Mass Diffusing Rate through Solid Boundary Sphere Solution

STEP 0: Pre-Calculation Summary
Formula Used
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)
ma = (4*pi*rinner*router*Dab*(ρa1-ρa2))/(router-rinner)
This formula uses 1 Constants, 6 Variables
Constants Used
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288
Variables Used
Mass Diffusing Rate - (Measured in Kilogram per Second) - Mass Diffusing Rate is the proportionality constant between the molar flux due to molecular diffusion and the gradient in the concentration of the species.
Inner Radius - (Measured in Meter) - The Inner Radius of any figure is the radius of its cavity and the smaller radius among two concentric circles.
Outer Radius - (Measured in Meter) - The Outer Radius of any figure is the radius of a larger circle of the two concentric circles that form its boundary.
Diffusion Coefficient - (Measured in Square Meter Per Second) - Diffusion Coefficient is the magnitude of the molar flux through a surface per unit concentration gradient out-of-plane.
Mass Concentration of Component A in Mixture 1 - (Measured in Kilogram per Cubic Meter) - Mass Concentration of Component A in Mixture 1 is the concentration of component A per unit volume in mixture 1.
Mass Concentration of Component A in Mixture 2 - (Measured in Kilogram per Cubic Meter) - The Mass Concentration of component A in Mixture 2 is the concentration of component A per unit volume in mixture 2.
STEP 1: Convert Input(s) to Base Unit
Inner Radius: 5 Meter --> 5 Meter No Conversion Required
Outer Radius: 7 Meter --> 7 Meter No Conversion Required
Diffusion Coefficient: 0.8 Square Meter Per Second --> 0.8 Square Meter Per Second No Conversion Required
Mass Concentration of Component A in Mixture 1: 40 Kilogram per Cubic Meter --> 40 Kilogram per Cubic Meter No Conversion Required
Mass Concentration of Component A in Mixture 2: 20 Kilogram per Cubic Meter --> 20 Kilogram per Cubic Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
ma = (4*pi*rinner*router*Dab*(ρa1a2))/(router-rinner) --> (4*pi*5*7*0.8*(40-20))/(7-5)
Evaluating ... ...
ma = 3518.58377202057
STEP 3: Convert Result to Output's Unit
3518.58377202057 Kilogram per Second --> No Conversion Required
FINAL ANSWER
3518.58377202057 Kilogram per Second <-- Mass Diffusing Rate
(Calculation completed in 00.031 seconds)

Credits

Created by Nishan Poojary
Shri Madhwa Vadiraja Institute of Technology and Management (SMVITM), Udupi
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10+ Molar Diffusion Calculators

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

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

Formula
`"N"_{"a"} = (("D"_{"AB"}*"P"_{"T"})/("[R]"*"T"*"δ"))*ln(("P"_{"T"}-"P"_{"A2"})/("P"_{"T"}-"P"_{"A1"}))`

Example
`"0.113624mol/s*m²"=(("0.007m²/s"*"101325Pa")/("[R]"*"298K"*"0.005m"))*ln(("101325Pa"-"450Pa")/("101325Pa"-"650Pa"))`

Calculator
LaTeX
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))
Mass Diffusing Rate through Hollow Cylinder with Solid Boundary

Mass Diffusing Rate through Hollow Cylinder with Solid Boundary

Formula
`"m"_{"a"} = (2*pi*"D"_{"ab"}*"l"*("ρ"_{"a1"}-"ρ"_{"a2"}))/ln("r"_{"2"}/"r"_{"1"})`

Example
`"549.0434kg/s"=(2*pi*"0.8m²/s"*"6m"*("40kg/m³"-"20kg/m³"))/ln("7.5m"/"2.5m")`

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

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

Formula
`"N"_{"a"} = (("D"_{"AB"}*"P"_{"T"})/("[R]"*"T"*"δ"))*ln("P"_{"B2"}/"P"_{"B1"}) `

Example
`"-23.213877mol/s*m²"=(("0.007m²/s"*"101325Pa")/("[R]"*"298K"*"0.005m"))*ln("400Pa"/"600Pa") `

Calculator
LaTeX
Go Molar Flux of Diffusing Component A = ((Diffusion Coefficient (DAB)*Total Pressure of Gas)/([R]*Temperature of Gas*Film Thickness))*ln(Partial Pressure of Component B in 2/Partial Pressure of Component B in 1)
Mass Diffusing Rate through Solid Boundary Sphere

Mass Diffusing Rate through Solid Boundary Sphere

Formula
`"m"_{"a"} = (4*pi*"r"_{"inner"}*"r"_{"outer"}*"D"_{"ab"}*("ρ"_{"a1"}-"ρ"_{"a2"}))/("r"_{"outer"}-"r"_{"inner"})`

Example
`"3518.584kg/s"=(4*pi*"5m"*"7m"*"0.8m²/s"*("40kg/m³"-"20kg/m³"))/("7m"-"5m")`

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

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

Formula
`"N"_{"a"} = (("D"_{"AB"}*"P"_{"T"})/("[R]"*"T"*"δ"))*("y"_{"A1"}-"y"_{"A2"})`

Example
`"14.31312mol/s*m²"=(("0.007m²/s"*"101325Pa")/("[R]"*"298K"*"0.005m"))*("0.6"-"0.35")`

Calculator
LaTeX
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

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

Formula
`"N"_{"a"} = (("D"_{"AB"}*("P"_{"T"}^2))/("δ"))*(("y"_{"A1"}-"y"_{"A2"})/"P"_{"BLM"}) `

Example
`"2.3E^6mol/s*m²"=(("0.007m²/s"*("101325Pa"^2))/("0.005m"))*(("0.6"-"0.35")/"1551Pa") `

Calculator
LaTeX
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 Mole Fractions of A and LMMF

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

Formula
`"N"_{"a"} = (("D"_{"AB"}*"P"_{"T"})/("δ"))*(("y"_{"A1"}-"y"_{"A2"})/"y"_{"BLM"}) `

Example
`"54559.62mol/s*m²"=(("0.007m²/s"*"101325Pa")/("0.005m"))*(("0.6"-"0.35")/"0.65") `

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

Logarithmic Mean Partial Pressure Difference

Formula
`"P"_{"bm"} = ("P"_{"b2"}-"P"_{"b1"})/(ln("P"_{"b2"}/"P"_{"b1"}))`

Example
`"10748.06Pa"=("10500Pa"-"11000Pa")/(ln("10500Pa"/"11000Pa"))`

Calculator
LaTeX
Go Logarithmic Mean Partial Pressure Difference = (Partial Pressure of Component B in Mixture 2-Partial Pressure of Component B in Mixture 1)/(ln(Partial Pressure of Component B in Mixture 2/Partial Pressure of Component B in Mixture 1))
Molar Flux of Diffusing Component A through Non-Diffusing B based on Mole Fractions of A

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

Formula
`"N"_{"a"} = (("D"_{"AB"}*"P"_{"T"})/("δ"))*ln((1-"y"_{"A2"})/(1-"y"_{"A1"}))`

Example
`"68871.71mol/s*m²"=(("0.007m²/s"*"101325Pa")/("0.005m"))*ln((1-"0.35")/(1-"0.6"))`

Calculator
LaTeX
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))
Convective Mass Transfer Coefficient

Convective Mass Transfer Coefficient

Formula
`"k"_{"L"} = ("m"_{"a"}"A")/("ρ"_{"a1"}-"ρ"_{"a2"})`

Example
`"0.45m/s"="9kg/s/m²"/("40kg/m³"-"20kg/m³")`

Calculator
LaTeX
Go Convective Mass Transfer Coefficient = Mass Flux of Diffusion Component A/(Mass Concentration of Component A in Mixture 1-Mass Concentration of Component A in Mixture 2)

3 Mass Diffusing Rate Calculators

Mass Diffusing Rate through Hollow Cylinder with Solid Boundary

Mass Diffusing Rate through Hollow Cylinder with Solid Boundary

Formula
`"m"_{"a"} = (2*pi*"D"_{"ab"}*"l"*("ρ"_{"a1"}-"ρ"_{"a2"}))/ln("r"_{"2"}/"r"_{"1"})`

Example
`"549.0434kg/s"=(2*pi*"0.8m²/s"*"6m"*("40kg/m³"-"20kg/m³"))/ln("7.5m"/"2.5m")`

Calculator
LaTeX
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

Mass Diffusing Rate through Solid Boundary Sphere

Formula
`"m"_{"a"} = (4*pi*"r"_{"inner"}*"r"_{"outer"}*"D"_{"ab"}*("ρ"_{"a1"}-"ρ"_{"a2"}))/("r"_{"outer"}-"r"_{"inner"})`

Example
`"3518.584kg/s"=(4*pi*"5m"*"7m"*"0.8m²/s"*("40kg/m³"-"20kg/m³"))/("7m"-"5m")`

Calculator
LaTeX
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)
Mass Diffusing Rate through Solid Boundary Plate

Mass Diffusing Rate through Solid Boundary Plate

Formula
`("m"_{"a"}"A") = ("D"_{"ab"}*("ρ"_{"a1"}-"ρ"_{"a2"}))/"t"`

Example
`"13.33333kg/s/m²"=("0.8m²/s"*("40kg/m³"-"20kg/m³"))/"1.2m"`

Calculator
LaTeX
Go Mass Flux of Diffusion Component A = (Diffusion Coefficient*(Mass Concentration of Component A in Mixture 1-Mass Concentration of Component A in Mixture 2))/Thickness of Solid Plate

Mass Diffusing Rate through Solid Boundary Sphere Formula

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)
ma = (4*pi*rinner*router*Dab*(ρa1-ρa2))/(router-rinner)

What is Molar diffusion

Molecular diffusion, often simply called diffusion, is the thermal motion of all (liquid or gas) particles at temperatures above absolute zero. The rate of this movement is a function of temperature, viscosity of the fluid and the size (mass) of the particles. Diffusion explains the net flux of molecules from a region of higher concentration to one of lower concentration. Once the concentrations are equal the molecules continue to move, but since there is no concentration gradient the process of molecular diffusion has ceased and is instead governed by the process of self-diffusion, originating from the random motion of the molecules. The result of diffusion is a gradual mixing of material such that the distribution of molecules is uniform. Since the molecules are still in motion, but an equilibrium has been established, the end result of molecular diffusion is called a "dynamic equilibrium".

How to Calculate Mass Diffusing Rate through Solid Boundary Sphere?

Mass Diffusing Rate through Solid Boundary Sphere calculator uses 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) to calculate the Mass Diffusing Rate, Mass Diffusing Rate through Solid Boundary Sphere is defined as amount of particles diffusing through Solid Boundary Sphere per unit time. Mass Diffusing Rate is denoted by ma symbol.

How to calculate Mass Diffusing Rate through Solid Boundary Sphere using this online calculator? To use this online calculator for Mass Diffusing Rate through Solid Boundary Sphere, enter Inner Radius (rinner), Outer Radius (router), Diffusion Coefficient (Dab), Mass Concentration of Component A in Mixture 1 a1) & Mass Concentration of Component A in Mixture 2 a2) and hit the calculate button. Here is how the Mass Diffusing Rate through Solid Boundary Sphere calculation can be explained with given input values -> 3518.584 = (4*pi*5*7*0.8*(40-20))/(7-5).

FAQ

What is Mass Diffusing Rate through Solid Boundary Sphere?
Mass Diffusing Rate through Solid Boundary Sphere is defined as amount of particles diffusing through Solid Boundary Sphere per unit time and is represented as ma = (4*pi*rinner*router*Dab*(ρa1-ρa2))/(router-rinner) or 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). The Inner Radius of any figure is the radius of its cavity and the smaller radius among two concentric circles, The Outer Radius of any figure is the radius of a larger circle of the two concentric circles that form its boundary, Diffusion Coefficient is the magnitude of the molar flux through a surface per unit concentration gradient out-of-plane, Mass Concentration of Component A in Mixture 1 is the concentration of component A per unit volume in mixture 1 & The Mass Concentration of component A in Mixture 2 is the concentration of component A per unit volume in mixture 2.
How to calculate Mass Diffusing Rate through Solid Boundary Sphere?
Mass Diffusing Rate through Solid Boundary Sphere is defined as amount of particles diffusing through Solid Boundary Sphere per unit time is calculated using 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). To calculate Mass Diffusing Rate through Solid Boundary Sphere, you need Inner Radius (rinner), Outer Radius (router), Diffusion Coefficient (Dab), Mass Concentration of Component A in Mixture 1 a1) & Mass Concentration of Component A in Mixture 2 a2). With our tool, you need to enter the respective value for Inner Radius, Outer Radius, Diffusion Coefficient, Mass Concentration of Component A in Mixture 1 & Mass Concentration of Component A in Mixture 2 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 Mass Diffusing Rate?
In this formula, Mass Diffusing Rate uses Inner Radius, Outer Radius, Diffusion Coefficient, Mass Concentration of Component A in Mixture 1 & Mass Concentration of Component A in Mixture 2. We can use 2 other way(s) to calculate the same, which is/are as follows -
  • 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 = (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)
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