Let do be the diffusivity of o2 in the gas mixture derive

Question

1. As indicated in the figure below, oxygen diffuses to a hot carbon surface, on which the following reaction occurs:

3C + 2O₂ → 2CO + CO₂

Let D_o be the diffusivity of O₂ in the gas mixture. Derive the profile of oxygen mole fraction (x) in the direction normal to the surface. Assume, as one boundary condition, that the oxygen mole fraction is constant (x₂) outside of a thin layer of gas of thickness δ adjacent to the surface. In addition, surface reaction follows a first order reaction kinetics (N_O2 = k_RCx, at the carbon surface). Derive the mole fraction distribution in the region [0, δ]. Although you cannot solve the ODE without all the numerical values provided, you are expected to express the mole fraction distribution and flux (N_O2) in terms of all the parameters specified above.

2. Revisit example 1 in class, i.e. "diffusion of naphthalene", determine the molar average velocity (v*) and velocity of species A (V_A) within the tube z (0 < z < L ). Assume that that outside environment contains very low concentration of Naphthalene. Although solution of the example has been posted, you still need to show all the steps.

Attachment:- Assignment Files.rar