At $550 \ K$,the $K_c$ for the following reaction is $10^4 \ mol^{-1} \ L$: $X_{(g)} + Y_{(g)} \rightleftharpoons Z_{(g)}$. At equilibrium,it was observed that $[X] = \frac{1}{2}[Y] = \frac{1}{2}[Z]$. What is the value of $[Z]$ (in $mol \ L^{-1}$) at equilibrium?

Which of the following statements is false?

The reaction $2H_2S_{(g)} \rightleftharpoons 2H_{2_{(g)}} + S_{2_{(g)}}$ is in equilibrium. If $0.5 \ mol$ of $H_2S$,$0.10 \ mol$ of $H_2$,and $0.4 \ mol$ of $S_2$ are taken in a $1 \ L$ vessel,the value of the equilibrium constant $(K)$ is .... $mol \ L^{-1}$.

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 a $1.0 \, L$ vessel at $90 \, ^\circ C$,$0.2 \, mol$ of $H_{2(g)}$ and $2.0 \, mol$ of $S_{(s)}$ are mixed. For the reaction $H_{2(g)} + S_{(s)} \rightleftharpoons H_2S_{(g)}$; $K_p = 6.8 \times 10^{-2}$,the partial pressure of $H_2S_{(g)}$ at equilibrium will be ............ $atm$.

$X_{2(g)} + Y_{2(g)} \rightleftharpoons 2Z_{(g)}$
$X_{2(g)}$ and $Y_{2(g)}$ are added to a $1 \ L$ flask and it is found that the system attains the above equilibrium at $T \ K$ with the number of moles of $X_{2(g)}$,$Y_{2(g)}$ and $Z_{(g)}$ being $3$,$3$ and $9 \ mol$ respectively (equilibrium moles). Under these conditions of equilibrium,$10 \ mol$ of $Z_{(g)}$ is added to the flask and the temperature is maintained at $T \ K$. Then the number of moles of $Z_{(g)}$ in the flask when the new equilibrium is established is . . . . . . . (Nearest integer).