Question

In a hot combustion chamber, oxygen diffuses through a stagnant film of air with thickness L to the carbon surface where it reacts to make CO and CO₂. The mole fraction of oxygen just outside the stagnant film (z = 0) is 0.21. The reaction may be assumed to be instantaneous. No reaction occurs in the gas film. The chamber is at 1 atm, 1000 K, and L = 10 cm. The diffusivity of oxygen at these conditions is 0.35 cm²/s. The following reaction occurs at the carbon surface: 4C + 3O₂ → 2CO + 2CO₂.

(a) Determine the molar flux of oxygen in mol/cm²·s.

(b) Determine the mole fraction of oxygen at z = 4 cm.

The answers to parts (a) and (b) are 8.66 × 10⁻⁸ mol/cm²·s and 0.12429, but I cannot figure out how to get these answers.

Answer 1

Bulk diffusive molar flux (NA) and Molar flux due to molecular diffusion(JA) are related as

NA= xA*(NA+NB)+JA

For molecular diffusion JA=-DAB*dCA/dx

For diffusion through stagnant gas film, NB=0

Hence NA*(1-XA)= -DAB*dCA/dx, CA= C*XA

NA*(1-XA)= -DAB*C*dXA/dZ

NA dZ =-DAB*C*dXA/(1-XA)

When integrated between , Z=0 XA1=0.21 and Z=10cm, XA2=0

NA*Z= DABC* ln{ (1-XA2)/(1-XA1)}

NA*Z= DAB*C*ln{(1/(1-0.21)}

Z=10 cm, DAB= 0.35 cm²/s

R= 0.0821 L.atm/mole.K= 0.0821*1000ccatm/mole.K= 82.1 cc.atm/mole.K

C =P/RT =(1/82.1*1000) =1.22*10^-5 moles/cc

Hence NA= 0.35* 1.22*10^-5*ln(1/0.79)/10 = 10.06*10^-8 cm2/s

At Z=4 cm

= 4*10.06*10^-8 = 0.35*1.22*10^-5*ln {(1-XA2)/0.79}

XA2=0.1319