The Welty et al$.$ book paves me expression for the steady$-$state flux through the top surface of a flat film in waich diffusion and firs$-$ceder resetion we oxturring $N_{Az}=C_{A0}(k_1{D}_e{)}^{\frac{2}{2}}$ tanh $(H\sqrt[\phantom{2}]{\frac{k_1}{D_e}})($Eqaitian $26\mathrm{.}43).$ This peublem wes also solved in the steschy$-$state portion of the $2023$ CHEN $3210.$ Lecture $42s_a$

A$.$ Shar hor the selution from bic lecture for $d\frac{C_1}{d}z$ cam be used to anive at the equation $(26-43)$ in the bock $($inese: $H=$ and $D_e=D_s$ are toxational differences$)$

B$.$ For $D_e={10}^{-5}c\frac{m^2}{s}$ nod $k_1=0\mathrm{.}1s^{-1},$ what is tbe maximum thickness $H$ that the film can be while beepieg the effectiveneor facior at $0\mathrm{.}5$ or grater? For this probiem, we the mathemabical shluive to get a mumerical answer $($neher than a scaling estimme$).$

C$.$ The talnoce of diffision and rastion leads to a muss$-$rnasfer boundary layer, in which specios A andysis to estimute boundary$-$layd llockness sa that diffusion and reaction are in balance. Usigg