Application of Equilibrium Constant

Derive mathematically value of $K_p$ for $\mathrm{A}\left(\mathrm{g}\right)+\mathrm{B}\left(\mathrm{g}\right)\rightleftharpoons \mathrm{C}\left(\mathrm{g}\right)+\mathrm{D}\left(\mathrm{g}\right)$.

Write an expression for equilibrium constant with respect to concentration.

The value of ${\mathrm{K}}_{\mathrm{c}}$ for the dissociation reaction 

${\mathrm{H}}_2\left(\mathrm{g}\right)\rightleftharpoons 2\mathrm{H}\left(\mathrm{g}\right)$ is $1.2\times {10}^{-42}$ at $500 \mathrm{K}$

Does the equilibrium mixture contain mainly hydrogen molecules or hydrogen atoms?

Comment on the extent to which the forward reaction will proceed, from the magnitude of the equilibrium constant for the following reaction:

${\mathrm{H}}_2\left(\mathrm{g}\right)+{\mathrm{Cl}}_2\left(\mathrm{g}\right)\rightleftharpoons 2\mathrm{HCl}\left(\mathrm{g}\right),{\mathrm{K}}_{\mathrm{c}}={10}^{18}$ at $550\mathrm{K}$

Comment on the extent to which the forward reaction will proceed, from the magnitude of the equilibrium constant for the following reaction:

${\mathrm{H}}_2\left(\mathrm{g}\right)+{\mathrm{I}}_2\left(\mathrm{g}\right)\rightleftharpoons 2\mathrm{HI}\left(\mathrm{g}\right),{\mathrm{K}}_{\mathrm{c}}=20$ at $550\mathrm{K}$

Mention various applications of equilibrium constant.

Write expression of ${\mathrm{K}}_{\mathrm{c}}$ for following chemical reaction.

${\mathrm{N}}_2{\mathrm{O}}_4\left(\mathrm{g}\right)\rightleftharpoons 2{\mathrm{NO}}_2\left(\mathrm{g}\right)$

Write expressions of ${\mathrm{K}}_{\mathrm{c}}$ for following chemical reaction.

$2{\mathrm{SO}}_2\left(\mathrm{g}\right)+{\mathrm{O}}_2\left(\mathrm{g}\right)\rightleftharpoons 2{\mathrm{SO}}_3\left(\mathrm{g}\right)$