A stream of ideal gas mixture A and

Stream of A and B

B flows slowly over the top of the tube as shown in the figure to keep the mole fraction of A $x_{AL}$ constant at $y=L.$ A is in liquid form at the bottom of the tube $($blue shaded volume$),$ and there is flow of gas A upward in the ydirection from the gas$-$liquid interface to the top of the tube. The mole fraction of $A$ at the liquid$-$gas interface is $x_{A0}$ The species B is stationary. The molar flux of $A$ in the tube is given by$,$ Here, $c$ is the constant concentration of the gas mixture, $D_{AB}$ diffusion constant and $x_A$ is the mole fraction of $A.$

a$)$ Do steady$-$state mass balance in molar units to derive the differential equation to solve $x_A$ in the y$-$direction.

b$)$ Write the boundary conditions to solve the differential equation for $x_A(y).$

c$)$ Solve for $x_A(y).$