$A$ plot of $\ln K$ against $\frac{1}{T}$ ($x$-axis) is expected to be a straight line,with intercept on $Y$-axis equal to

$0.5 \ mol$ of $CaCO_3(s)$ is heated in a $500 \ mL$ closed vessel at $400 \ K$. The reaction is $CaCO_{3(s)} \rightleftharpoons CaO(s) + CO_{2(g)}$. If the equilibrium constant $K_c = 0.9 \ mol \ L^{-1}$,calculate the amount of $CO_2$ in $mol$ at equilibrium and the percentage of the reaction completed.

In an alkaline medium,the sulfide ion reacts with solid sulfur to form polysulfide ions. The equilibrium constants for the formation of $S_2^{2-}$ and $S_3^{2-}$ from $S$ and $S^{2-}$ ions are $1.7$ and $5.3$,respectively. The equilibrium constant for the formation of $S_3^{2-}$ from $S_2^{2-}$ and $S$ will be .........

$A$ $1 \, M$ solution of glucose reaches dissociation equilibrium according to the equation $C_6H_{12}O_6 \rightleftharpoons 6HCHO$. What is the concentration of $HCHO$ at equilibrium if the equilibrium constant $K_c$ for the formation of glucose from formaldehyde is $6 \times 10^{22}$?

In a $1.0 \, L$ vessel at $90 \, ^\circ C$,$0.2 \, mol$ of $H_{2(g)}$ and $2.0 \, mol$ of $S_{(s)}$ are mixed. For the reaction $H_{2(g)} + S_{(s)} \rightleftharpoons H_2S_{(g)}$; $K_p = 6.8 \times 10^{-2}$,the partial pressure of $H_2S_{(g)}$ at equilibrium will be ............ $atm$.

The incorrect expression among the following is: