$\Delta _f G^o$ at $500 \, K$ for substance '$S$' in liquid state and gaseous state are $+100.7 \, kcal \, mol^{-1}$ and $+103 \, kcal \, mol^{-1}$,respectively. The vapour pressure of liquid '$S$' at $500 \, K$ is approximately equal to $(R = 2 \, cal \, K^{-1} \, mol^{-1}) \dots \dots \text{atm}$.

At $1000 \ K$ in a $0.654 \ L$ vessel,$CaCO_{3(s)}$ is taken. For the reaction $CaCO_{3(s)} \rightleftharpoons CaO_{(s)} + CO_{2(g)}$,the equilibrium constant $K_p$ is $3.9 \times 10^{-2} \ bar$. Find the weight of $CaO$ produced at equilibrium. $(Ca=40, C=12, O=16)$

$S_1$: In case of endothermic reactions,the equilibrium shifts in the forward direction on increasing temperature.
$S_2$: The value of $K_{eq}$ depends only on temperature and is independent of pressure.
$S_3$: For the reaction,$H_2(g) + I_2(g) \rightleftharpoons 2HI(g)$,the equilibrium constant,$K_{eq}$ is dimensionless because the number of moles of gaseous products equals the number of moles of gaseous reactants.

In an alkaline medium,the sulfide ion reacts with solid sulfur to form polysulfide ions. The equilibrium constants for the formation of $S_2^{2-}$ and $S_3^{2-}$ from $S$ and $S^{2-}$ ions are $1.7$ and $5.3$,respectively. The equilibrium constant for the formation of $S_3^{2-}$ from $S_2^{2-}$ and $S$ will be .........

$A$ $1 \, M$ solution of glucose reaches dissociation equilibrium according to the equation $C_6H_{12}O_6 \rightleftharpoons 6HCHO$. What is the concentration of $HCHO$ at equilibrium if the equilibrium constant $K_c$ for the formation of glucose from formaldehyde is $6 \times 10^{22}$?

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