Equilibrium Constant Questions

For the reaction $\text{A}(\text{g})\rightleftharpoons 2\text{B}(\text{g})$, the backward reaction rate constant is higher than the forward reaction rate constant by a factor of $2500$, at $1000\text{K}$.[Given : $R=0.0831{\text{L atm mol}}^{-1}{\text{K}}^{-1}$ ]$K_p$ for the reaction at $1000\text{K}$ is:

The following equilibrium constants are given:

The value of equilibrium constant of the reaction $HI(g)\rightleftharpoons \frac{1}{2}{H}_2(g)+\frac{1}{2}{I}_2(g)$ is $8.0$. The equilibrium constant of the reaction $H_2(g)+I_2(g)\rightleftharpoons 2HI(g)$ will be:

The dissociation constants for acetic acid and $\text{HCN}$ at $25^{\circ }\text{C}$ are $1.5\times 10^{-5}$ and $4.5\times 10^{-10}$ respectively. The equilibrium constant for the equilibrium ${\text{CN}}^{-}+{\text{CH}}_3\text{COOH}\rightleftharpoons \text{HCN}+{\text{CH}}_3{\text{COO}}^{-}$ would be:

In which of the following equilibrium $K_c$ and $K_p$ are not equal?

Given that the equilibrium constant for the reaction $2{\text{SO}}_{2(\text{g})}+{\text{O}}_{2(\text{g})}\rightleftharpoons 2{\text{SO}}_{3(\text{g})}$ has a value of $278$ at a particular temperature. What is the value of the equilibrium constant for the following reaction at the same temperature:
$${\text{SO}}_{3(\text{g})}\rightleftharpoons {\text{SO}}_{2(\text{g})}+\frac{1}{2}{\text{O}}_{2(\text{g})}$$

Given the reaction between $2$ gases represented by ${\text{A}}_2$ and ${\text{B}}_2$ to give the compound ${\text{AB}}_{(\text{g})}$. At equilibrium, the concentration of:$[{\text{A}}_2]=3.0\times 10^{-3}\text{M}$$[{\text{B}}_2]=4.2\times 10^{-3}\text{M}$$[\text{AB}]=2.8\times 10^{-3}\text{M}$ If the reaction takes place in a sealed vessel at $527^{\circ }\text{C}$, then the value of $K_c$ for the reaction ${\text{A}}_2+{\text{B}}_2\rightleftharpoons 2\text{AB}$ will be: