For the reaction $A + B \rightleftharpoons C + D$,the initial concentrations of $A$ and $B$ are equal. If the equilibrium concentration of $D$ is twice the equilibrium concentration of $A$,then the equilibrium constant $K_c$ is:

In a $500 \,mL$ flask,the degree of dissociation of $PCl_5$ at equilibrium is $40 \%$ and the initial amount is $5 \,moles$. The value of equilibrium constant in $mol \,L^{-1}$ for the decomposition of $PCl_5$ is

For a gaseous reaction $pA + qB \rightleftharpoons qC + pD$,which of the following relationships is true?

$A$ mixture of $0.3 \ mol$ of $H_2$ and $0.3 \ mol$ of $I_2$ is allowed to react in a $10 \ L$ evacuated flask at $500 \ ^oC$. The reaction is $H_2 + I_2 \rightleftharpoons 2HI$,and the equilibrium constant $K_c$ is found to be $64$. The amount of unreacted $I_2$ at equilibrium is $...... \ mol$.

For a given exothermic reaction,$K_p$ and $K'_p$ are the equilibrium constants at temperatures $T_1$ and $T_2,$ respectively. Assuming that the heat of reaction is constant in the temperature range between $T_1$ and $T_2,$ where $T_2 > T_1,$ it is readily observed that:

For the reaction $SO_2 + \frac{1}{2} O_2 \rightleftharpoons SO_3$, if we write $K_p = K_c(RT)^x$, then $x$ becomes