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:

In a $13 \ L$ vessel at $1027 \ ^oC$,the reaction $C_{(s)} + S_{2_{(g)}} \rightleftharpoons CS_{2_{(g)}}$ is carried out with $12 \ g$ of $C$,$64 \ g$ of $S_2$,and $76 \ g$ of $CS_2$. What is the total pressure in terms of $R$ (in $R$)?

Which of the following statements is/are true about equilibrium?
$(a)$ Equilibrium is possible only in a closed system at a given temperature.
$(b)$ All the measurable properties of the system remain constant at equilibrium.
$(c)$ Equilibrium constant for the reverse reaction is the inverse of the equilibrium constant for the reaction in the forward direction.

At $67\,^{\circ}C$ and $1\ bar$ pressure,dinitrogen tetraoxide is $50\%$ dissociated into nitrogen dioxide. $\Delta G^{\circ}$ for the process $N_2O_{4(g)} \rightleftharpoons 2NO_{2(g)}$ is $(R = \frac{25}{3} \ J \ K^{-1} \ mol^{-1}, \ln 2 = 0.7, \ln 3 = 1.1)$.

If the reaction is started with $NH_4COONH_{2(s)}$ and the equilibrium mixture has a total pressure of $3 \ atm$,then the $K_P$ for the reaction $NH_4COONH_{2(s)} \rightleftharpoons 2NH_{3(g)} + CO_{2(g)}$ is ..... $atm^3$.

Calculate the partial pressure of carbon monoxide from the following data:
$CaCO_{3(s)} \rightleftharpoons CaO_{(s)} + CO_{2(g)}, K_p = 8 \times 10^{-2}$
$CO_{2(g)} + C_{(s)} \rightleftharpoons 2CO_{(g)}, K_p = 2$