A student ran the following reaction in the laboratory at $639$ K:

$2$ HI$($g$)$ H$2($g$)+$ I$2($g$)$

When she introduced $0\mathrm{.}352$ moles of HI$($g$)$ into a $1\mathrm{.}00$ liter container, she found the equilibrium concentration of HI$($g$)$ to be $0\mathrm{.}282$ M$.$

Calculate the equilibrium constant, Kc$,$ she obtained for this reaction.

Kc $=$