248 CHEMICAL ENGINEERING VOLUME 1 SOLUTIONS
PROBLEM 10.26
A pure gas is absorbed into a liquid with which it reacts. The concentration in the liquid
is sufficiently low for the mass transfer to be governed by Fick’s law and the reaction
is first order with respect to the solute gas. It may be assumed that the film theory may
be applied to the liquid and that the concentration of solute gas falls from the saturation
value to zero across the film. Obtain an expression for the mass transfer rate across the
gas-liquid interface in terms of the molecular diffusivity,D, the first-order reaction rate
constantk, the film thicknessLand the concentrationCASof solute in a saturated solution.
The reaction is initially carried out at 293 K. By what factor will the mass transfer rate
across the interface change, if the temperature is raised to 313 K? Reaction rate constant
at 293 KD 2. 5 ð 10 ^6 s^1. Energy of activation for reaction (in Arrhenius equation)D
26430 kJ/kmol. Universal gas constantRD 8 .314 kJ/kmol K. Molecular diffusivityDD
10 ^9 m^2 /s. Film thickness,LD10 mm. Solubility of gas at 313 K is 80% of solubility
at 293 K.
Solution
See Volume 1, Example 10.11
PROBLEM 10.27
Using Maxwell’s law of diffusion obtain an expression for the effective diffusivity for a
gasAin a binary mixture ofBandC, in terms of the diffusivities ofAin the two pure
components and the molar concentrations ofA,BandC.
Carbon dioxide is absorbed in water from a 25 per cent mixture in nitrogen. How will its
absorption rate compare with that from a mixture containing 35 per cent carbon dioxide, 40
per cent hydrogen and 25 per cent nitrogen? It may be assumed that the gas-film resistance
is controlling, that the partial pressure of carbon dioxide at the gas – liquid interface is
negligible and that the two-film theory is applicable, with the gas film thickness the
same in the two cases. Diffusivity of CO 2 in hydrogenD 3. 5 ð 10 ^5 m^2 /s; in nitrogenD
- 6 ð 10 ^5 m^2 /s.
Solution
Maxwell’s Law of Diffusion is discussed in Section 10.3.2 where for a two component
gaseous mixture:
dPA/dyDFABCACBuAuB (equation 10.77)For an ideal gas, PADCART (equation 10.9a)
and from equation 10.78: uADN^0 A/CA (equation 10.9b)