For the reaction $A + B \rightleftharpoons 2C$,the value of equilibrium constant is $100$ at $298 \ K$. If the initial concentration of all the three species is $1 \ M$ each,then the equilibrium concentration of $C$ is $X \times 10^{-1} \ M$. The value of $X$ is $.....$ (Nearest integer)

The equilibrium constant $K_c$ for the following equilibrium:
$2 SO_{2(g)} + O_{2(g)} \rightleftharpoons 2 SO_{3(g)}$
at $563 \ K$ is $100$. At equilibrium,the number of moles of $SO_3$ in the $10 \ L$ flask is twice the number of moles of $SO_2$. Calculate the number of moles of oxygen.

For the reaction $A + B \rightleftharpoons C + D$ at $250^\circ C$ in a $1 \ L$ vessel,the initial concentration of $A$ is $3$ and $B$ is $n$. If the equilibrium concentration of $C$ is equal to the equilibrium concentration of $B$,what is the equilibrium concentration of $D$?

For the reaction $Br_2 \rightleftharpoons 2Br$,the equilibrium constants at $327\,^oC$ and $527\,^oC$ are $6.1 \times 10^{-12}$ and $1.0 \times 10^{-7}$ respectively. The reaction is ...........

Explain the relationship between the time taken to reach equilibrium and thermodynamics.

For the reaction $X(s) \rightleftharpoons Y(s) + Z(g)$,the plot of $\ln \frac{p_z}{p^\ominus}$ versus $\frac{10^4}{T}$ is given below,where $p_z$ is the pressure (in bar) of the gas $Z$ at temperature $T$ and $p^\ominus = 1 \ bar$.
(Given,$\frac{d(\ln K)}{d(\frac{1}{T})} = -\frac{\Delta H^\ominus}{R}$,where the equilibrium constant,$K = \frac{p_z}{p^\ominus}$ and the gas constant,$R = 8.314 \ J \ K^{-1} \ mol^{-1}$)
$(1)$ The value of standard enthalpy,$\Delta H^\ominus$ (in $kJ \ mol^{-1}$) for the reaction is. . . . . . .
$(2)$ The value of $\Delta S^\ominus$ (in $J \ K^{-1} \ mol^{-1}$) for the given reaction,at $1000 \ K$ is. . . . . .
Give the answer for $(1)$ and $(2)$