For the reaction $X_{(g)} + Y_{(g)} \rightleftharpoons Z_{(g)}$ at $550 \ K$,the value of $K_c$ is $10^{-4} \ mol^{-1} \ L$. If at equilibrium $[X] = \frac{1}{2}[Y] = \frac{1}{2}[Z]$,then the value of $[Z]$ at equilibrium will be:

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?

$13.8 \,g$ of $N_{2}O_{4}$ was placed in a $1 \,L$ reaction vessel at $400 \,K$ and allowed to attain equilibrium.
$N_{2}O_{4(g)} \rightleftharpoons 2NO_{2(g)}$
The total pressure at equilibrium was found to be $9.15 \,bar$. Calculate $K_{c}$,$K_{p}$,and the partial pressures at equilibrium.

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:

Consider the reaction,$P(aq) \rightleftharpoons Q(aq)$ with an equilibrium constant $K=1.5$. The reaction is started in a vessel with a concentration of $[P]$ of $2 \ M$ and concentration of $[Q]=0$. When the equilibrium is established,half the amount of $P$ is removed,and the reaction is allowed to re-equilibrate. The concentration of $Q$ in the vessel (in $M$) is closest to

For the reaction $N_2 + 3H_2 \rightleftharpoons 2NH_3$,what is the relationship between $\Delta H$ and $\Delta E$?