For a gaseous reversible reaction,the enthalpy of reaction at constant pressure is $1.8 \ Kcal/mol$ greater than that at constant volume at $300 \ K$. The value of $\left( \frac{K_P}{K_C} \right)$ for the reaction at $T = \left( \frac{1}{0.00821} \right) \ K$ is:

For the following gas phase equilibrium reaction at constant temperature, $NH_{3(g)} \rightleftharpoons \frac{1}{2} N_{2(g)} + \frac{3}{2} H_{2(g)}$. If the total pressure is $\sqrt{3} \ atm$ and the pressure equilibrium constant $(K_p)$ is $9 \ atm$, then the degree of dissociation is given as $(x \times 10^{-2})^{-1/2}$. The value of $x$ is . . . . . . (Nearest integer)

At $-20^{\circ} C$ and $1 \ atm$ pressure,a cylinder is filled with equal number of $H_2$,$I_2$ and $HI$ molecules for the reaction $H_{2(g)} + I_{2(g)} \rightleftharpoons 2 HI_{(g)}$. The $K_p$ for the process is $x \times 10^{-1}$. Find the value of $x$. [Given: $R = 0.082 \ L \ atm \ K^{-1} \ mol^{-1}$]

$A$ mixture of $1 \ mol$ of $H_2O$ and $1 \ mol$ of $CO$ is taken in a $10 \ L$ container and heated to $725 \ K$. At equilibrium,$40\%$ of water reacts with carbon monoxide according to the equation:
$CO_{(g)} + H_2O_{(g)} \rightleftharpoons CO_{2(g)} + H_{2(g)}$
The equilibrium constant $K_C \times 10^2$ for the reaction is $.......$ (Nearest integer).

For which of the following reactions is the relation $\log \frac{K_P}{K_C} + \log RT = 0$ correct?

At $800 \ K$ in a closed vessel,the molar concentrations of $N_2, O_2$ and $NO$ at equilibrium are $3.2 \times 10^{-3} \ M, 4.2 \times 10^{-3} \ M$ and $2.8 \times 10^{-3} \ M$ respectively. The approximate values of $K_{c}$ and $\frac{1}{K_{c}}$ for the following reaction are respectively: $N_{2(g)} + O_{2(g)} \rightleftharpoons 2 NO_{(g)}$