$26\mathrm{.}29$ The following problem illustrates the gas$-$phase diffusion in the neighborhood of a flat catalytic surface. Component A diffuses through a stagnant film containing only A and $B.$ Upon reaching the catalytic surface, it is instantaneously converted into species $B$ by the reaction $AB.$ When $B$ diffuses back into the stagnant film, it begins to decompose by the first$-$order reaction $BA.$ The rate of formation of component A with the film is equal to $R_A=k_1{y}_B,$ moles A produced$/($time$)($volume$),$ where $y_A$ is the concentration of $B$ expressed in mole fraction.

Determine the rate at which A enters the gas film if this is a steady$-$state process.