When $5.1 \ g$ of solid $NH_4HS$ is introduced into a two litre evacuated flask at $27^{\circ}C$,$20\%$ of the solid decomposes into gaseous ammonia and hydrogen sulphide. The $K_p$ for the reaction at $27^{\circ}C$ is $x \times 10^{-2}$.
The value of $x$ is ....... . (Integer answer)
[Given $R=0.082 \ L \ atm \ K^{-1} \ mol^{-1}$]

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?

$1 \ mol$ of $N_2$ and $2 \ mol$ of $H_2$ are allowed to react in a $1 \ dm^3$ vessel. At equilibrium,$0.8 \ mol$ of $NH_3$ is formed. What is the concentration of $H_2$ at equilibrium (in $M$)?

For the following reactions,which oxide is more stable?
$X_2 + O_2 \rightleftharpoons 2XO, K_1 = 5$
$X_2 + 2O_2 \rightleftharpoons 2XO_2, K_2 = 10$

Using the data provided,find the value of the equilibrium constant for the following reaction at $298 \ K$ and $1 \ atm$ pressure: $NO_{(g)} + \frac{1}{2} O_{2(g)} \rightleftharpoons NO_{2(g)}$
$\Delta_{f} H^0(NO_{(g)}) = 90.4 \ kJ \cdot mol^{-1}$
$\Delta_{f} H^0(NO_{2(g)}) = 32.48 \ kJ \cdot mol^{-1}$
$\Delta S^{\circ} = -70.8 \ J \cdot K^{-1} \cdot mol^{-1}$
$\text{antilog}(6.4) = 2.51 \times 10^6$ (Note: Calculation based on standard thermodynamic relations)

If $8 \, \text{mol}$ of $PCl_5$ is heated in a closed vessel of $10 \, L$ capacity and $25\%$ of it dissociates into $PCl_3$ and $Cl_2$ at equilibrium,then the value of $K_p$ is .....