At $413 \ K$ temperature and $100 \ atm$ pressure,$1 \ mol$ $N_2$ and $3 \ mol$ $H_2$ are heated in a closed vessel. At equilibrium,$0.50 \ mol$ $NH_3$ is present. Find $K_p$.

The reaction between $N_2$ and $H_2$ to form ammonia has $K_c = 6 \times 10^{-2}$ at the temperature $500 \ ^oC$. The numerical value of $K_p$ for this reaction is

For the reactions $(i) \ N_{2(g)} + 3H_{2(g)} \rightleftharpoons 2NH_{3(g)}$ and $(ii) \ \frac{1}{2}N_{2(g)} + \frac{3}{2}H_{2(g)} \rightleftharpoons NH_{3(g)}$,if their equilibrium constants are $K_c(1)$ and $K_c(2)$ respectively,what is the relation between them?

The value of $\log \ K$ for the reaction $A \rightleftharpoons B$ at $298 \ K$ is (Nearest integer).
Given: $\Delta H^{\circ} = -54.07 \ kJ \ mol^{-1}$
$\Delta S^{\circ} = 10 \ J \ K^{-1} \ mol^{-1}$
(Take $2.303 \times 8.314 \times 298 = 5705$)

$18.4 \ g$ of $N_2O_4$ was placed in a $1 \ L$ vessel at $400 \ K$ and allowed to attain the following equilibrium: $N_2O_{4(g)} \rightleftharpoons 2NO_{2(g)}$. If the total pressure at equilibrium was $10.64 \ bar$,the approximate $K_p$ is (Given: $R = 0.083 \ L \ bar \ K^{-1} \ mol^{-1}$,assume $N_2O_4$ and $NO_2$ behave as ideal gases).

$1.1 \ mol$ of $A$ are mixed with $2.2 \ mol$ of $B$ and the mixture is kept in a $1 \ L$ vessel till the equilibrium is established in the reaction. If the molar concentration of $C$ at the equilibrium point is $0.2 \ M$,then find the value of the equilibrium constant $(K_c)$ for the reaction: $A + 2B \rightleftharpoons 2C + D$