As indicated in the figure below, oxygen diffuses to a hot carbon surface, on which the

following reaction occurs:

$3$C $+2$O$22$CO $+$ CO$2$

Let Do be the diffusivity of O$2$ in the gas mixture. Derive the profile of oxygen mole fraction $($x$)$ in the

direction normal to the surface. Assume, as one boundary condition, that the oxygen mole fraction

is constant $($x$2)$ outside of a thin layer of gas of thickness $\backslash$delta adjacent to the surface. In addition,

surface reaction follows a first order reaction kinetics $($NO$2=$ kRCx$,$ at the carbon surface$).$ Derive the

mole fraction distribution in the region $[0,\backslash$delta $].$ Although you cannot solve the ODE without all the

numerical values provided, you are expected to express the mole fraction distribution and flux $($NO$2)$

in terms of all the parameters specified above.$(20$ pts$)$ As indicated in the figure below, oxygen diffuses to a hot carbon surface, on which the

following reaction occurs:

$3C+2O_{2}2CO+C{O}_2$

Let $D_o$ be the diffusivity of $O_2$ in the gas mixture. Derive the profile of oxygen mole fraction $(x)$ in the

direction normal to the surface. Assume, as one boundary condition, that the oxygen mole fraction

is constant $)$ outside of a thin layer of gas of thickness $$ adjacent to the surface. In addition,

surface reaction follows a first order reaction kinetics $(N_{O2}=k_{R}Cx,$ at the carbon surface$).$ Derive the

mole fraction distribution in the region $0,.$ Although you cannot solve the ODE without all the

numerical values provided, you are expected to express the mole fraction distribution and flux $(N{O}_{O_2})$

in terms of all the parameters specified above.

Carbon Surface $,3C+2O_{2}2CO+C{O}_2$