$CH_3COCH_{3(g)} \rightleftharpoons C_2H_{6(g)} + CO_{(g)}$. The initial pressure of $CH_3COCH_3$ is $100 \ mm$. When equilibrium is set up,the mole fraction of $CO_{(g)}$ is $\frac{1}{4}$. Hence,the partial pressure of $CO$ is:

$\Delta _f G^o$ at $500 \, K$ for substance '$S$' in liquid state and gaseous state are $+100.7 \, kcal \, mol^{-1}$ and $+103 \, kcal \, mol^{-1}$,respectively. The vapour pressure of liquid '$S$' at $500 \, K$ is approximately equal to $(R = 2 \, cal \, K^{-1} \, mol^{-1}) \dots \dots \text{atm}$.

Consider the following two equilibrium reactions:
$i$. $2NH_{3(g)} \rightleftharpoons N_{2(g)} + 3H_{2(g)}$
$ii$. $2ND_{3(g)} \rightleftharpoons N_{2(g)} + 3D_{2(g)}$
What is the difference in their equilibrium constants $(K_c)$?

$5 \, \text{moles}$ of $PCl_5$ are heated in a closed vessel of $5 \, \text{L}$ capacity. At equilibrium,$40\%$ of $PCl_5$ is found to be dissociated. What is the value of $K_c$ (in $, \text{M}$)?

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?

The following lists contain reactions and their corresponding equilibrium constants at different temperatures:

List-$I$ (Reaction)	List-$II$ $(K_p)$
$2 SO_{2(g)} + O_{2(g)} \rightleftharpoons 2 SO_{3(g)}$ at $298 \ K$	$4.0 \times 10^{24}$
$2 SO_{2(g)} + O_{2(g)} \rightleftharpoons 2 SO_{3(g)}$ at $700 \ K$	$3.0 \times 10^{4}$
$N_2O_{4(g)} \rightleftharpoons 2 NO_{2(g)}$ at $298 \ K$	$0.98$
$N_2O_{4(g)} \rightleftharpoons 2 NO_{2(g)}$ at $500 \ K$	$1700$

If $\Delta H_1^0$ and $\Delta H_2^0$ are the standard enthalpies for the reactions $2 SO_{2(g)} + O_{2(g)} \rightleftharpoons 2 SO_{3(g)}$ and $N_2O_{4(g)} \rightleftharpoons 2 NO_{2(g)}$ respectively, then: