# Consider a single, porous, spherical, inert mineral particle. The pores inside the particle are…

Consider a single, porous, spherical, inert
mineral particle. The pores inside the particle are filled with liquid water
(species B). We are interested in analyzing the molecular diffusion of the
contaminant benzene C6H6 species A within the
water-filled pores of the particle. The average diameter of the pores is 150 nm
and the void fraction (porosity) is 0.40. The benzene solute does not adsorb
onto the inter surfaces of the pores. Benzene is very sparingly soluble in water,
and has a molecular diameter of 0.15 nm. The process is isothermal at 298 K.
The concentration of dissolved benzene
»

Consider a single, porous, spherical, inert
mineral particle. The pores inside the particle are filled with liquid water
(species B). We are interested in analyzing the molecular diffusion of the
contaminant benzene C6H6 species A within the
water-filled pores of the particle. The average diameter of the pores is 150 nm
and the void fraction (porosity) is 0.40. The benzene solute does not adsorb
onto the inter surfaces of the pores. Benzene is very sparingly soluble in water,
and has a molecular diameter of 0.15 nm. The process is isothermal at 298 K.
The concentration of dissolved benzene in the water surrounding the particle, , is constant with
time. The critical volume () of benzene is 259
cm3/gmol. The effective diffusion coefficient of benzene inside the
porous particle was to be calculated in Problem 24.25.

Starting with the general differential
equation for mass transfer of benzene, develop a differential model to describe
the concentration profile of benzene, species A within the single, porous,
spherical, inert mineral particle. State reasonable assumptions and
boundary/initial conditions for the process.

Problem 24.25

Consider a single, porous, spherical, inert
mineral particle. The pores inside the particle are filled with liquid water
(species B). We are interested in analyzing the molecular diffusion of the
contaminant benzene C6H6, species A within the
water-filled pores of the particle. The average diameter of the pores is 150 nm
and the void fraction is 0.40. The benzene solute does not adsorb onto the
intersurfaces of the pores. Benzene is very sparingly soluble in water and has
a molecular diameter of 0.15 nm. The process is isothermal at 298 K. The
concentration of dissolved benzene in the water surrounding the particle,  ,

is constant with time. Initially, there is
no dissolved benzene inside the water-filled pores. The critical volume () of benzene is 259
cm3/gmol.

What is the effective diffusion coefficient
of benzene inside the porous particle? Is pore diffusion important?

»

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