For the reaction $N_{2(g)} + O_{2(g)} \rightleftharpoons 2NO_{(g)}$,the equilibrium constant is $K_1$. For the reaction $2NO_{(g)} + O_{2(g)} \rightleftharpoons 2NO_{2(g)}$,the equilibrium constant is $K_2$. The equilibrium constant $K$ for the reaction $NO_{2(g)} \rightleftharpoons \frac{1}{2}N_{2(g)} + O_{2(g)}$ will be:

The following reaction is performed at $298 \, K$.
$2 NO_{(g)} + O_{2(g)} \rightleftharpoons 2 NO_{2(g)}$
The standard free energy of formation of $NO_{(g)}$ is $86.6 \, kJ/mol$ at $298 \, K$. What is the standard free energy of formation of $NO_{2(g)}$ at $298 \, K$? $(K_p = 1.6 \times 10^{12})$

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:

The thermal dissociation equilibrium of $CaCO_{3(s)}$ is studied under different conditions.
$CaCO_{3(s)} \rightleftharpoons CaO_{(s)} + CO_{2(g)}$
For this equilibrium,the correct statement$(s)$ is (are):
$(A)$ $\Delta H$ is dependent on $T$
$(B)$ $K$ is independent of the initial amount of $CaCO_{3}$
$(C)$ $K$ is dependent on the pressure of $CO_{2}$ at a given $T$
$(D)$ $\Delta H$ is independent of the catalyst,if any

For the ideal gas reaction,$X + Y \rightleftharpoons Z$,a mixture with $n_{X} = 1 \, mol$,$n_{Y} = 3 \, mol$ and $n_{Z} = 2 \, mol$ is at equilibrium at $300 \, K$ and $1 \, bar$. If the pressure is isothermally increased to $2 \, bar$,the number of moles of $X$ in the new equilibrium is closest to $......$

$K_{c}$ for the following reaction is $99.0$: $A_{2(g)} \rightleftharpoons B_{2(g)}$. In a $1 \ L$ flask,$2 \ moles$ of $A_{2}$ were heated to $T(K)$ and equilibrium was reached. The concentrations at equilibrium of $A_{2}$ and $B_{2}$ are $C_{1}(A_{2})$ and $C_{2}(B_{2})$ respectively. Now,$1 \ mole$ of $A_{2}$ was added to the flask and heated to $T(K)$ to establish equilibrium again. The concentrations of $A_{2}$ and $B_{2}$ are $C_{3}(A_{2})$ and $C_{4}(B_{2})$ respectively. What is the value of $C_{3}(A_{2})$ in $mol \ L^{-1}$?