Exam (elaborations) Mass Transfer Diffusion, ISBN: 9780521564779

Find the overall MTC for Diffusion and First-Order
Heterogeneous Reaction?


1. Reagent diffusing to the surface.
𝑟2 = 𝑛1 = 𝑘1 (𝑐1 − 𝑐1𝑖 ) (1)
2. Reversible first order reaction at the surface.
𝑠𝑝𝑒𝑐𝑖𝑒𝑠1 ⇄ 𝑠𝑝𝑒𝑐𝑖𝑒𝑠2
𝑟2 = 𝑘2 𝑐1𝑖 − 𝑘−2 𝑐2𝑖
𝑘2
𝐾2 =
𝑘−2
1
𝑟2 = 𝑘2 (𝑐1𝑖 − 𝑐 ) (2)
𝐾2 2𝑖

3. Product diffusing away from the surface.
𝑟2 = −𝑛2 = 𝑘3 (𝑐2𝑖 − 𝑐2 ) (3)


From eqn. (3)
𝑟
𝑐2𝑖 = 𝑘2 + 𝑐2 (4)
3

Sub eqn. (4) in eqn.(2).
1 𝑟
𝑟2 = 𝑘2 (𝑐1𝑖 − 𝐾 (𝑘2 + 𝑐2 ))
2 3
𝑟2 1 𝑟 𝑐
= 𝑐1𝑖 − 𝐾 ∗ 𝑘2 − 𝐾2
𝑘2 2 3 2
𝑟2 1 𝑟 𝑐
𝑐1𝑖 = + ∗ 𝑘2 + 𝐾2 (5)
𝑘2 𝐾2 3 2

Sub. Eqn. (5) in eqn. (1)