While ethanol $($CH$3$CH$2$OH$)$ is produced naturally by fermentation, e$.$g$.$ in beer$-$ and wine$-$making, industrially it is synthesized by reacting ethylene $($CH$2$CH$2)$with water vapor at elevated temperatures.

A chemical engineer studying this reaction fills a $25$L tank with $8\mathrm{.}6$ mol of ethylene gas and $11.$mol of water vapor. When the mixture has come to equilibrium she determines that it contains $3\mathrm{.}1$mol of ethylene gas and $5\mathrm{.}5$ mol of water vapor.

The engineer then adds another $5\mathrm{.}5$mol of water, and allows the mixture to come to equilibrium again. Calculate the moles of ethanol after equilibrium is reached the second time. Round your answer to $2$ significant digits.