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