Chapter 14, Problem 14.30P

Pulverized coal pellets, which may be approximated as carbon spheres of radius r, 1 mm, are burned in a pure oxygen atmosphere at 1450 K and 1 atm. Oxygen is transferred to the particle surface by diffusion, where it is consumed in the reaction $\text{C}+{\text{O}}_2\to {\text{CO}}_2$ . The reaction rate is first order and of the form $N_{{\text{O}}_2}^{"}=-k_1^{"}{C}_{{\text{O}}_2}\left(r_0\right)$ , where $k_1^{"}=0.1$ m/s. Neglecting changes in $r_0$ , determine the steady-state O₂, molar consumption rate in kmol/s. At 1450 K. the binary diffusion coefficient for ${\text{O}}_2$ and ${\text{CO}}_2$ , is $1.71\times {10}^{-4}$ m²/s.