Chapman Enskog Equation for Gas Phase Diffusivity Calculator

✖The temperature of Gas is the measure of the hotness or coldness of a gas.ⓘ Temperature of Gas [T]			+10% -10%
✖Molecular Weight A is the mass of a given molecule a.ⓘ Molecular Weight A [M_A]			+10% -10%
✖Molecular Weight B is the mass of a given molecule b.ⓘ Molecular Weight B [M_b]			+10% -10%
✖Total pressure of Gas is the sum of all the forces that the gas molecules exert on the walls of their container.ⓘ Total Pressure of Gas [P_T]			+10% -10%
✖Characteristic Length Parameter of the binary mixture is the average of the geometric and arithmetic average of the collision diameter of the molecules of the two gases.ⓘ Characteristic Length Parameter [σ_AB]			+10% -10%
✖The Collision Integral is a function of k*T/εAB, where k is the Boltzmann's constant and εAB is a characteristic binary parameter of the Lennard Jones Potential.ⓘ Collision Integral [Ω_D]			+10% -10%

✖The Diffusion Coefficient (DAB) is the amount of a particular substance that diffuses across a unit area in 1 second under the influence of a gradient of one unit.ⓘ Chapman Enskog Equation for Gas Phase Diffusivity [D_AB]

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Chapman Enskog Equation for Gas Phase Diffusivity

Formula

`"D"_{"AB"} = (1.858*(10^(-7))*("T"^(3/2))*(((1/"M"_{"A"})+(1/"M"_{"b"}))^(1/2)))/("P"_{"T"}*"σ"_{"AB"}^2*"Ω"_{"D"})`

Example

`"0.000727m²/s"=(1.858*(10^(-7))*(("298K")^(3/2))*(((1/"4kg/mol")+(1/"2.01kg/mol"))^(1/2)))/("101325Pa"*("1E^9A")^2*"110")`

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Chapman Enskog Equation for Gas Phase Diffusivity Solution

STEP 0: Pre-Calculation Summary

Formula Used

Diffusion Coefficient (DAB) = (1.858*(10^(-7))*(Temperature of Gas^(3/2))*(((1/Molecular Weight A)+(1/Molecular Weight B))^(1/2)))/(Total Pressure of Gas*Characteristic Length Parameter^2*Collision Integral)
D_AB = (1.858*(10^(-7))*(T^(3/2))*(((1/M_A)+(1/M_b))^(1/2)))/(P_T*σ_AB^2*Ω_D)
This formula uses 7 Variables

Variables Used

Diffusion Coefficient (DAB) - (Measured in Square Meter Per Second) - The Diffusion Coefficient (DAB) is the amount of a particular substance that diffuses across a unit area in 1 second under the influence of a gradient of one unit.
Temperature of Gas - (Measured in Kelvin) - The temperature of Gas is the measure of the hotness or coldness of a gas.
Molecular Weight A - (Measured in Kilogram Per Mole) - Molecular Weight A is the mass of a given molecule a.
Molecular Weight B - (Measured in Kilogram Per Mole) - Molecular Weight B is the mass of a given molecule b.
Total Pressure of Gas - (Measured in Atmosphere Technical) - Total pressure of Gas is the sum of all the forces that the gas molecules exert on the walls of their container.
Characteristic Length Parameter - (Measured in Meter) - Characteristic Length Parameter of the binary mixture is the average of the geometric and arithmetic average of the collision diameter of the molecules of the two gases.
Collision Integral - The Collision Integral is a function of k*T/εAB, where k is the Boltzmann's constant and εAB is a characteristic binary parameter of the Lennard Jones Potential.

STEP 1: Convert Input(s) to Base Unit

Temperature of Gas: 298 Kelvin --> 298 Kelvin No Conversion Required
Molecular Weight A: 4 Kilogram Per Mole --> 4 Kilogram Per Mole No Conversion Required
Molecular Weight B: 2.01 Kilogram Per Mole --> 2.01 Kilogram Per Mole No Conversion Required
Total Pressure of Gas: 101325 Pascal --> 1.03322745279989 Atmosphere Technical (Check conversion here)
Characteristic Length Parameter: 1000000000 Angstrom --> 0.1 Meter (Check conversion here)
Collision Integral: 110 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

D_AB = (1.858*(10^(-7))*(T^(3/2))*(((1/M_A)+(1/M_b))^(1/2)))/(P_T*σ_AB^2*Ω_D) --> (1.858*(10^(-7))*(298^(3/2))*(((1/4)+(1/2.01))^(1/2)))/(1.03322745279989*0.1^2*110)

Evaluating ... ...

D_AB = 0.000727094225273136

STEP 3: Convert Result to Output's Unit

0.000727094225273136 Square Meter Per Second --> No Conversion Required

FINAL ANSWER

0.000727094225273136 ≈ 0.000727 Square Meter Per Second <-- Diffusion Coefficient (DAB)

(Calculation completed in 00.004 seconds)

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Home » Engineering » Chemical Engineering » Mass Transfer Operations » Diffusion » Diffusivity: Measurement & Prediction » Chapman Enskog Equation for Gas Phase Diffusivity

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< 5 Diffusivity: Measurement & Prediction Calculators

Diffusivity by Stefan Tube Method

Go Diffusion Coefficient (DAB) = ([R]*Temperature of Gas*Log Mean Partial Pressure of B*Density of Liquid*(Height of Column 1^2-Height of Column 2^2))/(2*Total Pressure of Gas*Molecular Weight A*(Partial Pressure of Component A in 1-Partial Pressure of Component A in 2)*Diffusion Time)

Diffusivity by Twin Bulb Method

Go Diffusion Coefficient (DAB) = ((Length of Tube/(Inner Cross Section Area*Diffusion Time))*(ln(Total Pressure of Gas/(Partial Pressure of Component A in 1-Partial Pressure of Component A in 2))))/((1/Volume of Gas 1)+(1/Volume of Gas 2))

Fuller-Schettler-Giddings for Binary Gas Phase Diffusivity

Go Diffusion Coefficient (DAB) = ((1.0133*(10^(-7))*(Temperature of Gas^1.75))/(Total Pressure of Gas*(((Total Atomic Diffusion Volume A^(1/3))+(Total Atomic Diffusion Volume B^(1/3)))^2)))*(((1/Molecular Weight A)+(1/Molecular Weight B))^(1/2))

Chapman Enskog Equation for Gas Phase Diffusivity

Go Diffusion Coefficient (DAB) = (1.858*(10^(-7))*(Temperature of Gas^(3/2))*(((1/Molecular Weight A)+(1/Molecular Weight B))^(1/2)))/(Total Pressure of Gas*Characteristic Length Parameter^2*Collision Integral)

Wilke Chang Equation for Liquid Phase Diffusivity

Go Diffusion Coefficient (DAB) = (1.173*(10^(-16))*((Association Factor*Molecular Weight B)^(1/2))*Temperature of Gas)/(Dynamic Viscosity of Liquid*((Molar Volume of Liquid/1000)^0.6))

< 16 Important Formulas in Diffusion Calculators

Diffusivity by Stefan Tube Method

Molar Flux of Diffusing Component A through Non-Diffusing B based on Partial Pressure of A

Go Molar Flux of Diffusing Component A = ((Diffusion Coefficient (DAB)*Total Pressure of Gas)/([R]*Temperature of Gas*Film Thickness))*ln((Total Pressure of Gas-Partial Pressure of Component A in 2)/(Total Pressure of Gas-Partial Pressure of Component A in 1))

Diffusivity by Twin Bulb Method

Molar Flux of Diffusing Component A through Non-Diffusing B based on Log Mean Partial Pressure

Go Molar Flux of Diffusing Component A = ((Diffusion Coefficient (DAB)*Total Pressure of Gas)/([R]*Temperature of Gas*Film Thickness))*((Partial Pressure of Component A in 1-Partial Pressure of Component A in 2)/Log Mean Partial Pressure of B)

Mass Diffusing Rate through Hollow Cylinder with Solid Boundary

Go Mass Diffusing Rate = (2*pi*Diffusion Coefficient*Length of Cylinder*(Mass Concentration of Component A in Mixture 1-Mass Concentration of Component A in Mixture 2))/ln(Outer Radius of Cylinder/Inner Radius of Cylinder)

Mass Diffusing Rate through Solid Boundary Sphere

Go Mass Diffusing Rate = (4*pi*Inner Radius*Outer Radius*Diffusion Coefficient*(Mass Concentration of Component A in Mixture 1-Mass Concentration of Component A in Mixture 2))/(Outer Radius-Inner Radius)

Fuller-Schettler-Giddings for Binary Gas Phase Diffusivity

Molar Flux of Diffusing Component A for Equimolar Diffusion with B based on Mole Fraction of A

Go Molar Flux of Diffusing Component A = ((Diffusion Coefficient (DAB)*Total Pressure of Gas)/([R]*Temperature of Gas*Film Thickness))*(Mole Fraction of Component A in 1-Mole Fraction of Component A in 2)

Molar Flux of Diffusing Component A through Non-Diffusing B based on Mole Fractions of A and LMPP

Go Molar Flux of Diffusing Component A = ((Diffusion Coefficient (DAB)*(Total Pressure of Gas^2))/(Film Thickness))*((Mole Fraction of Component A in 1-Mole Fraction of Component A in 2)/Log Mean Partial Pressure of B)

Molar Flux of Diffusing Component A through Non-Diffusing B based on Concentration of A

Go Molar Flux of Diffusing Component A = ((Diffusion Coefficient (DAB)*Total Pressure of Gas)/(Film Thickness))*((Concentration of Component A in 1-Concentration of Component A in 2)/Log Mean Partial Pressure of B)

Chapman Enskog Equation for Gas Phase Diffusivity

Molar Flux of Diffusing Component A through Non-Diffusing B based on Mole Fractions of A

Go Molar Flux of Diffusing Component A = ((Diffusion Coefficient (DAB)*Total Pressure of Gas)/(Film Thickness))*ln((1-Mole Fraction of Component A in 2)/(1-Mole Fraction of Component A in 1))

Molar Flux of Diffusing Component A for Equimolar Diffusion with B based on Partial Pressure of A

Go Molar Flux of Diffusing Component A = (Diffusion Coefficient (DAB)/([R]*Temperature of Gas*Film Thickness))*(Partial Pressure of Component A in 1-Partial Pressure of Component A in 2)

Mass Diffusing Rate through Solid Boundary Plate

Go Mass Diffusing Rate = (Diffusion Coefficient*(Mass Concentration of Component A in Mixture 1-Mass Concentration of Component A in Mixture 2)*Area of Solid Boundary Plate)/Thickness of Solid Plate

Wilke Chang Equation for Liquid Phase Diffusivity

Go Diffusion Coefficient (DAB) = (1.173*(10^(-16))*((Association Factor*Molecular Weight B)^(1/2))*Temperature of Gas)/(Dynamic Viscosity of Liquid*((Molar Volume of Liquid/1000)^0.6))

Molar Flux of Diffusing Component A for Equimolar Diffusion with B based on Concentration of A

Go Molar Flux of Diffusing Component A = (Diffusion Coefficient (DAB)/(Film Thickness))*(Concentration of Component A in 1-Concentration of Component A in 2)

Chapman Enskog Equation for Gas Phase Diffusivity Formula

What is Chapman Enskog Equation ?

The Chapman Enskog Equation is a useful and reasonably accurate theoretical equation based on the kinetic theory of gases, suggested independently by Chapman and Enskog. The Diffusivity DAB strongly depends on the binary interaction parameters of the A-B pair. Chapman and Enskog used the Lennard Jones Potential function to calculate the interacton parameters.

How to Calculate Chapman Enskog Equation for Gas Phase Diffusivity?

Chapman Enskog Equation for Gas Phase Diffusivity calculator uses Diffusion Coefficient (DAB) = (1.858*(10^(-7))*(Temperature of Gas^(3/2))*(((1/Molecular Weight A)+(1/Molecular Weight B))^(1/2)))/(Total Pressure of Gas*Characteristic Length Parameter^2*Collision Integral) to calculate the Diffusion Coefficient (DAB), The Chapman Enskog Equation for Gas Phase Diffusivity formula is defined as the predictive equation suggested by Chapman and Enskog for predicting Gas Phase Diffusion. Diffusion Coefficient (DAB) is denoted by D_AB symbol.

How to calculate Chapman Enskog Equation for Gas Phase Diffusivity using this online calculator? To use this online calculator for Chapman Enskog Equation for Gas Phase Diffusivity, enter Temperature of Gas (T), Molecular Weight A (M_A), Molecular Weight B (M_b), Total Pressure of Gas (P_T), Characteristic Length Parameter (σ_AB) & Collision Integral (Ω_D) and hit the calculate button. Here is how the Chapman Enskog Equation for Gas Phase Diffusivity calculation can be explained with given input values -> 0.000728 = (1.858*(10^(-7))*(298^(3/2))*(((1/4)+(1/2.01))^(1/2)))/(101325*0.1^2*110).

FAQ

What is Chapman Enskog Equation for Gas Phase Diffusivity?

The Chapman Enskog Equation for Gas Phase Diffusivity formula is defined as the predictive equation suggested by Chapman and Enskog for predicting Gas Phase Diffusion and is represented as D_AB = (1.858*(10^(-7))*(T^(3/2))*(((1/M_A)+(1/M_b))^(1/2)))/(P_T*σ_AB^2*Ω_D) or Diffusion Coefficient (DAB) = (1.858*(10^(-7))*(Temperature of Gas^(3/2))*(((1/Molecular Weight A)+(1/Molecular Weight B))^(1/2)))/(Total Pressure of Gas*Characteristic Length Parameter^2*Collision Integral). The temperature of Gas is the measure of the hotness or coldness of a gas, Molecular Weight A is the mass of a given molecule a, Molecular Weight B is the mass of a given molecule b, Total pressure of Gas is the sum of all the forces that the gas molecules exert on the walls of their container, Characteristic Length Parameter of the binary mixture is the average of the geometric and arithmetic average of the collision diameter of the molecules of the two gases & The Collision Integral is a function of k*T/εAB, where k is the Boltzmann's constant and εAB is a characteristic binary parameter of the Lennard Jones Potential.

How to calculate Chapman Enskog Equation for Gas Phase Diffusivity?

The Chapman Enskog Equation for Gas Phase Diffusivity formula is defined as the predictive equation suggested by Chapman and Enskog for predicting Gas Phase Diffusion is calculated using Diffusion Coefficient (DAB) = (1.858*(10^(-7))*(Temperature of Gas^(3/2))*(((1/Molecular Weight A)+(1/Molecular Weight B))^(1/2)))/(Total Pressure of Gas*Characteristic Length Parameter^2*Collision Integral). To calculate Chapman Enskog Equation for Gas Phase Diffusivity, you need Temperature of Gas (T), Molecular Weight A (M_A), Molecular Weight B (M_b), Total Pressure of Gas (P_T), Characteristic Length Parameter (σ_AB) & Collision Integral (Ω_D). With our tool, you need to enter the respective value for Temperature of Gas, Molecular Weight A, Molecular Weight B, Total Pressure of Gas, Characteristic Length Parameter & Collision Integral and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Diffusion Coefficient (DAB)?

In this formula, Diffusion Coefficient (DAB) uses Temperature of Gas, Molecular Weight A, Molecular Weight B, Total Pressure of Gas, Characteristic Length Parameter & Collision Integral. We can use 8 other way(s) to calculate the same, which is/are as follows -

Diffusion Coefficient (DAB) = ((Length of Tube/(Inner Cross Section Area*Diffusion Time))*(ln(Total Pressure of Gas/(Partial Pressure of Component A in 1-Partial Pressure of Component A in 2))))/((1/Volume of Gas 1)+(1/Volume of Gas 2))
Diffusion Coefficient (DAB) = ([R]*Temperature of Gas*Log Mean Partial Pressure of B*Density of Liquid*(Height of Column 1^2-Height of Column 2^2))/(2*Total Pressure of Gas*Molecular Weight A*(Partial Pressure of Component A in 1-Partial Pressure of Component A in 2)*Diffusion Time)
Diffusion Coefficient (DAB) = ((1.0133*(10^(-7))*(Temperature of Gas^1.75))/(Total Pressure of Gas*(((Total Atomic Diffusion Volume A^(1/3))+(Total Atomic Diffusion Volume B^(1/3)))^2)))*(((1/Molecular Weight A)+(1/Molecular Weight B))^(1/2))
Diffusion Coefficient (DAB) = (1.173*(10^(-16))*((Association Factor*Molecular Weight B)^(1/2))*Temperature of Gas)/(Dynamic Viscosity of Liquid*((Molar Volume of Liquid/1000)^0.6))
Diffusion Coefficient (DAB) = ([R]*Temperature of Gas*Log Mean Partial Pressure of B*Density of Liquid*(Height of Column 1^2-Height of Column 2^2))/(2*Total Pressure of Gas*Molecular Weight A*(Partial Pressure of Component A in 1-Partial Pressure of Component A in 2)*Diffusion Time)
Diffusion Coefficient (DAB) = ((Length of Tube/(Inner Cross Section Area*Diffusion Time))*(ln(Total Pressure of Gas/(Partial Pressure of Component A in 1-Partial Pressure of Component A in 2))))/((1/Volume of Gas 1)+(1/Volume of Gas 2))
Diffusion Coefficient (DAB) = ((1.0133*(10^(-7))*(Temperature of Gas^1.75))/(Total Pressure of Gas*(((Total Atomic Diffusion Volume A^(1/3))+(Total Atomic Diffusion Volume B^(1/3)))^2)))*(((1/Molecular Weight A)+(1/Molecular Weight B))^(1/2))
Diffusion Coefficient (DAB) = (1.173*(10^(-16))*((Association Factor*Molecular Weight B)^(1/2))*Temperature of Gas)/(Dynamic Viscosity of Liquid*((Molar Volume of Liquid/1000)^0.6))

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