As shown in the figure below, liquid A evaporates in the z-direction and passes through a layer of gas B occupying the region between z=0 and z=L. Suppose that the species A undergoes a chemical reaction (-r_A = kC_A²) where C_A is the concentration of species A. Also, suppose that N_B = -N_A/2 throughout the system where N_A and N_B are the molar fluxes of species A and B, respectively. Furthermore, the diffusion coefficient (D_AB) of species A varies with its mole fraction (x_A) as D_AB = D₀(1-x_A²/4) where D₀ is a constant. Find the steady-state concentration (or mole fraction) profile of species A as a function of z. Use the boundary condition of x_A=x_A0 at z = 0 and x_A=x_AL at z=L. Assume that diffusion occurs only in the z-direction and the total concentration C of the gas mixture is constant.

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