molecular diffusion in gases
DESCRIPTION
Molecular Diffusion in Gases. Diffusion plus Convection. ). Molecular Diffusion in Gases. Equimolar Counterdiffusion. In terms of mole fraction,. B. A. A. B. Molecular Diffusion in Gases. Uni -component Diffusion. - PowerPoint PPT PresentationTRANSCRIPT
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Molecular Diffusion in Gases
Diffusion plus Convection
)
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Molecular Diffusion in Gases
Equimolar Counterdiffusion
A B
BA
ππ΄=π π₯π΄
π½ π΄π§β =βππ· π΄π΅
ππ₯π΄
ππ§
In terms of mole fraction,
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Molecular Diffusion in Gases
Uni-component Diffusion
http://sst-web.tees.ac.uk/external/U0000504/Notes/ProcessPrinciples/Diffusion/Default.htm
π π΄=βππ·π΄π΅
ππ₯π΄
ππ§+ππ΄
π π΄
π
π π΄=βππ· π΄π΅
π₯π΅
ππ₯π΄
ππ§
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Molecular Diffusion in Gases
Example
Water in the bottom of a narrow metal tune is held a t a constant temperature of 293 K. The total pressure of air (assumed dry) is 1.01325 105 Pa and the temperature is 293 K.
Water evaporates and diffuses through the air in the tube, and the diffusion path z2-z1 is 0.1524m long. Calculate the rate of evaporation of water vapor at 293 K and 1 atm pressure. The diffusivity of water in air is 0.250 x 10-4 m2/s. Assume that the system is isothermal.
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Introduction to Mass Transfer II
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Outline
3. Molecular Diffusion in GasesDiffusion with Varying Cross-sectional Area
4. Molecular Diffusion in Liquids 5. Molecular Diffusion in Solids6. Prediction of Diffusivities
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Molecular Diffusion in Gases
Example: Diffusion through a varying cross-sectional area
A sphere of naphthalene having a radius of 2.0 mm is suspended in a large volume of still air at 318 K and 1.01325x105 Pa. The surface temperature of the naphthalene can be assumed to be at 318 K and its vapor pressure at 318 K is 0.555 mm Hg. The DAB of naphthalene in air at 318 K is 6.92x10-6 m2/s. Calculate the rate of evaporation of naphthalene from the surface.
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Molecular Diffusion in Gases
Given:
DAB = 6.92x10-6 m2/spA1 = (0.555/760)*(101325) = 74.0 PapA2 = 0r1 = 0.002 m
* The radius of the sphere decreases slowly with time
π π΄=βπ· π΄π΅ππ π ππ΅
πππ΄
ππ§
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Molecular Diffusion in Gases
π π΄=βπ· π΄π΅ππ π ππ΅
πππ΄
ππ§
αΉ π΄π΄
=βπ·π΄π΅π
π π (π βππ΄)πππ΄
π π
Where
αΉ π΄4π π2
ππ=βπ· π΄π΅π
π π (πβππ΄)πππ΄
Substitution and rearranging,
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Molecular Diffusion in Gases
β«π 1
β αΉ π΄4ππ 2
ππ=βπ·π΄π΅ππ π β«
π π΄1
ππ΄21
(πβππ΄)πππ΄
The left side of the equation will be
β«π 1
β αΉ π΄4ππ 2
ππ=αΉ π΄4πβ«
π 1
β1π2ππ=
αΉ π΄4 π
[ 1π 1β1β
]
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Molecular Diffusion in Gases
β«π 1
β αΉ π΄4ππ 2
ππ=βπ·π΄π΅ππ π β«
π π΄1
ππ΄21
(πβππ΄)πππ΄
The right side of the equation will be
βπ· π΄π΅ππ π β«
ππ΄1
ππ΄21
(π βππ΄ )πππ΄=β
π· π΄π΅ππ π
πππ βππ΄1
π βππ΄2
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Molecular Diffusion in Gases
β«π 1
β αΉ π΄4ππ 2
ππ=βπ·π΄π΅ππ π β«
π π΄1
ππ΄21
(πβππ΄)πππ΄
Solving for the rate of evaporation,
αΉ π΄=β4 ππ1π· π΄π΅ππ π
πππ βππ΄1
π βππ΄2ANS: 4.9 x 10-9 mol/s
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Outline
3. Molecular Diffusion in GasesDiffusion with Varying Cross-sectional Area
4. Molecular Diffusion in Liquids 5. Molecular Diffusion in Solids6. Prediction of Diffusivities
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Molecular Diffusion in Liquids
For gases,Kinetic theory is well developed
http://www.bbc.co.uk/bitesize/ks3/science/chemical_material_behaviour/behaviour_of_matter/revision/4/
Gas ModelGases are made of
continuous free space throughout which are
distributed moving molecules.
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Molecular Diffusion in Liquids
Liquid Model
A continuous phase of arranged molecules close to
each other but held together by strong intermolecular forces
Dispersed throughout the phase are βholesβ of free space
The structure is more complex.
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Molecular Diffusion in Liquids
Rate of DiffusionBUT only about 100 times fasterβ¦.
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Molecular Diffusion in Liquids
Equations for Diffusion
)
1. For equimolarcounterdiffusion,
π π΄=βππ·π΄π΅
ππ₯π΄
ππ§
where
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Molecular Diffusion in Liquids
Equations for Diffusion
)
2. For unicomponent diffusion,
π π΄=βπ·π΄π΅ (1+ππ΄
ππ΅
)ππ π΄
ππ§ ππ΄+ππ΅=ΒΏNOTE:
average value for the molar density of the mixture
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Molecular Diffusion in Liquids
Example
An ethanol (A) β water (B) solution in the form of a stagnant film 2.0 mm thick at 293 K is in contact at one surface with an organic solvent in which ethanol is soluble and water is insoluble. Hence NB = 0. At point 1 the concentration of ethanol is 16.8 wt% and the solution density Ο1 = 972.8 kg/m3. At point 2 ethanol concentration is 6.8 wt% and Ο2 = 988.1 kg/m3. The diffusivity of ethanol is 0.740x10-9 m2/s. Calculate the steady-state flux NA.
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Outline
3. Molecular Diffusion in GasesDiffusion with Varying Cross-sectional Area
4. Molecular Diffusion in Liquids 5. Molecular Diffusion in Solids6. Prediction of Diffusivities
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Molecular Diffusion in Solids
Rate of DiffusionWhat do we expect?
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Outline
3. Molecular Diffusion in GasesDiffusion with Varying Cross-sectional Area
4. Molecular Diffusion in Liquids 5. Molecular Diffusion in Solids6. Prediction of Diffusivities
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Predicting Diffusivities
For gases at low density- almost independent of concentration- increase with temperature - vary inversely with pressure
For liquids and solids, - strongly concentration-dependent - generally increase with temperature
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Predicting Diffusivities
Empirical EquationsFor gases,1. See Table 2-324 Perryβs2. Chapman and Enskog Equation
DAB = diffusivity in m2/sT = temperature in KMA = molecular weight of A in kg/kmol
MB = molecular weight of B in kg/kmolΟAB = average collision diameterΞ©D,AB= collision integral based on Lennard-Jones potential
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Predicting Diffusivities
Empirical EquationsFor gases,3. Gilliland Equation
DAB = diffusivityT = temperature
MA = molecular weightV = molar volume
P= pressure
π· π΄π΅=1.38 π₯10β 7βπ 3( 1
ππ
+ 1ππ
)
π (π π
13+π π
13 )2
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Predicting Diffusivities
Empirical EquationsFor liquids,4. See Table 2-325 Perryβs5. Stokes Einstein Equation
4. Wilke and Chang Equation
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Predicting Diffusivities
All diffusivities have units m2/sTherefore, their ratios are dimensionless groups
Dim. Group Ratio Equation
Prandtl, Pr molecular diffusivity of momentum / molecular diffusivity of heat
Schmidt, Sc momentum diffusivity/ mass diffusivity
Lewis, Le thermal diffusivity/ mass diffusivity