Chapter 14, Problem 14.36P

Consider combustion of hydrogen gas in a mixture of hydrogen and oxygen adjacent to the metal wall of a combustion chamber. Combustion occurs at constant temperature and pressure according to the chemical reaction ${\text{2H}}_{\text{2}}+\text{O}\to {\text{2H}}_{\text{2}}\text{O}$ . Measurements under steady-state conditions at a distance of 10mm from the wall indicate that the molar concentrations of hydrogen, oxygen, and water vapor are 0.10, 0.10, and 0.20 ${\text{kmol/m}}^{\text{3}}$ , respectively. The generation rate of water vapor is $0.96\times {10}^{-2}$ ${\text{kmol/m}}^{\text{3}}\cdot \text{s}$ throughout the region of interest. The binary diffusion coefficient for each of the species (H₂,O₂, and H₂O) in the remaining species is $0.6\times {10}^{-5}$ ${\text{m}}^{\text{2}}\text{/s}$ .

(a) Determine an expression for and make a qualitative plot of $C_{H_2}$ as a function of distance from the wall.
(b) Determine the value of $C_{H_2}$ at the wall.
(c) On the same coordinates used in part (a), sketch curves for the concentrations of oxygen and water vapor.
(d) What is the molar flux of water vapor at $x=10mm$ ?