Component A reacts reversibly in a liquid film of thickness $L$ as shown by the expression:

$A{}_{k_2}^{k_1}2P$

The reaction is rapid enough that equilibrium is maintained in the film, that is: $\frac{C_A}{C_P}=K=\frac{k_2}{k_1}$ Diffusion coefficients are constant and equal for both A and $P$ in the film. Both components A and $P$ are present in trace amounts in the quiescent liquid film, so convective transport can be neglected. The concentration of $A$ at the edges of the film and $z=L$ and $c_A,$ are fixed and $c_{A0}>c_A.$ Assume that the reaction kinetics are first order: $R_A=-k_1{C}_A+k_2{C}_p.$

$($a$)$ obtain an algebraic expression for the steady state concentration profile of $A$ in the film.

$($b$)$ obtain an algebraic expression for the steady state total molar flux of A$,N_{Az}.$ Note that the chemical reaction of $A$ to form $P$ provides two pathways for the transfer of $A$ in the system: $(1)$ a flux of A along its concentration gradient, and $(2)$ a flux of $P($which may be converted to A due to the reversibility of the chemical reaction$)$ along its concentration gradient.