$PCl_5$,$PCl_3$,and $Cl_2$ are at equilibrium at $500 \ K$ with concentrations $[PCl_3] = 1.59 \ M$,$[Cl_2] = 1.59 \ M$,and $[PCl_5] = 1.41 \ M$. Calculate $K_c$ for the reaction:
$PCl_5 \rightleftharpoons PCl_3 + Cl_2$

In the equilibrium $AB \rightleftharpoons A + B$; if the equilibrium concentration of $A$ is doubled,the equilibrium concentration of $B$ would become:

If the equilibrium constants for the given reactions are $K_1$ and $K_2$ respectively,find the relationship between $K_2$ and $K_1$.
$2SO_{2(g)} + O_{2(g)} \rightleftharpoons 2SO_{3(g)}$
$SO_{2(g)} + \frac{1}{2} O_{2(g)} \rightleftharpoons SO_{3(g)}$

$4.5$ moles each of hydrogen and iodine are heated in a sealed $10 \ L$ vessel. At equilibrium,$3$ moles of $HI$ are found. The equilibrium constant for ${H_2}_{(g)} + {I_2}_{(g)} \rightleftharpoons 2HI_{(g)}$ is

The equilibrium of formation of phosgene is represented as:
$CO_{(g)} + Cl_{2(g)} \rightleftharpoons COCl_{2(g)}$
The reaction is carried out in a $500 \ mL$ flask. At equilibrium,$0.3 \ mol$ of phosgene,$0.1 \ mol$ of $CO,$ and $0.1 \ mol$ of $Cl_2$ are present. The equilibrium constant $(K_c)$ of the reaction is:

For the reaction ${N_2}_{(g)} + 2{O_2}_{(g)} \rightleftharpoons 2{NO_2}_{(g)}$,the equilibrium constant is $100$. Find the equilibrium constant for the following reactions:
$(1)$ $2{NO_2}_{(g)} \rightleftharpoons {N_2}_{(g)} + 2{O_2}_{(g)}$
$(2)$ ${NO_2}_{(g)} \rightleftharpoons \frac{1}{2}{N_2}_{(g)} + {O_2}_{(g)}$