CHEMICAL ENGINEERING

262 CHEMICAL ENGINEERING VOLUME 1 SOLUTIONS

and:

dCA

dy

DCT

dxA

dy

D 9 .16 kmol/m^4.

PROBLEM 10.35

For the diffusion of carbon dioxide at atmospheric pressure and a temperature of 293 K,
at what time will the concentration of solute 1 mm below the surface reach 1 per cent of
the value at the surface? At that time, what will the mass transfer rate (kmol m^2 s^1 be:

(a) At the free surface?

(b) At the depth of 1 mm?

The diffusivity of carbon dioxide in water may be taken as 1. 5 ð 10 ^9 m^2 s^1 .Inthe
literature, Henry’s law constantK for carbon dioxide at 293 K is given as 1. 08 ð 106
whereKDP/X,Pbeing the partial pressure of carbon dioxide (mm Hg) andXthe
corresponding mol fraction in the water.

Solution

∂CA

∂t

DD

∂^2 CA

∂y^2

whereCAis concentration of solvent undergoing mass transfer.
The boundary conditions are:
yD0 (interface) CADCAs(solution value) t> 0
yD1 CAD 0
tD 0 CAD 00 <y< 1
Taking Laplace transforms then:
∂CA
∂t

D

∫ 1

0

(

∂CA

∂t

)

eptdt

D[CAept]^10 

∫ 1

0

pept

CAdtD 0 CpCNA

∂^2 CA

∂y^2

D

∂^2 CNA

∂y^2

Thus: pCNADD

∂^2 CNA

∂y^2

∂^2 CNA

∂y^2



p

D

CNAD 0

CNADAe

p

p/DyCBe

p

p/Dy

Fort>0; when yD1 CAD 0 , CNAD 0 ∴AD 0.

when yD 0 CADCAs CNAsD

∫ 1

0

CAseptdtDCAs

[

ept

p

] 1

0

D

CAs

p

.