaction $(2)$ is the reverse of reaction $(1)$,then $K_2 = \frac{1}{K_1}$. Given the options,please re-verify the input. Assuming the question asks for the equilibrium constant of a reaction derived from these,if the target reaction is $CO_{(g)} + H_2O_{(g)} \rightleftharpoons CO_{2(g)} + H_{2(g)}$,the answer is $K_1^{-1}$. Given the options,if we assume the target reaction is the reverse of reaction $(1)$,then $K = \frac{1}{K_1}$.

The values of $K_p$ for the reactions,
$X \rightleftharpoons Y + Z$ $...(i)$
$A \rightleftharpoons 2B$ $...(ii)$
are in the ratio $9 : 1$. If the degree of dissociation of $X$ and $A$ is equal,then the ratio of total pressure at equilibrium for $(i)$ and $(ii)$ is:

Using the data provided,find the value of the equilibrium constant for the following reaction at $298 \ K$ and $1 \ atm$ pressure: $NO_{(g)} + \frac{1}{2} O_{2(g)} \rightleftharpoons NO_{2(g)}$
$\Delta_{f} H^0(NO_{(g)}) = 90.4 \ kJ \cdot mol^{-1}$
$\Delta_{f} H^0(NO_{2(g)}) = 32.48 \ kJ \cdot mol^{-1}$
$\Delta S^{\circ} = -70.8 \ J \cdot K^{-1} \cdot mol^{-1}$
$\text{antilog}(6.4) = 2.51 \times 10^6$ (Note: Calculation based on standard thermodynamic relations)

For the equilibrium reaction $A + B \rightleftharpoons C + D$,if we start with equal concentrations of $A$ and $B$,at equilibrium,the concentration of $C$ is $2$ times that of $A$. Find the value of $K_c$.