For the reaction,$H_{2(g)} + I_{2(g)} \rightleftharpoons 2 HI_{(g)}$,which of the following relations is correct?

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:

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 $K_p$.

Consider the reaction $N_{2}O_{4(g)} \rightleftharpoons 2NO_{2(g)}$. The temperature at which $K_{C}=20.4$ and $K_{P}=600.1$ is ....... $K$. (Round off to the nearest integer).
[Assume all gases are ideal and $R=0.0831 \, L \, bar \, K^{-1} \, mol^{-1}$]

For a reversible reaction $A \rightleftharpoons B$,the pre-exponential factor is the same for both the forward and backward reactions and has a value of $20 \ s^{-1}$. If the enthalpy change for the forward reaction is $-41.5 \ kJ \ mol^{-1}$,the value of the equilibrium constant at $500 \ K$ is:

For the reaction $A_{(g)} + 2B_{(g)} \rightleftharpoons 2C_{(g)}$,$1 \ mol$ of $A$ and $1.5 \ mol$ of $B$ are taken in a $2 \ L$ vessel. If the concentration of $C$ at equilibrium is $0.35 \ M$,then the equilibrium constant $K_c$ of the reaction will be ....... $M^{-1}$.