A $-->4$B irreversible gas phase reaction takes place on a non$-$porous catalyst surface. The reaction rate expression for this reaction, which takes place in a very slow reaction regime, is $(-$rA$)=$kCa. There is a $5$ mm thick film layer, assumed to be stagnant, between the catalyst surface where the reaction takes place and the large volume gas mass consisting of pure A$.$ The system is under a constant temperature of $25\backslash$deg C and a constant pressure of $101\mathrm{.}3$ kPa. Under these conditions, the reaction rate constant value is k$=0\mathrm{.}01$ m$/$s and Dab$=1\mathrm{.}25$x$105$ m$^2/$s for the A$-$B binary system. Calculate the mole fraction of A on the catalyst surface under settling condition.

Data:

Ideal gas constant R$=8314$ m$^3$ Pa$/$kmol K