$10$mol of $S{O}_2$ and $6$mol of $O_2$ are added to a $2L$ vessel. $30$ seconds later, the concentration of $S{O}_3$ is

measured as $4M.$

$2S{O}_{2(g)}+O_{2(g)}2S{O}_{3(g)},K_c=2\mathrm{.}0{10}^{-2}$

Evaluate this information to:

a$.$ calculate $Q_c$

b$.$ communicate in which direction the reaction must proceed to reach equilibrium and justify

your answer using the $K$ and $Q$ values.