$21$:$26314$

Consider the new bottle shown below that will be used to store volatile liquid. It is claimed by the designer that the bottle will minimize evaporation of liquid stored even without a cover. The key to design is the cross$-$sectional area of the bottle which can be represented by the function $A(z)=A_0{e}^{-z},$ where $z$ is the distance from the bottom. Assume dilute solutions, constant concentration, constant diffusivity, steady state operation and the liquid level does not change. The mole fraction of $A$ at the liquid surface is $x_{A0}$ and the mole fraction of $A$ at the top of the bottle is $x_A.$ At the top of the bottle component A is convected in to the bulk air by an average mass transfer coefficient $($:$k_c$:$).$ What is the evaporation rate of A$?$