$A$ gaseous reaction $A_{2(g)} \to B_{(g)} + \frac{1}{2} C_{(g)}$ shows an increase in pressure from $100 \ mm$ of $Hg$ to $120 \ mm$ of $Hg$ in $5 \ min$. What will be the rate of disappearance of $A_2$ in $mm$ of $Hg/min$?

For a given reaction,$2 A \rightleftharpoons B + C$,the equilibrium constant is $2 \times 10^{-3}$. If at any given time the composition of the reaction mixture is $[A]=[B]=[C]=6 \times 10^{-5} \ M$; predict in which direction the reaction will proceed and the correct value for reaction quotient.

For the ideal gas reaction,$X + Y \rightleftharpoons Z$,a mixture with $n_{X} = 1 \, mol$,$n_{Y} = 3 \, mol$ and $n_{Z} = 2 \, mol$ is at equilibrium at $300 \, K$ and $1 \, bar$. If the pressure is isothermally increased to $2 \, bar$,the number of moles of $X$ in the new equilibrium is closest 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.

$S_1$: In case of endothermic reactions,the equilibrium shifts in the forward direction on increasing temperature.
$S_2$: The value of $K_{eq}$ depends only on temperature and is independent of pressure.
$S_3$: For the reaction,$H_2(g) + I_2(g) \rightleftharpoons 2HI(g)$,the equilibrium constant,$K_{eq}$ is dimensionless because the number of moles of gaseous products equals the number of moles of gaseous reactants.

$PCl_{5} \rightleftharpoons PCl_{3} + Cl_{2} \quad K_{c} = 1.844$
$3.0 \ \text{moles}$ of $PCl_{5}$ is introduced in a $1 \ \text{L}$ closed reaction vessel at $380 \ \text{K}$. The number of moles of $PCl_{5}$ at equilibrium is $..... \times 10^{-3}$. (Round off to the Nearest Integer)