A steel cylinder contains $5\mathrm{.}00$ mole of graphite $($pure carbon$)$ and $5\mathrm{.}00$ moles of $O_2.$ The mixture is ignited and all the graphite reacts. Combustion produces a mixture of $CO$ gas and $C{O}_2$ gas. After the cylinder has cooled to its original temperature, it is found that the pressure of the cylinder has increased by $17\mathrm{.}0\%.$ Calculate the mole fractions of $CO,C{O}_2,$ and $O_2$ in the final gaseous mixture.