Post on 06-Apr-2022
MOLECULAR DIFFUSION IN LIQUIDS
For gases, π·π΄π΅ β π(π)
For liquid, π·π΄π΅ = π(π)
1. Equimolar Counter Diffusion in Liquids
For this case,
ππ΄ = βππ΅
Therefore, the following equation,
ππ΄ = βππ·π΄π΅
π(π₯π΄)
ππ§+
ππ΄
π(ππ΄ + ππ΅)
leads to,
ππ΄ = βππ·π΄π΅
π(π₯π΄)
ππ§+ 0
ππ΄ =π·π΄π΅πππ£(π₯π΄1 β π₯π΄2)
(π§2 β π§1)=
π·π΄π΅(ππ΄1 β ππ΄2)
(π§2 β π§1)
where,
πππ£ = (π
π)
ππ£= (
π1
π1+
π2
π2) 2β
2. Diffusion of A through non-diffusing B in liquid phase
ππ΄ =π·π΄π΅
(π§2 β π§1)
π
π π
ππ΄1 β ππ΄2
ππ΅π
can be rewritten as,
ππ΄ =π·π΄π΅
(π§2 β π§1)πππ£
π₯π΄1 β π₯π΄2
π₯π΅π
π₯π΅π =π₯π΅2 β π₯π΅1
πππ₯π΅2
π₯π΅1
For dilute solutions (small concentration of A), π₯π΅π β 1. Therefore,
ππ΄ =π·π΄π΅
(π§2 β π§1)(ππ΄1 β ππ΄2)
Diffusion Coefficients for Liquids
1. Experimental determination of liquid diffusivities
π·π΄π΅ = π(π) π·π΄π΅ β π·π΅π΄
Dilute solution and relatively concentrated solution are placed in chambers on opposite sides of a porous membrane of sintered glass.
Diffusion length = πΎ1πΏ, πΎ1 > 1
Another solute with known diffusivity is used to determine the diffusion length. Then,
ππ΄ =νπ·π΄π΅
πΎ1πΏ(π β πβ²)
ν is the fraction of the open area for diffusion across the membrane. For V=Vβ,
ln(π0 β π0
β² )
(π β πβ²)= (
2νπ΄
πΎ1πΏπ) π·π΄π΅π‘
where, π0 is the initial concentration. Another solute (e.g. KCl) with known diffusivity
is used to determine the cell constant (2 π΄
πΎ1πΏπ)
2. Experimental liquid diffusivity data
Range 0.5 Γ 10β9β 5 Γ 10β9 π2
π
3. Prediction of Diffusivities in Liquids
For dilute solutes in liquids (Eq. 6.3-8 in C. J. Geankoplis):
π·π΄π΅ = 9.96 Γ 10β16
ππ΄1 3β
(π) (1
π)
where, A is solute molecule present in low concentration in solvent B, π·π΄π΅is the
diffusivity (m2/s), T is the absolute temperature (K), π is the viscosity (PaΒ·s or
kg/(mΒ·s) ) and VA is the solute molar volume at its normal boiling point
(π3 ππ πππβ ). This equation give good predictions for very large un-hydrated and
spherical-like solute molecules of molecular weight more than 1000 or where VA>
0.5 π3 ππ πππβ in aqueous solution.
For smaller solute molar volume, the Wilke-Chang correlation can be used (Eq. 6.3-
9 in C. J. Geankoplis):
π·π΄π΅ = 1.173 Γ 10β16(πππ΅)1 2β (π
ππ΅ππ΄0.6)
where, A is solute molecule present in low concentration
in solvent B, π·π΄π΅is the diffusivity (m2/s), T is the absolute
temperature (K), π is the viscosity (PaΒ·s or kg/(mΒ·s) ) and
VA (see Table 6.3-2) is the solute molar volume at its
normal boiling point (π3 ππ πππβ ). π is an association
parameter of the solvent.
Solvent π
Water 2.6
Methanol 1.9
Ethanol 1.5
Benzene 1.0
Ether 1.0
Heptane 1.0
Unassociated 1.0