CHEMICAL ENGINEERING

238 CHEMICAL ENGINEERING VOLUME 1 SOLUTIONS

Mass transfer rate at the surfaceDD

(

∂CA

∂y

)

yD 0

∂CA

∂y

DCAs

∂

∂y

{

2

p



∫ 1

y/ 2

p

Dt

ey

(^2) / 4 Dt
d

(

y

2

p

Dt

)}

DCAs

2

p



(



1

2

p

Dt

)

ey

(^2) / 4 Dt
(equation 10.111)

∴

(

∂CA

dy

)

yD 0

D

CAs

p

Dt

NA (^) tDD

(

∂CA

∂t

)

yD 0

DCAs

√

D

t

The mass transfer in timetD

∫t

0

√

D

t

dtD 2

√

D



p

t

and the mass transfer is proportional to

p

t

Thus:

M 1

M 2

D

√

t 1

t 2

M 1 D5%,M 2 D10%, andt 1 D300 s

and: 0. 5 D

p

300 /t 2 andt 2 D1200 s

PROBLEM 10.20

In a continuous steady state reactor, a slightly soluble gas is absorbed into a liquid in
which it dissolves and reacts, the reaction being second-order with respect to the dissolved
gas. Calculate the reaction rate constant on the assumption that the liquid is semi-infinite
in extent and that mass transfer resistance in the gas phase is negligible. The diffusivity of
the gas in the liquid is 10^8 m^2 /s, the gas concentration in the liquid falls to one half of
its value in the liquid over a distance of 1 mm, and the rate of absorption at the interface
is 4ð 10 ^6 kmol/m^2 s.

Solution

The equation for mass transfer with chemical reaction is:

∂CA

∂t

DD

∂^2 CA

∂y^2

kCnA (equation 10.170)

For steady state second order reaction wherenD2:

D

d^2 CA

dy^2

kC^2 AD 0