Page 343 - Modelling in Transport Phenomena A Conceptual Approach

PROBLEMS 323

b) Plot 0 versus E for A = 1, a, and 4. Show why the solution given by Ea. (1)
is valid only for A I: a.

c) For A > a, only a fraction 4 (0 < 4 < 1) of the surface is available for
the chemical reaction. Under these circumstances show that the concentration
distribution is given by

8.7 Consider a spherical catalyst particle of radius R over which a first-order
heterogeneous reaction
A+B
takes place. The concentration of species A at a distance far away from the catalyst
particle is CA, .

a) Show that the concentration distribution is

--
CA
‘Am
where A is defined by

b) Show that the molar rate of consumption of species A, +LA, is given by

8.8 Consider a spherical carbon particle of initial radius R, surrounded by an
atmosphere of oxygen. A very rapid heterogeneous reaction

2c + 02 --+ 2co

takes place on the surface of the carbon particle. Show that the time it takes for
the carbon particle to disappear completely is

where pc is the density of carbon.