For a reaction $X + Y \rightleftharpoons 2 Z$,$1.0 \ mol$ of $X$,$1.5 \ mol$ of $Y$ and $0.5 \ mol$ of $Z$ were taken in a $1 \ L$ vessel and allowed to react. At equilibrium,the concentration of $Z$ was $1.0 \ mol \ L^{-1}$. The equilibrium constant of the reaction is $-\frac{x}{15}$. The value of $x$ is........

The two substances $A$ and $B$ are in equilibrium with $C$ and $D$ as $2A + B \rightleftharpoons 3C + 2D$. If the initial pressure of $A$ and $B$ are in the ratio of $4:1$ and at equilibrium,the partial pressures of $A$ and $D$ are equal,find the correct relation.

$37.8 \ g$ $N_2O_5$ was taken in a $1 \ L$ reaction vessel and allowed to undergo the following reaction at $500 \ K$:
$2N_2O_{5(g)} \rightarrow 2N_2O_{4(g)} + O_{2(g)}$
The total pressure at equilibrium was found to be $18.65 \ bar$. Then,$K_p = \text{ . . . . . . } \times 10^{-2}$ [nearest integer].
Assume $N_2O_5$ to behave ideally under these conditions.
Given: $R = 0.082 \ bar \ L \ mol^{-1} \ K^{-1}$

$\Delta _f G^o$ 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 $(R = 2 \, cal \, K^{-1} \, mol^{-1}) \dots \dots \text{atm}$.

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

If the equilibrium constant $K_c = 0.04$,how many moles/liter of $PCl_5$ are required to obtain $0.1$ mole of $Cl_2$?