Consider a stationary, semi$-$infinite liquid in the region $x_1>0.$ Initially, the liquid is pure $B,$ and, for $t>$

$0,$ the liquid is brought into contact with a gas such that, at $x_1=0,$ the concentration of species $A$ is

maintained at $x_{\text{A}\text{e}\text{q}}.$ As A diffuses in the liquid, an irreversible reaction $A+BC$ takes place with reaction

rate constant $k.$ The liquid mixture is dilute in species $A(x_{A}1).$ In this case, the molar density of the

mixture $c$ and the diffusivity $D_{AB}$ can be taken as constants, and the process can be assumed to be

isothermal. Find a solution for the evolution of $x_A.$