Consider the following reversible first-order reaction of $X$ at an initial concentration $[X]_{0}$. The values of the rate constants are $K_{f} = 2 \ s^{-1}$ and $K_{b} = 1 \ s^{-1}$.
$X \underset{K_{b}}{\stackrel{K_{f}}{\rightleftharpoons}} Y$
Which of the following plots correctly represents the concentration of $X$ and $Y$ as a function of time?

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 .........

One mole each of $He$ and $A(g)$ are taken in a $10 \text{ L}$ closed flask and heated to $400 \text{ K}$ to establish the following equilibrium: $A(g) \rightleftharpoons B(g)$. $K_{c}$ for this reaction at $400 \text{ K}$ is $4.0$. The partial pressures (in $\text{atm}$) of $He$ and $B(g)$ are respectively (at equilibrium) (Assume $He$, $A(g)$ and $B(g)$ behave as ideal gases) (Given: $R = 0.082 \text{ L atm K}^{-1} \text{ mol}^{-1}$)

The equilibrium constant at $298 \ K$ for a reaction $A + B \rightleftharpoons C + D$ is $100$. If the initial concentration of all the four species were $1 \ M$ each,then the equilibrium concentration of $D$ (in $mol \ L^{-1}$) will be:

In a $10 \ L$ vessel,$1 \ mol$ each of $PCl_5$ and $PCl_3$ are present. If the vessel is heated,some $PCl_5$ dissociates. What are the concentrations of $PCl_5$,$PCl_3$,and $Cl_2$ at equilibrium,respectively?

$AB_{3(g)}$ dissociates as:
$AB_3(g) \rightleftharpoons AB_2(g) + \frac{1}{2}B_2(g)$
When the initial pressure of $AB_3$ is $800 \ torr$ and the total pressure developed at equilibrium is $900 \ torr$,what fraction of $AB_{3(g)}$ is dissociated? .....$\%$