By means of a plate column, acetone is absorbed from its mixture with air in a nonvolatile absorption oil. The entering gas contains $30$ mole percent acetone, and the entering oil is acetone$-$free. Of the acetone in the air $97$ percent is to be absorbed$,$ and the concentrated liquor at the bottom of the tower is to contain $10$ mole percent acetone. The equilibrium relationship is y$=1\mathrm{.}9$x

Solve the number of ideal stages analytically.