A species A is contained in a mixture, the total molar concentration of the mixture being constant and uniform with the value c, but the mole fraction of A, denoted a being spatially non-uniform, and hence varying with coordinate z.
At a specific location z = 0, species A has a fixed known mole fraction Ao. Starting from this location, the species A undergoes mass transfer towards a catalyst surface located at z = 2c
The mass transfer is characterised by a diffusivity Da whilst the flux of A is NA
At the catalyst surface, a chemical reaction occurs and species A is converted into species B, with species B then being transported away from the surface with a flux NB, in the direction opposite from the transport of A. The relationship for Na then becomes
NA=-DAcOxA/Oz+xA(NA+NB)
It is known that the chemical reaction is extremely rapid, so that the mole fraction of A at z = zc is zero. However the stoichiometry of the reaction is unknown.
It is proposed to determine the stoichiometry of the reaction by installing sensors at various locations z between z = 0 and z = zc: These sensors are able to detect the mole fraction of A and determine a profile z vs A given by
z/zc=(log(1+ 2xAo))-1log((1+ 2xAo)/(1+2x4)
and hence
TA
-1+(1+2xAo) exp(-(z/zc)log(1+2xao))
What is the stoichiometry of reaction that results in such a profile?
