HOMEWORK 5 CENG 101C

Date posted: 05/21/2015 (Thu) Due date: 05/28/2015 (Thu)

As usual, only four randomly picked problems will be graded! 1. Problem 26.7 WWWR

2. Problem 26.17 WWWR

3. Problem 26.22 WWWR

4. Consider a spherical graphite particle of radius R that reacts with atmospheric oxygen at its surface according to the following reaction: 2C (s) + O2 (g) 2CO (g) (a) Derive an expression for the net rate of oxygen consumption at the surface of

catalyst if the above reaction occurs instantaneously, the diffusion constant of oxygen is DAB, and concentration of oxygen far from the catalyst is c0.

(b) Derive an expression for the concentration profile of oxygen outside the catalyst particle as a function of distance r from the center of the catalyst particle.

(c) Repeat part (a) for the case where O2 consumption is not instantaneous but occurs at a finite rate such that the consumption rate per unit area is given by kcO2, where k is a first-order rate constant and cO2 is the concentration of O2 at the surface.

5. Consider a liquid film of thickness L that contains tiny catalyst particles homogenously distributed within its volume. These particles react with the dissolved oxygen in the liquid such that the effective rate of consumption of oxygen in the liquid is given by RA = k cA, where k is first-order rate constant and cA is the local concentration of oxygen. Take the diffusion constant of oxygen within the liquid film to be DAB and its solubility as c0. (a) Derive the concentration profile cA(z) of oxygen within the liquid film as a

function of location z from the film centerline (b) Derive the expression for the flux of oxygen NA entering the liquid surface.

6. Derive the concentration profile and flux in Eq. 26-48 and 26-49 of WWWR, respectively, beginning with the governing equation and boundary conditions.