In a chemical equilibrium,the rate constant of the backward reaction is $7.5 \times 10^{-4}$ and the equilibrium constant is $1.5$. The rate constant of the forward reaction is:

For the reaction $PCl_5 \, (g) \rightleftharpoons PCl_3 \, (g) + Cl_2 \, (g)$,the two reaction constants $K_p$ and $K_c$ are related to each other by the expression

At $1127 \, K$ and $1 \, atm$ pressure,a gaseous mixture of $CO$ and $CO_2$ in equilibrium with solid carbon has $90.55 \%$ $CO$ by mass.
$C_{(s)} + CO_{2(g)} \longleftrightarrow 2CO_{(g)}$
Calculate $K_c$ for this reaction at the above temperature.

In which of the following reactions is $K_p$ less than $K_c$?

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: $R = 0.082 \ L \ atm \ K^{-1} \ mol^{-1}$]

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