A gas stream containing 95 mol\% CO\(_2\) and 5 mol\% ethanol is to be scrubbed with pure water in a counter-current, isothermal absorption column to remove ethanol. The desired composition of ethanol in the exit gas stream is 0.5 mol\%. The equilibrium mole fraction of ethanol in the gas phase, \( y^* \), is related to that in the liquid phase, \( x \), as \( y^* = 2x \). Assume CO\(_2\) is insoluble in water and neglect evaporation of water. If the water flow rate is twice the minimum, the mole fraction of ethanol in the spent water is: